problem solving fractions examples with answers

Word Problems on Fraction

In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

I. Word Problems on Addition of Fractions:

1. Nairitee took \(\frac{7}{8}\) hour to paint a table and \(\frac{2}{3}\) hour to paint a chair. How much time did he take in painting both items?

Total time taken in painting both items = \(\frac{7}{8}\) h + \(\frac{2}{3}\) h                                                          = (\(\frac{7}{8}\) + \(\frac{2}{3}\)) h

                                                         = (\(\frac{21 + 16}{24}\)) h

                                                         = \(\frac{37}{24}\) h

                                                         = 1\(\frac{13}{24}\) h

Therefore, Nairitee took 1\(\frac{13}{24}\) hours in painting both items.

2. Nitheeya and Nairitee \(\frac{3}{10}\) and \(\frac{1}{6}\) of a cake respectively. What portion of the cake did they eat together? 

The portion of cake ate by Nitheeya = \(\frac{3}{10}\)

The portion of cake ate by Nitheeya = \(\frac{1}{6}\)  The portion they ate together = \(\frac{3}{10}\) + \(\frac{1}{6}\) 

                                           = \(\frac{9}{30}\) + \(\frac{5}{30}\); [Since, LCM of 10 and 6 = 30]

                                           = \(\frac{9 + 5}{30}\)

                                           = \(\frac{14}{30}\)

                                           = \(\frac{7}{15}\)

Therefore, together Nitheeya and Nairitee ate \(\frac{7}{15}\) of the cake.

3.  Rachel took \(\frac{1}{2}\) hour to paint a table and \(\frac{1}{3}\) hour to paint a chair. How much time did she take in all?

II. Word Problems on Subtraction of Fractions:

1.  Out of \(\frac{12}{17}\)  m  of cloth given to a tailor, \(\frac{1}{5}\)  m  were used. Find the length of cloth unused. 

Length of the cloth given to the tailors = \(\frac{12}{17}\)  m

Length of cloth used = \(\frac{1}{5}\)  m

Length of the unused cloth = \(\frac{12}{17}\)  m -  \(\frac{1}{5}\)  m

                                        = (\(\frac{12}{17}\)  -  \(\frac{1}{5}\))  m

                                        = (\(\frac{12 × 5}{17 × 5}\)  -  \(\frac{1 × 17}{5 × 17}\))  m;  [Since, LCM of 17 and 5 = 85]

                                        = (\(\frac{60}{85}\)  -  \(\frac{17}{85}\))  m

                                        = (\(\frac{60 - 17}{85}\)  m

                                        = (\(\frac{43}{85}\)  m

2.  Nairitee has $6\(\frac{4}{7}\). She gives $4\(\frac{2}{3}\) to her mother. How much money does she have now?

Money with Nairitee = $6\(\frac{4}{7}\)

Money given to her mother = $4\(\frac{2}{3}\)

Money left with Nairitee = $6\(\frac{4}{7}\) - $4\(\frac{2}{3}\)

                                   = $(6\(\frac{4}{7}\) - 4\(\frac{2}{3}\))

                                   = $(\(\frac{46}{7}\) - \(\frac{14}{3}\))

                                   = $(\(\frac{46 × 3}{7 × 3}\) - \(\frac{14 × 7}{3 × 7}\)) ;  [Since, LCM of 7 and 3 = 21]

                                   = $(\(\frac{138}{21}\) - \(\frac{98}{21}\))

                                   = $\(\frac{40}{21}\)

                                   = $1\(\frac{19}{21}\)

Therefore, Nairitee has $1\(\frac{19}{21}\).

3.  If 3\(\frac{1}{2}\) m of wire is cut from a piece of 10 m long wire, how much of wire is left?

Total length of the wire = 10 m

Fraction of the wire cut out = 3\(\frac{1}{2}\) m = \(\frac{7}{2}\) m

Length of the wire left = 10 m – 3\(\frac{1}{2}\) m

            = [\(\frac{10}{1}\) - \(\frac{7}{2}\)] m,    [L.C.M. of 1, 2 is 2]

            = [\(\frac{20}{2}\) - \(\frac{7}{2}\)] m,    [\(\frac{10}{1}\) × \(\frac{2}{2}\)]

            = [\(\frac{20 - 7}{2}\)] m

            = \(\frac{13}{2}\) m

            = 6\(\frac{1}{2}\) m

III. Word Problems on Multiplication of Fractions:

1.  \(\frac{4}{7}\) of a number is 84. Find the number. Solution: According to the problem, \(\frac{4}{7}\) of a number = 84 Number = 84 × \(\frac{7}{4}\) [Here we need to multiply 84 by the reciprocal of \(\frac{4}{7}\)]

= 21 × 7 = 147 Therefore, the number is 147.

2.  One half of the students in a school are girls, \(\frac{3}{5}\) of these girls are studying in lower classes. What fraction of girls are studying in lower classes?

Fraction of girls studying in school = \(\frac{1}{2}\)

Fraction of girls studying in lower classes = \(\frac{3}{5}\) of \(\frac{1}{2}\)

                                                            = \(\frac{3}{5}\) × \(\frac{1}{2}\)

                                                            = \(\frac{3 × 1}{5 × 2}\)

                                                            = \(\frac{3}{10}\)

Therefore, \(\frac{3}{10}\) of girls studying in lower classes.

3.  Maddy reads three-fifth of 75 pages of his lesson. How many more pages he need to complete the lesson? Solution: Maddy reads = \(\frac{3}{5}\) of 75 = \(\frac{3}{5}\) × 75

= 45 pages. Maddy has to read = 75 – 45. = 30 pages. Therefore, Maddy has to read 30 more pages.

IV. Word Problems on Division of Fractions:

1.  A herd of cows gives 4 litres of milk each day. But each cow gives one-third of total milk each day. They give 24 litres milk in six days. How many cows are there in the herd?

Solution: A herd of cows gives 4 litres of milk each day. Each cow gives one-third of total milk each day = \(\frac{1}{3}\) of 4 Therefore, each cow gives \(\frac{4}{3}\) of milk each day. Total no. of cows = 4 ÷ \(\frac{4}{3}\)                          = 4 × \(\frac{3}{4}\)                          = 3 Therefore there are 3 cows in the herd.

Worksheet on Word problems on Fractions:

1. Shelly walked \(\frac{1}{3}\) km. Kelly walked \(\frac{4}{15}\) km. Who walked farther? How much farther did one walk than the other?

2. A frog took three jumps. The first jump was \(\frac{2}{3}\) m long, the second was \(\frac{5}{6}\) m long and the third was \(\frac{1}{3}\) m long. How far did the frog jump in all?

3. A vessel contains 1\(\frac{1}{2}\) l of milk. John drinks \(\frac{1}{4}\) l of milk; Joe drinks \(\frac{1}{2}\) l of milk. How much of milk is left in the vessel?

4. Between 4\(\frac{2}{3}\)and 3\(\frac{2}{3}\) which is greater and by how much?

5. What must be subtracted from 5\(\frac{1}{6}\) to get 2\(\frac{1}{8}\)?

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●   Multiplication is Repeated Addition.

●  Multiplication of Fractional Number by a Whole Number.

●  Multiplication of a Fraction by Fraction.

●  Properties of Multiplication of Fractional Numbers.

●  Multiplicative Inverse.

●  Worksheet on Multiplication on Fraction.

●  Division of a Fraction by a Whole Number.

●  Division of a Fractional Number.

●  Division of a Whole Number by a Fraction.

●  Properties of Fractional Division.

●  Worksheet on Division of Fractions.

●  Simplification of Fractions.

●  Worksheet on Simplification of Fractions.

●  Word Problems on Fraction.

●  Worksheet on Word Problems on Fractions.

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Fraction Word Problem Worksheets

Featured here is a vast collection of fraction word problems, which require learners to simplify fractions, add like and unlike fractions; subtract like and unlike fractions; multiply and divide fractions. The fraction word problems include proper fraction, improper fraction, and mixed numbers. Solve each word problem and scroll down each printable worksheet to verify your solutions using the answer key provided. Thumb through some of these word problem worksheets for free!

Represent and Simplify the Fractions: Type 1

Presented here are the fraction pdf worksheets based on real-life scenarios. Read the basic fraction word problems, write the correct fraction and reduce your answer to the simplest form.

• Download the set

Represent and Simplify the Fractions: Type 2

Before representing in fraction, children should perform addition or subtraction to solve these fraction word problems. Write your answer in the simplest form.

Adding Fractions Word Problems Worksheets

Conjure up a picture of how adding fractions plays a significant role in our day-to-day lives with the help of the real-life scenarios and circumstances presented as word problems here.

(15 Worksheets)

Subtracting Fractions Word Problems Worksheets

Crank up your skills with this set of printable worksheets on subtracting fractions word problems presenting real-world situations that involve fraction subtraction!

Multiplying Fractions Word Problems Worksheets

This set of printables is for the ardently active children! Explore the application of fraction multiplication and mixed-number multiplication in the real world with this exhilarating practice set.

Fraction Division Word Problems Worksheets

Gift children a broad view of the real-life application of dividing fractions! Let them divide fractions by whole numbers, divide 2 fractions, divide mixed numbers, and solve the word problems here.

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» Decimal Word Problems

» Ratio Word Problems

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Fraction Word Problems: Addition, Subtraction, and Mixed Numbers

In today’s post, we’re going to see how to solve some of the problems that we’ve introduced in Smartick: fraction word problems. They appear during the word problems section at the end of the daily session.

We’re going to look at how to solve problems involving addition and subtraction of fractions, including mixed fractions (the ones that are made up of a whole number and a fraction).

Try and solve the fraction word problems by yourself first, before you look for the solutions and their respective explanations below.

Fraction Word Problems

Problem nº 1.

Problem nº 2

Problem nº 3

Solution to Problem nº 1

This is an example of a problem involving the addition of a whole number and a fraction.

The simplest way to show the number of cookies I ate is to write it as a mixed number. And the data given in the word problem gives us the result: 9 biscuits and 5 / 6 of a biscuit = 9 5 / 6 biscuits.

Solution to Problem nº 2

In this example, we have to subtract two fractions with the same denominator.

To calculate how full the gas tank is, we have to subtract both fractions. Since we are given fractions, the best way to present the solution is in the form of a fraction. Additionally, we’re dealing with two fractions with the same denominator, so we just have to subtract the numerators of both fractions to get the result. 8 / 10 – 4 / 10 = 4 / 10

Solution to Problem nº 3

This problem requires us to subtract a mixed number and a fraction.

To solve this problem, we need to subtract the number of episodes that were downloaded this morning from the total number of episodes that are now downloaded.

To do this, we need to change the mixed number into a fraction: the 5 becomes 60 / 12 (5 x 12 = 60) and we add it to the fraction 60 / 12 + 8 / 12 = 68 / 12 .

We’ve converted the mixed number 5 8 / 12 to 68 / 12 . Now we just have to subtract the number of episodes that were downloaded yesterday ( 7 / 12 ),   68 / 12 – 7 / 12 = 61 / 12 .

Hopefully, you didn’t need the explanations and were able to solve them yourself without any help!

Fraction Video Tutorials

In the following video tutorials, you can learn a bit more about fractions. And if you would like to learn more math concepts, check out Smartick’s Youtube channel !

Simplifying Fractions

Simplification Using the GCD

Equivalent Fractions

If you would like to practice more fraction word problems like these and others, log in to Smartick and enjoy learning math.

Learn More:

• Word Problems with Fractions
• What Is a Fraction? Learn Everything There Is to Know!
• Using Mixed Numbers to Represent Improper Fractions
• Learning How to Subtract Fractions
• Learn How to Subtract Fractions
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Fraction Worksheets

Conversion :: Addition :: Subtraction :: Multiplication :: Division

Conversions

Fractions - addition, fractions - subtraction, fractions - multiplication, fractions - division.

Fractions Worksheets

Welcome to the fractions worksheets page at Math-Drills.com where the cup is half full! This is one of our more popular pages most likely because learning fractions is incredibly important in a person's life and it is a math topic that many approach with trepidation due to its bad rap over the years. Fractions really aren't that difficult to master especially with the support of our wide selection of worksheets.

This page includes Fractions worksheets for understanding fractions including modeling, comparing, ordering, simplifying and converting fractions and operations with fractions. We start you off with the obvious: modeling fractions. It is a great idea if students can actually understand what a fraction is, so please do spend some time with the modeling aspect. Relating modeling to real life helps a great deal too as it is much easier to relate to half a cookie than to half a square. Ask most students what you get if you add half a cookie and another half a cookie, and they'll probably let you know that it makes one delicious snack.

The other fractions worksheets on this page are devoted to helping students understand the concept of fractions. From comparing and ordering to simplifying and converting... by the time students master the material on this page, operations of fractions will be a walk in the park.

Most Popular Fractions Worksheets this Week

Fraction Circles

Fraction circle manipulatives are mainly used for comparing fractions, but they can be used for a variety of other purposes such as representing and identifying fractions, adding and subtracting fractions, and as probability spinners. There are a variety of options depending on your purpose. Fraction circles come in small and large versions, labeled and unlabeled versions and in three different color schemes: black and white, color, and light gray. The color scheme matches the fraction strips and use colors that are meant to show good contrast among themselves. Do note that there is a significant prevalence of color-blindness in the population, so don't rely on all students being able to differentiate the colors.

Suggested activity for comparing fractions: Photocopy the black and white version onto an overhead projection slide and another copy onto a piece of paper. Alternatively, you can use two pieces of paper and hold them up to the light for this activity. Use a pencil to represent the first fraction on the paper copy. Use a non-permanent overhead pen to represent the second fraction. Lay the slide over the paper and compare the two circles. You should easily be able to tell which is greater or lesser or if the two fractions are equal. Re-use both sheets by erasing the pencil and washing off the marker.

Adding fractions with fraction circles will involve two copies on paper. Cut out the fraction circles and segments of one copy and leave the other copy intact. To add 1/3 + 1/2, for example, place a 1/3 segment and a 1/2 segment into a circle and hold it over various fractions on the intact copy to see what 1/2 + 1/3 is equivalent to. 5/6 or 10/12 should work.

• Small Fraction Circles Small Fraction Circles in Black and White with Labels Small Fraction Circles in Color with Labels Small Fraction Circles in Light Gray with Labels Small Fraction Circles in Black and White Unlabeled Small Fraction Circles in Color Unlabeled Small Fraction Circles in Light Gray Unlabeled
• Large Fraction Circles Large Fraction Circles in Black and White with Labels Large Fraction Circles in Color with Labels Large Fraction Circles in Light Gray with Labels Large Fraction Circles in Black and White Unlabeled Large Fraction Circles in Color Unlabeled Large Fraction Circles in Light Gray Unlabeled

Fraction Strips

Fractions strips are often used for comparing fractions. Students are able to see quite easily the relationships and equivalence between fractions with different denominators. It can be quite useful for students to have two copies: one copy cut into strips and the other copy kept intact. They can then use the cut-out strips on the intact page to individually compare fractions. For example, they can use the halves strip to see what other fractions are equivalent to one-half. This can also be accomplished with a straight edge such as a ruler without cutting out any strips. Pairs or groups of strips can also be compared side-by-side if they are cut out. Addition and subtraction (etc.) are also possibilities; for example, adding a one-quarter and one-third can be accomplished by shifting the thirds strip so that it starts at the end of one-quarter then finding a strip that matches the end of the one-third mark (7/12 should do it).

Teachers might consider copying the fraction strips onto overhead projection acetates for whole class or group activities. Acetate versions are also useful as a hands-on manipulative for students in conjunction with an uncut page.

The "Smart" Fraction Strips include strips in a more useful order, eliminate the 7ths and 11ths strips as they don't have any equivalents and include 15ths and 16ths. The colors are consistent with the classic versions, so the two sets can be combined.

• Classic Fraction Strips with Labels Classic Fraction Strips in Black and White With Labels Classic Fraction Strips in Color With Labels Classic Fraction Strips in Gray With Labels
• Unlabeled Classic Fraction Strips Classic Fraction Strips in Black and White Unlabeled Classic Fraction Strips in Color Unlabeled Classic Fraction Strips in Gray Unlabeled
• Smart Fraction Strips with Labels Smart Fraction Strips in Black and White With Labels Smart Fraction Strips in Color With Labels Smart Fraction Strips in Gray With Labels

Modeling fractions

Fractions can represent parts of a group or parts of a whole. In these worksheets, fractions are modeled as parts of a group. Besides using the worksheets in this section, you can also try some more interesting ways of modeling fractions. Healthy snacks can make great models for fractions. Can you cut a cucumber into thirds? A tomato into quarters? Can you make two-thirds of the grapes red and one-third green?

• Modeling Fractions with Groups of Shapes Coloring Groups of Shapes to Represent Fractions Identifying Fractions from Colored Groups of Shapes (Only Simplified Fractions up to Eighths) Identifying Fractions from Colored Groups of Shapes (Halves Only) Identifying Fractions from Colored Groups of Shapes (Halves and Thirds) Identifying Fractions from Colored Groups of Shapes (Halves, Thirds and Fourths) Identifying Fractions from Colored Groups of Shapes (Up to Fifths) Identifying Fractions from Colored Groups of Shapes (Up to Sixths) Identifying Fractions from Colored Groups of Shapes (Up to Eighths) Identifying Fractions from Colored Groups of Shapes (OLD Version; Print Too Light)
• Modeling Fractions with Rectangles Modeling Halves Modeling Thirds Modeling Halves and Thirds Modeling Fourths (Color Version) Modeling Fourths (Grey Version) Coloring Fourths Models Modeling Fifths Coloring Fifths Models Modeling Sixths Coloring Sixths Models
• Modeling Fractions with Circles Modeling Halves, Thirds and Fourths Coloring Halves, Thirds and Fourths Modeling Halves, Thirds, Fourths, and Fifths Coloring Halves, Thirds, Fourths, and Fifths Modeling Halves to Sixths Coloring Halves to Sixths Modeling Halves to Eighths Coloring Halves to Eighths Modeling Halves to Twelfths Coloring Halves to Twelfths

Ratio and Proportion Worksheets

The equivalent fractions models worksheets include only the "baking fractions" in the A versions. To see more difficult and varied fractions, please choose the B to J versions after loading the A version. More picture ratios can be found on holiday and seasonal pages. Try searching for picture ratios to find more.

• Picture Ratios Autumn Trees Part-to-Part Picture Ratios ( Grouped ) Autumn Trees Part-to-Part and Part-to-Whole Picture Ratios ( Grouped )
• Equivalent Fractions Equivalent Fractions With Blanks ( Multiply Right ) ✎ Equivalent Fractions With Blanks ( Divide Left ) ✎ Equivalent Fractions With Blanks ( Multiply Right or Divide Left ) ✎ Equivalent Fractions With Blanks ( Divide Right ) ✎ Equivalent Fractions With Blanks ( Multiply Left ) ✎ Equivalent Fractions With Blanks ( Multiply Left or Divide Right ) ✎ Equivalent Fractions With Blanks ( Multiply or Divide Right ) ✎ Equivalent Fractions With Blanks ( Multiply or Divide Left ) ✎ Equivalent Fractions With Blanks ( Multiply or Divide in Either Direction ) ✎ Are These Fractions Equivalent? (Multiplier 2 to 5) Are These Fractions Equivalent? (Multiplier 5 to 15) Equivalent Fractions Models Equivalent Fractions Models with the Simplified Fraction First Equivalent Fractions Models with the Simplified Fraction Second
• Equivalent Ratios Equivalent Ratios with Blanks Only on Right Equivalent Ratios with Blanks Anywhere Equivalent Ratios with x 's

Comparing and Ordering Fractions

Comparing fractions involves deciding which of two fractions is greater in value or if the two fractions are equal in value. There are generally four methods that can be used for comparing fractions. First is to use common denominators . If both fractions have the same denominator, comparing the fractions simply involves comparing the numerators. Equivalent fractions can be used to convert one or both fractions, so they have common denominators. A second method is to convert both fractions to a decimal and compare the decimal numbers. Visualization is the third method. Using something like fraction strips , two fractions can be compared with a visual tool. The fourth method is to use a cross-multiplication strategy where the numerator of the first fraction is multiplied by the denominator of the second fraction; then the numerator of the second fraction is multiplied by the denominator of the first fraction. The resulting products can be compared to decide which fraction is greater (or if they are equal).

• Comparing Proper Fractions Comparing Proper Fractions to Sixths ✎ Comparing Proper Fractions to Ninths (No Sevenths) ✎ Comparing Proper Fractions to Ninths ✎ Comparing Proper Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Proper Fractions to Twelfths ✎

The worksheets in this section also include improper fractions. This might make the task of comparing even easier for some questions that involve both a proper and an improper fraction. If students recognize one fraction is greater than one and the other fraction is less than one, the greater fraction will be obvious.

• Comparing Proper and Improper Fractions Comparing Proper and Improper Fractions to Sixths ✎ Comparing Proper and Improper Fractions to Ninths (No Sevenths) ✎ Comparing Proper and Improper Fractions to Ninths ✎ Comparing Proper and Improper Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Proper and Improper Fractions to Twelfths ✎ Comparing Improper Fractions to Sixths ✎ Comparing Improper Fractions to Ninths (No Sevenths) ✎ Comparing Improper Fractions to Ninths ✎ Comparing Improper Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Improper Fractions to Twelfths ✎

This section additionally includes mixed fractions. When comparing mixed and improper fractions, it is useful to convert one of the fractions to the other's form either in writing or mentally. Converting to a mixed fraction is probably the better route since the first step is to compare the whole number portions, and if one is greater than the other, the proper fraction portion can be ignored. If the whole number portions are equal, the proper fractions must be compared to see which number is greater.

• Comparing Proper, Improper and Mixed Fractions Comparing Proper, Improper and Mixed Fractions to Sixths ✎ Comparing Proper, Improper and Mixed Fractions to Ninths (No Sevenths) ✎ Comparing Proper, Improper and Mixed Fractions to Ninths ✎ Comparing Proper, Improper and Mixed Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Proper, Improper and Mixed Fractions to Twelfths ✎
• Comparing Improper and Mixed Fractions Comparing Improper and Mixed Fractions to Sixths ✎ Comparing Improper and Mixed Fractions to Ninths (No Sevenths) ✎ Comparing Improper and Mixed Fractions to Ninths ✎ Comparing Improper and Mixed Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Improper and Mixed Fractions to Twelfths ✎
• Comparing Mixed Fractions Comparing Mixed Fractions to Sixths ✎ Comparing Mixed Fractions to Ninths (No Sevenths) ✎ Comparing Mixed Fractions to Ninths ✎ Comparing Mixed Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Mixed Fractions to Twelfths ✎

Many of the same strategies that work for comparing fractions also work for ordering fractions. Using manipulatives such as fraction strips, using number lines, or finding decimal equivalents will all have your student(s) putting fractions in the correct order in no time. We've probably said this before, but make sure that you emphasize that when comparing or ordering fractions, students understand that the whole needs to be the same. Comparing half the population of Canada with a third of the population of the United States won't cut it. Try using some visuals to reinforce this important concept. Even though we've included number lines below, feel free to use your own strategies.

• Ordering Fractions with Easy Denominators on a Number Line Ordering Fractions with Easy Denominators to 10 on a Number Line Ordering Fractions with Easy Denominators to 24 on a Number Line Ordering Fractions with Easy Denominators to 60 on a Number Line Ordering Fractions with Easy Denominators to 100 on a Number Line
• Ordering Fractions with Easy Denominators on a Number Line (Including Negative Fractions) Ordering Fractions with Easy Denominators to 10 + Negatives on a Number Line Ordering Fractions with Easy Denominators to 24 + Negatives on a Number Line Ordering Fractions with Easy Denominators to 60 + Negatives on a Number Line Ordering Fractions with Easy Denominators to 100 + Negatives on a Number Line
• Ordering Fractions with All Denominators on a Number Line Ordering Fractions with All Denominators to 10 on a Number Line Ordering Fractions with All Denominators to 24 on a Number Line Ordering Fractions with All Denominators to 60 on a Number Line Ordering Fractions with All Denominators to 100 on a Number Line
• Ordering Fractions with All Denominators on a Number Line (Including Negative Fractions) Ordering Fractions with All Denominators to 10 + Negatives on a Number Line Ordering Fractions with All Denominators to 24 + Negatives on a Number Line Ordering Fractions with All Denominators to 60 + Negatives on a Number Line Ordering Fractions with All Denominators to 100 + Negatives on a Number Line

The ordering fractions worksheets in this section do not include a number line, to allow for students to use various sorting strategies.

• Ordering Positive Fractions Ordering Positive Fractions with Like Denominators Ordering Positive Fractions with Like Numerators Ordering Positive Fractions with Like Numerators or Denominators Ordering Positive Fractions with Proper Fractions Only Ordering Positive Fractions with Improper Fractions Ordering Positive Fractions with Mixed Fractions Ordering Positive Fractions with Improper and Mixed Fractions
• Ordering Positive and Negative Fractions Ordering Positive and Negative Fractions with Like Denominators Ordering Positive and Negative Fractions with Like Numerators Ordering Positive and Negative Fractions with Like Numerators or Denominators Ordering Positive and Negative Fractions with Proper Fractions Only Ordering Positive and Negative Fractions with Improper Fractions Ordering Positive and Negative Fractions with Mixed Fractions Ordering Positive and Negative Fractions with Improper and Mixed Fractions

Simplifying & Converting Fractions Worksheets

Rounding fractions helps students to understand fractions a little better and can be applied to estimating answers to fractions questions. For example, if one had to estimate 1 4/7 × 6, they could probably say the answer was about 9 since 1 4/7 is about 1 1/2 and 1 1/2 × 6 is 9.

• Rounding Fractions with Helper Lines Rounding Fractions to the Nearest Whole with Helper Lines Rounding Mixed Numbers to the Nearest Whole with Helper Lines Rounding Fractions to the Nearest Half with Helper Lines Rounding Mixed Numbers to the Nearest Half with Helper Lines
• Rounding Fractions Rounding Fractions to the Nearest Whole Rounding Mixed Numbers to the Nearest Whole Rounding Fractions to the Nearest Half Rounding Mixed Numbers to the Nearest Half

Learning how to simplify fractions makes a student's life much easier later on when learning operations with fractions. It also helps them to learn that different-looking fractions can be equivalent. One way of demonstrating this is to divide out two equivalent fractions. For example 3/2 and 6/4 both result in a quotient of 1.5 when divided. By practicing simplifying fractions, students will hopefully recognize unsimplified fractions when they start adding, subtracting, multiplying and dividing with fractions.

• Simplifying Fractions Simplify Fractions (easier) Simplify Fractions (harder) Simplify Improper Fractions (easier) Simplify Improper Fractions (harder)
• Converting Between Improper and Mixed Fractions Converting Mixed Fractions to Improper Fractions Converting Improper Fractions to Mixed Fractions Converting Between (both ways) Mixed and Improper Fractions
• Converting Between Fractions and Decimals Converting Fractions to Terminating Decimals Converting Fractions to Terminating and Repeating Decimals Converting Terminating Decimals to Fractions Converting Terminating and Repeating Decimals to Fractions Converting Fractions to Hundredths
• Converting Between Fractions, Decimals, Percents and Ratios with Terminating Decimals Only Converting Fractions to Decimals, Percents and Part-to- Part Ratios ( Terminating Decimals Only) Converting Fractions to Decimals, Percents and Part-to- Whole Ratios ( Terminating Decimals Only) Converting Decimals to Fractions, Percents and Part-to- Part Ratios ( Terminating Decimals Only) Converting Decimals to Fractions, Percents and Part-to- Whole Ratios ( Terminating Decimals Only) Converting Percents to Fractions, Decimals and Part-to- Part Ratios ( Terminating Decimals Only) Converting Percents to Fractions, Decimals and Part-to- Whole Ratios ( Terminating Decimals Only) Converting Part-to-Part Ratios to Fractions, Decimals and Percents ( Terminating Decimals Only) Converting Part-to-Whole Ratios to Fractions, Decimals and Percents ( Terminating Decimals Only) Converting Various Fractions, Decimals, Percents and Part-to- Part Ratios ( Terminating Decimals Only) Converting Various Fractions, Decimals, Percents and Part-to- Whole Ratios ( Terminating Decimals Only)
• Converting Between Fractions, Decimals, Percents and Ratios with Terminating and Repeating Decimals Converting Fractions to Decimals, Percents and Part-to- Part Ratios Converting Fractions to Decimals, Percents and Part-to- Whole Ratios Converting Decimals to Fractions, Percents and Part-to- Part Ratios Converting Decimals to Fractions, Percents and Part-to- Whole Ratios Converting Percents to Fractions, Decimals and Part-to- Part Ratios Converting Percents to Fractions, Decimals and Part-to- Whole Ratios Converting Part-to-Part Ratios to Fractions, Decimals and Percents Converting Part-to-Whole Ratios to Fractions, Decimals and Percents Converting Various Fractions, Decimals, Percents and Part-to- Part Ratios Converting Various Fractions, Decimals, Percents and Part-to- Whole Ratios Converting Various Fractions, Decimals, Percents and Part-to- Part Ratios with 7ths and 11ths Converting Various Fractions, Decimals, Percents and Part-to- Whole Ratios with 7ths and 11ths

Multiplying Fractions

Multiplying fractions is usually less confusing operationally than any other operation and can be less confusing conceptually if approached in the right way. The algorithm for multiplying is simply multiply the numerators then multiply the denominators. The magic word in understanding the multiplication of fractions is, "of." For example what is two-thirds OF six? What is a third OF a half? When you use the word, "of," it gets much easier to visualize fractions multiplication. Example: cut a loaf of bread in half, then cut the half into thirds. One third OF a half loaf of bread is the same as 1/3 x 1/2 and tastes delicious with butter.

• Multiplying Two Proper Fraction Multiplying Two Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ ✎ Multiplying Two Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Proper Fractions with No Simplifying (Printable Only) Multiplying Two Proper Fractions with All Simplifying (Printable Only) Multiplying Two Proper Fractions with Some Simplifying (Printable Only)
• Multiplying Proper and Improper Fractions Multiplying Proper and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Improper Fractions with No Simplifying (Printable Only) Multiplying Proper and Improper Fractions with All Simplifying (Printable Only) Multiplying Proper and Improper Fractions with Some Simplifying (Printable Only)
• Multiplying Two Improper Fractions Multiplying Two Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Improper Fractions with No Simplifying (Printable Only) Multiplying Two Improper Fractions with All Simplifying (Printable Only) Multiplying Two Improper Fractions with Some Simplifying (Printable Only)
• Multiplying Proper and Mixed Fractions Multiplying Proper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Mixed Fractions with No Simplifying (Printable Only) Multiplying Proper and Mixed Fractions with All Simplifying (Printable Only) Multiplying Proper and Mixed Fractions with Some Simplifying (Printable Only)
• Multiplying Two Mixed Fractions Multiplying Two Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Mixed Fractions with No Simplifying (Printable Only) Multiplying Two Mixed Fractions with All Simplifying (Printable Only) Multiplying Two Mixed Fractions with Some Simplifying (Printable Only)
• Multiplying Whole Numbers and Proper Fractions Multiplying Whole Numbers and Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Proper Fractions with No Simplifying (Printable Only) Multiplying Whole Numbers and Proper Fractions with All Simplifying (Printable Only) Multiplying Whole Numbers and Proper Fractions with Some Simplifying (Printable Only)
• Multiplying Whole Numbers and Improper Fractions Multiplying Whole Numbers and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Improper Fractions with No Simplifying (Printable Only) Multiplying Whole Numbers and Improper Fractions with All Simplifying (Printable Only) Multiplying Whole Numbers and Improper Fractions with Some Simplifying (Printable Only)
• Multiplying Whole Numbers and Mixed Fractions Multiplying Whole Numbers and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Mixed Fractions with No Simplifying (Printable Only) Multiplying Whole Numbers and Mixed Fractions with All Simplifying (Printable Only) Multiplying Whole Numbers and Mixed Fractions with Some Simplifying (Printable Only)
• Multiplying Proper, Improper and Mixed Fractions Multiplying Proper, Improper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper, Improper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper, Improper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper, Improper and Mixed Fractions with No Simplifying (Printable Only) Multiplying Proper, Improper and Mixed Fractions with All Simplifying (Printable Only) Multiplying Proper, Improper and Mixed Fractions with Some Simplifying (Printable Only)
• Multiplying 3 Fractions Multiplying 3 Proper Fractions (Fillable, Savable, Printable) ✎ Multiplying 3 Proper and Improper Fractions (Fillable, Savable, Printable) ✎ Multiplying Proper and Improper Fractions and Whole Numbers (3 factors) (Fillable, Savable, Printable) ✎ Multiplying Fractions and Mixed Fractions (3 factors) (Fillable, Savable, Printable) ✎ Multiplying 3 Mixed Fractions (Fillable, Savable, Printable) ✎

Dividing Fractions

Conceptually, dividing fractions is probably the most difficult of all the operations, but we're going to help you out. The algorithm for dividing fractions is just like multiplying fractions, but you find the inverse of the second fraction or you cross-multiply. This gets you the right answer which is extremely important especially if you're building a bridge. We told you how to conceptualize fraction multiplication, but how does it work with division? Easy! You just need to learn the magic phrase: "How many ____'s are there in ______? For example, in the question 6 ÷ 1/2, you would ask, "How many halves are there in 6?" It becomes a little more difficult when both numbers are fractions, but it isn't a giant leap to figure it out. 1/2 ÷ 1/4 is a fairly easy example, especially if you think in terms of U.S. or Canadian coins. How many quarters are there in a half dollar?

• Dividing Two Proper Fractions Dividing Two Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Proper Fractions with No Simplifying (Printable Only) Dividing Two Proper Fractions with All Simplifying (Printable Only) Dividing Two Proper Fractions with Some Simplifying (Printable Only)
• Dividing Proper and Improper Fractions Dividing Proper and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Improper Fractions with No Simplifying (Printable Only) Dividing Proper and Improper Fractions with All Simplifying (Printable Only) Dividing Proper and Improper Fractions with Some Simplifying (Printable Only)
• Dividing Two Improper Fractions Dividing Two Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Improper Fractions with No Simplifying (Printable Only) Dividing Two Improper Fractions with All Simplifying (Printable Only) Dividing Two Improper Fractions with Some Simplifying (Printable Only)
• Dividing Proper and Mixed Fractions Dividing Proper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Mixed Fractions with No Simplifying (Printable Only) Dividing Proper and Mixed Fractions with All Simplifying (Printable Only) Dividing Proper and Mixed Fractions with Some Simplifying (Printable Only)
• Dividing Two Mixed Fractions Dividing Two Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Mixed Fractions with No Simplifying (Printable Only) Dividing Two Mixed Fractions with All Simplifying (Printable Only) Dividing Two Mixed Fractions with Some Simplifying (Printable Only)
• Dividing Whole Numbers and Proper Fractions Dividing Whole Numbers and Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Proper Fractions with No Simplifying (Printable Only) Dividing Whole Numbers and Proper Fractions with All Simplifying (Printable Only) Dividing Whole Numbers and Proper Fractions with Some Simplifying (Printable Only)
• Dividing Whole Numbers and Improper Fractions Dividing Whole Numbers and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Improper Fractions with No Simplifying (Printable Only) Dividing Whole Numbers and Improper Fractions with All Simplifying (Printable Only) Dividing Whole Numbers and Improper Fractions with Some Simplifying (Printable Only)
• Dividing Whole Numbers and Mixed Fractions Dividing Whole Numbers and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Mixed Fractions with No Simplifying (Printable Only) Dividing Whole Numbers and Mixed Fractions with All Simplifying (Printable Only) Dividing Whole Numbers and Mixed Fractions with Some Simplifying (Printable Only)
• Dividing Proper, Improper and Mixed Fractions Dividing Proper, Improper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper, Improper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper, Improper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper, Improper and Mixed Fractions with No Simplifying (Printable Only) Dividing Proper, Improper and Mixed Fractions with All Simplifying (Printable Only) Dividing Proper, Improper and Mixed Fractions with Some Simplifying (Printable Only)
• Dividing 3 Fractions Dividing 3 Fractions Dividing 3 Fractions (Some Whole Numbers) Dividing 3 Fractions (Some Mixed) Dividing 3 Mixed Fractions

Multiplying and Dividing Fractions

This section includes worksheets with both multiplication and division mixed on each worksheet. Students will have to pay attention to the signs.

• Multiplying and Dividing Two Proper Fractions Multiplying and Dividing Two Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Proper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Two Proper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Two Proper Fractions with Some Simplifying (Printable Only)
• Multiplying and Dividing Proper and Improper Fractions Multiplying and Dividing Proper and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Improper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Proper and Improper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Proper and Improper Fractions with Some Simplifying (Printable Only)
• Multiplying and Dividing Two Improper Fractions Multiplying and Dividing Two Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Improper Fractions (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Improper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Two Improper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Two Improper Fractions (Printable Only)
• Multiplying and Dividing Proper and Mixed Fractions Multiplying and Dividing Proper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Mixed Fractions with No Simplifying (Printable Only) Multiplying and Dividing Proper and Mixed Fractions with All Simplifying (Printable Only) Multiplying and Dividing Proper and Mixed Fractions with Some Simplifying (Printable Only)
• Multiplying and Dividing Two Mixed Fractions Multiplying and Dividing Two Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Mixed Fractions with No Simplifying (Printable Only) Multiplying and Dividing Two Mixed Fractions with All Simplifying (Printable Only) Multiplying and Dividing Two Mixed Fractions with Some Simplifying (Printable Only)
• Multiplying and Dividing Whole Numbers and Proper Fractions Fractions Multiplying and Dividing Whole Numbers and Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Proper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Proper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Proper Fractions with Some Simplifying (Printable Only)
• Multiplying and Dividing Whole Numbers and Improper Fractions Multiplying and Dividing Whole Numbers and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Improper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Improper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Improper Fractions with Some Simplifying (Printable Only)
• Multiplying and Dividing Whole Numbers and Mixed Fractions Multiplying and Dividing Whole Numbers and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Mixed Fractions with No Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Mixed Fractions with All Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Mixed Fractions with Some Simplifying (Printable Only)
• Multiplying and Dividing Proper, Improper and Mixed Fractions Multiplying and Dividing Proper, Improper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper, Improper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper, Improper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper, Improper and Mixed Fractions with No Simplifying (Printable Only) Multiplying and Dividing Proper, Improper and Mixed Fractions with All Simplifying (Printable Only) Multiplying and Dividing Proper, Improper and Mixed Fractions with Some Simplifying (Printable Only)
• Multiplying and Dividing 3 Fractions Multiplying/Dividing Fractions (three factors) Multiplying/Dividing Mixed Fractions (3 factors)

Adding Fractions

Adding fractions requires the annoying common denominator. Make it easy on your students by first teaching the concepts of equivalent fractions and least common multiples. Once students are familiar with those two concepts, the idea of finding fractions with common denominators for adding becomes that much easier. Spending time on modeling fractions will also help students to understand fractions addition. Relating fractions to familiar examples will certainly help. For example, if you add a 1/2 banana and a 1/2 banana, you get a whole banana. What happens if you add a 1/2 banana and 3/4 of another banana?

• Adding Two Proper Fractions with Equal Denominators and Proper Fraction Results Adding Two Proper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Proper Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Equal Denominators, Proper Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Equal Denominators, Proper Fractions Result, and Some Simplifying (Printable Only)
• Adding Two Proper Fractions with Equal Denominators and Mixed Fraction Results Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Result, and Some Simplifying (Printable Only)
• Adding Two Proper Fractions with Similar Denominators and Proper Fraction Results Adding Two Proper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Proper Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Similar Denominators, Proper Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Similar Denominators, Proper Fractions Result, and Some Simplifying (Printable Only)
• Adding Two Proper Fractions with Similar Denominators and Mixed Fraction Results Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Result, and Some Simplifying (Printable Only)
• Adding Two Proper Fractions with Unlike Denominators and Proper Fraction Results Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Result, and Some Simplifying (Printable Only)
• Adding Two Proper Fractions with Unlike Denominators and Mixed Fraction Results Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Result, and Some Simplifying (Printable Only)
• Adding Proper and Improper Fractions with Equal Denominators Adding Proper and Improper Fractions with Equal Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Equal Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Equal Denominators and No Simplifying (Printable Only) Adding Proper and Improper Fractions with Equal Denominators and All Simplifying (Printable Only) Adding Proper and Improper Fractions with Equal Denominators and Some Simplifying (Printable Only)
• Adding Proper and Improper Fractions with Similar Denominators Adding Proper and Improper Fractions with Similar Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Similar Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Similar Denominators and No Simplifying (Printable Only) Adding Proper and Improper Fractions with Similar Denominators and All Simplifying (Printable Only) Adding Proper and Improper Fractions with Similar Denominators and Some Simplifying (Printable Only)
• Adding Proper and Improper Fractions with Unlike Denominators Adding Proper and Improper Fractions with Unlike Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Unlike Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Unlike Denominators and No Simplifying (Printable Only) Adding Proper and Improper Fractions with Unlike Denominators and All Simplifying (Printable Only) Adding Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Printable Only)

A common strategy to use when adding mixed fractions is to convert the mixed fractions to improper fractions, complete the addition, then switch back. Another strategy which requires a little less brainpower is to look at the whole numbers and fractions separately. Add the whole numbers first. Add the fractions second. If the resulting fraction is improper, then it needs to be converted to a mixed number. The whole number portion can be added to the original whole number portion.

• Adding Two Mixed Fractions with Equal Denominators Adding Two Mixed Fractions with Equal Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Equal Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Equal Denominators and No Simplifying (Printable Only) Adding Two Mixed Fractions with Equal Denominators and All Simplifying (Printable Only) Adding Two Mixed Fractions with Equal Denominators and Some Simplifying (Printable Only)
• Adding Two Mixed Fractions with Similar Denominators Adding Two Mixed Fractions with Similar Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Similar Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Similar Denominators and Some Simplifying Adding Two Mixed Fractions with Similar Denominators and No Simplifying (Printable Only) Adding Two Mixed Fractions with Similar Denominators and All Simplifying (Printable Only) Adding Two Mixed Fractions with Similar Denominators and Some Simplifying (Printable Only)
• Adding Two Mixed Fractions with Unlike Denominators Adding Two Mixed Fractions with Unlike Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Unlike Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Unlike Denominators and No Simplifying (Printable Only) Adding Two Mixed Fractions with Unlike Denominators and All Simplifying (Printable Only) Adding Two Mixed Fractions with Unlike Denominators and Some Simplifying (Printable Only)

Subtracting Fractions

There isn't a lot of difference between adding and subtracting fractions. Both require a common denominator which requires some prerequisite knowledge. The only difference is the second and subsequent numerators are subtracted from the first one. There is a danger that you might end up with a negative number when subtracting fractions, so students might need to learn what it means in that case. When it comes to any concept in fractions, it is always a good idea to relate it to a familiar or easy-to-understand situation. For example, 7/8 - 3/4 = 1/8 could be given meaning in the context of a race. The first runner was 7/8 around the track when the second runner was 3/4 around the track. How far ahead was the first runner? (1/8 of the track).

• Subtracting Two Proper Fractions with Equal Denominators and Proper Fraction Results Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
• Subtracting Two Proper Fractions with Similar Denominators and Proper Fraction Results Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
• Subtracting Two Proper Fractions with Unlike Denominators and Proper Fraction Results Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
• Subtracting Proper and Improper Fractions with Equal Denominators and Proper Fraction Results Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
• Subtracting Proper and Improper Fractions with Similar Denominators and Proper Fraction Results Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
• Subtracting Proper and Improper Fractions with Unlike Denominators and Proper Fraction Results Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
• Subtracting Proper and Improper Fractions with Equal Denominators and Mixed Fraction Results Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and Some Simplifying (Printable Only)
• Subtracting Proper and Improper Fractions with Similar Denominators and Mixed Fraction Results Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and Some Simplifying (Printable Only)
• Subtracting Proper and Improper Fractions with Unlike Denominators and Mixed Fraction Results Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and Some Simplifying (Printable Only)
• Subtracting Mixed Fractions with Equal Denominators Subtracting Mixed Fractions with Equal Denominators, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Equal Denominators, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Equal Denominators, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Equal Denominators, and No Simplifying (Printable Only) Subtracting Mixed Fractions with Equal Denominators, and All Simplifying (Printable Only) Subtracting Mixed Fractions with Equal Denominators, and Some Simplifying (Printable Only)
• Subtracting Mixed Fractions with Similar Denominators Subtracting Mixed Fractions with Similar Denominators, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Similar Denominators, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Similar Denominators, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Similar Denominators, and No Simplifying (Printable Only) Subtracting Mixed Fractions with Similar Denominators, and All Simplifying (Printable Only) Subtracting Mixed Fractions with Similar Denominators, and Some Simplifying (Printable Only)
• Subtracting Mixed Fractions with Unlike Denominators Subtracting Mixed Fractions with Unlike Denominators, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Unlike Denominators, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Unlike Denominators, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Unlike Denominators, and No Simplifying (Printable Only) Subtracting Mixed Fractions with Unlike Denominators, and All Simplifying (Printable Only) Subtracting Mixed Fractions with Unlike Denominators, and Some Simplifying (Printable Only)

Adding and Subtracting Fractions

Mixing up the signs on operations with fractions worksheets makes students pay more attention to what they are doing and allows for a good test of their skills in more than one operation.

• Adding and Subtracting Proper and Improper Fractions Adding and Subtracting Proper and Improper Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Proper and Improper Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Proper and Improper Fractions with Equal Denominators and Some Simplifying (Printable Only) Adding and Subtracting Proper and Improper Fractions with Similar Denominators and Some Simplifying (Printable Only) Adding and Subtracting Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Printable Only)
• Adding and Subtracting Mixed Fractions Adding and Subtracting Mixed Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Mixed Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Mixed Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Mixed Fractions with Equal Denominators and Some Simplifying (Printable Only) Adding and Subtracting Mixed Fractions with Similar Denominators and Some Simplifying (Printable Only) Adding and Subtracting Mixed Fractions with Unlike Denominators and Some Simplifying (Printable Only) Adding/Subtracting Three Fractions/Mixed Fractions

All Operations Fractions Worksheets

• All Operations with Two Proper Fractions with Equal Denominators and Proper Fraction Results All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and No Simplifying (Printable Only) All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and All Simplifying (Printable Only) All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and Some Simplifying (Printable Only)
• All Operations with Two Proper Fractions with Similar Denominators and Proper Fraction Results All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and No Simplifying (Printable Only) All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and All Simplifying (Printable Only) All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and Some Simplifying (Printable Only)
• All Operations with Two Proper Fractions with Unlike Denominators and Proper Fraction Results All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and No Simplifying (Printable Only) All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and All Simplifying (Printable Only) All Operations with Two Proper Fractions with Unlike Denominators, Mixed Fractions Results and Some Simplifying (Printable Only)
• All Operations with Proper and Improper Fractions with Equal Denominators All Operations with Proper and Improper Fractions with Equal Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Equal Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Equal Denominators and No Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Equal Denominators and All Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Equal Denominators and Some Simplifying (Printable Only)
• All Operations with Proper and Improper Fractions with Similar Denominators All Operations with Proper and Improper Fractions with Similar Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Similar Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Similar Denominators and No Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Similar Denominators and All Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Similar Denominators and Some Simplifying (Printable Only)
• All Operations with Proper and Improper Fractions with Unlike Denominators All Operations with Proper and Improper Fractions with Unlike Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Unlike Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Unlike Denominators and No Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Unlike Denominators and All Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Printable Only)
• All Operations with Two Mixed Fractions with Equal Denominators All Operations with Two Mixed Fractions with Equal Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Equal Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Equal Denominators and No Simplifying (Printable Only) All Operations with Two Mixed Fractions with Equal Denominators and All Simplifying (Printable Only) All Operations with Two Mixed Fractions with Equal Denominators and Some Simplifying (Printable Only)
• All Operations with Two Mixed Fractions with Similar Denominators All Operations with Two Mixed Fractions with Similar Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Similar Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Similar Denominators and No Simplifying (Printable Only) All Operations with Two Mixed Fractions with Similar Denominators and All Simplifying (Printable Only) All Operations with Two Mixed Fractions with Similar Denominators and Some Simplifying (Printable Only)
• All Operations with Two Mixed Fractions with Unlike Denominators All Operations with Two Mixed Fractions with Unlike Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Unlike Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Unlike Denominators and No Simplifying (Printable Only) All Operations with Two Mixed Fractions with Unlike Denominators and All Simplifying (Printable Only) All Operations with Two Mixed Fractions with Unlike Denominators and Some Simplifying (Printable Only)
• All Operations with 3 Fractions All Operations with Three Fractions Including Some Improper Fractions All Operations with Three Fractions Including Some Negative and Some Improper Fractions

Operations with Negative Fractions Worksheets

Although some of these worksheets are single operations, it should be helpful to have all of these in the same location. There are some special considerations when completing operations with negative fractions. It is usually very helpful to change any mixed numbers to an improper fraction before proceeding. It is important to pay attention to the signs and know the rules for multiplying positives and negatives (++ = +, +- = -, -+ = - and -- = +).

• Adding with Negative Fractions Adding Negative Proper Fractions with Unlike Denominators Up to Sixths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Negative Proper Fractions with Unlike Denominators Up to Twelfths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Negative Mixed Fractions with Unlike Denominators Up to Sixths, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Adding Negative Mixed Fractions with Unlike Denominators Up to Twelfths, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Adding Negative Proper Fractions with Denominators Up to Sixths, Proper Fraction Results and Some Simplifying (Printable Only) Adding Negative Proper Fractions with Denominators Up to Twelfths, Proper Fraction Results and Some Simplifying (Printable Only) Adding Negative Mixed Fractions with Denominators Up to Sixths and Some Simplifying (Printable Only) Adding Negative Mixed Fractions with Denominators Up to Twelfths and Some Simplifying (Printable Only)
• Subtracting with Negative Fractions Subtracting Negative Proper Fractions with Unlike Denominators Up to Sixths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Negative Proper Fractions with Unlike Denominators Up to Twelfths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Negative Mixed Fractions with Unlike Denominators Up to Sixths, Mixed Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Negative Mixed Fractions with Unlike Denominators Up to Twelfths, Mixed Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Negative Proper Fractions with Denominators Up to Sixths, Proper Fraction Results and Some Simplifying (Printable Only) Subtracting Negative Proper Fractions with Denominators Up to Twelfths, Proper Fraction Results and Some Simplifying (Printable Only) Subtracting Negative Mixed Fractions with Denominators Up to Sixths and Some Simplifying (Printable Only) Subtracting Negative Mixed Fractions with Denominators Up to Twelfths and Some Simplifying (Printable Only)
• Multiplying with Negative Fractions Multiplying Negative Proper Fractions with Denominators Up to Sixths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Negative Proper Fractions with Denominators Up to Twelfths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Negative Mixed Fractions with Denominators Up to Sixths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Negative Mixed Fractions with Denominators Up to Twelfths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Negative Proper Fractions with Denominators Up to Sixths, Proper Fraction Results and Some Simplifying (Printable Only) Multiplying Negative Proper Fractions with Denominators Up to Twelfths, Proper Fraction Results and Some Simplifying (Printable Only) Multiplying Negative Mixed Fractions with Denominators Up to Sixths and Some Simplifying (Printable Only) Multiplying Negative Mixed Fractions with Denominators Up to Twelfths and Some Simplifying (Printable Only)
• Dividing with Negative Fractions Dividing Negative Proper Fractions with Denominators Up to Sixths, Mixed Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Negative Proper Fractions with Denominators Up to Twelfths, Mixed Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Negative Mixed Fractions with Denominators Up to Twelfths, Mixed Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Dividing Negative Mixed Fractions with Denominators Up to Twelfths, Mixed Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Dividing Negative Proper Fractions with Denominators Up to Sixths, Proper Fraction Results and Some Simplifying (Printable Only) Dividing Negative Proper Fractions with Denominators Up to Twelfths, Proper Fraction Results and Some Simplifying (Printable Only) Dividing Negative Mixed Fractions with Denominators Up to Sixths and Some Simplifying (Printable Only) Dividing Negative Mixed Fractions with Denominators Up to Twelfths and Some Simplifying (Printable Only)

Order of Operations with Fractions Worksheets

The order of operations worksheets in this section actually reside on the Order of Operations page, but they are included here for your convenience.

• Order of Operations with Fractions 2-Step Order of Operations with Fractions 3-Step Order of Operations with Fractions 4-Step Order of Operations with Fractions 5-Step Order of Operations with Fractions 6-Step Order of Operations with Fractions
• Order of Operations with Fractions (No Exponents) 2-Step Order of Operations with Fractions (No Exponents) 3-Step Order of Operations with Fractions (No Exponents) 4-Step Order of Operations with Fractions (No Exponents) 5-Step Order of Operations with Fractions (No Exponents) 6-Step Order of Operations with Fractions (No Exponents)
• Order of Operations with Positive and Negative Fractions 2-Step Order of Operations with Positive & Negative Fractions 3-Step Order of Operations with Positive & Negative Fractions 4-Step Order of Operations with Positive & Negative Fractions 5-Step Order of Operations with Positive & Negative Fractions 6-Step Order of Operations with Positive & Negative Fractions

Copyright © 2005-2024 Math-Drills.com You may use the math worksheets on this website according to our Terms of Use to help students learn math.

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How to Solve Fraction Questions in Math

Last Updated: September 1, 2024 Approved

This article was co-authored by Mario Banuelos, PhD and by wikiHow staff writer, Sophia Latorre . Mario Banuelos is an Associate Professor of Mathematics at California State University, Fresno. With over eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical models for genome evolution, and data science. Mario holds a BA in Mathematics from California State University, Fresno, and a Ph.D. in Applied Mathematics from the University of California, Merced. Mario has taught at both the high school and collegiate levels. There are 7 references cited in this article, which can be found at the bottom of the page. wikiHow marks an article as reader-approved once it receives enough positive feedback. This article has 17 testimonials from our readers, earning it our reader-approved status. This article has been viewed 1,217,593 times.

Fraction questions can look tricky at first, but they become easier with practice and know-how. Start by learning the terminology and fundamentals, then pratice adding, subtracting, multiplying, and dividing fractions. [1] X Research source Once you understand what fractions are and how to manipulate them, you'll be breezing through fraction problems in no time.

How to Solve Fractions

• If two fractions have the same denominator, add or subtract the numerators from each other.
• If the fractions don’t have the same denominator, change them to a common multiple. For example, 4/5 and 3/2 can become 8/10 and 15/10.
• Multiply fractions by multiplying the numerators, then the denominators. Divide fractions by inverting one and then multiplying the new fractions’ numerators and denominators.

Doing Calculations with Fractions

• For instance, to solve 5/9 + 1/9, just add 5 + 1, which equals 6. The answer, then, is 6/9 which can be reduced to 2/3.

• For instance, to solve 6/8 - 2/8, all you do is take away 2 from 6. The answer is 4/8, which can be reduced to 1/2.

• For example, if you need to add 1/2 and 2/3, start by determining a common multiple. In this case, the common multiple is 6 since both 2 and 3 can be converted to 6. To turn 1/2 into a fraction with a denominator of 6, multiply both the numerator and denominator by 3: 1 x 3 = 3 and 2 x 3 = 6, so the new fraction is 3/6. To turn 2/3 into a fraction with a denominator of 6, multiply both the numerator and denominator by 2: 2 x 2 = 4 and 3 x 2 = 6, so the new fraction is 4/6. Now, you can add the numerators: 3/6 + 4/6 = 7/6. Since this is an improper fraction, you can convert it to the mixed number 1 1/6.
• On the other hand, say you're working on the problem 7/10 - 1/5. The common multiple in this case is 10, since 1/5 can be converted into a fraction with a denominator of 10 by multiplying it by 2: 1 x 2 = 2 and 5 x 2 = 10, so the new fraction is 2/10. You don't need to convert the other fraction at all. Just subtract 2 from 7, which is 5. The answer is 5/10, which can also be reduced to 1/2.

• For instance, to multiply 2/3 and 7/8, find the new numerator by multiplying 2 by 7, which is 14. Then, multiply 3 by 8, which is 24. Therefore, the answer is 14/24, which can be reduced to 7/12 by dividing both the numerator and denominator by 2.

• For example, to solve 1/2 ÷ 1/6, flip 1/6 upside down so it becomes 6/1. Then just multiply 1 x 6 to find the numerator (which is 6) and 2 x 1 to find the denominator (which is 2). So, the answer is 6/2 which is equal to 3.

Joseph Meyer

Think about fractions as portions of a whole. Imagine dividing objects like pizzas or cakes into equal parts. Visualizing fractions this way improves comprehension, compared to relying solely on memorization. This approach can be helpful when adding, subtracting, and comparing fractions.

Practicing the Basics

• For instance, in 3/5, 3 is the numerator so there are 3 parts and 5 is the denominator so there are 5 total parts. In 7/8, 7 is the numerator and 8 is the denominator.

• If you need to turn 7 into a fraction, for instance, write it as 7/1.

• For example, if you have the fraction 15/45, the greatest common factor is 15, since both 15 and 45 can be divided by 15. Divide 15 by 15, which is 1, so that's your new numerator. Divide 45 by 15, which is 3, so that's your new denominator. This means that 15/45 can be reduced to 1/3.

• Say you have the mixed number 1 2/3. Stary by multiplying 3 by 1, which is 3. Add 3 to 2, the existing numerator. The new numerator is 5, so the mixed fraction is 5/3.

Tip: Typically, you'll need to convert mixed numbers to improper fractions if you're multiplying or dividing them.

• Say that you have the improper fraction 17/4. Set up the problem as 17 ÷ 4. The number 4 goes into 17 a total of 4 times, so the whole number is 4. Then, multiply 4 by 4, which is equal to 16. Subtract 16 from 17, which is equal to 1, so that's the remainder. This means that 17/4 is the same as 4 1/4.

Fraction Calculator, Practice Problems, and Answers

Community Q&A

• Check with your teacher to find out if you need to convert improper fractions into mixed numbers and/or reduce fractions to their lowest terms to get full marks. Thanks Helpful 3 Not Helpful 1
• Take the time to carefully read through the problem at least twice so you can be sure you know what it's asking you to do. Thanks Helpful 3 Not Helpful 2
• To take the reciprocal of a whole number, just put a 1 over it. For example, 5 becomes 1/5. Thanks Helpful 2 Not Helpful 1

You Might Also Like

• ↑ https://tlp-lpa.ca/math-tutorials/fractions
• ↑ https://www.bbc.co.uk/bitesize/articles/z9n4k7h
• ↑ https://www.mathsisfun.com/fractions_multiplication.html
• ↑ https://www.mathsisfun.com/fractions_division.html
• ↑ https://pressbooks-dev.oer.hawaii.edu/math111/chapter/what-is-a-fraction/
• ↑ https://www.purplemath.com/modules/fraction.htm
• ↑ https://www.calculatorsoup.com/calculators/math/mixed-number-to-improper-fraction.php
• ↑ https://www.inchcalculator.com/fraction-to-mixed-number-calculator/

About This Article

To solve a fraction multiplication question in math, line up the 2 fractions next to each other. Multiply the top of the left fraction by the top of the right fraction and write that answer on top, then multiply the bottom of each fraction and write that answer on the bottom. Simplify the new fraction as much as possible. To divide fractions, flip one of the fractions upside-down and multiply them the same way. If you need to add or subtract fractions, keep reading! Did this summary help you? Yes No

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Fractions operations

Here you will learn about fractions operations, including how to add, subtract, multiply and divide with fractions.

Students will first learn about fractions operations as part of number and operations in fractions in elementary school. They will continue to build on this knowledge in the number system in 6th grade and 7th grade.

Every week, we teach lessons on fractions operations to students in schools and districts across the US as part of our online one-on-one math tutoring programs. On this page we’ve broken down everything we’ve learnt about teaching this topic effectively.

What are fractions operations?

Fractions operations are when you add, subtract, multiply or divide with fractions.

For example,

[FREE] Fraction Operations Worksheet (Grade 4 to 6)

Use this quiz to check your grade 4 to 6 students’ understanding of fraction operations. 10+ questions with answers covering a range of 4th to 6th grade fraction operations topics to identify areas of strength and support!

Adding and subtracting fractions

Adding and subtracting fractions means finding the sum or the difference of two or more fractions. To do this, find a common denominator (bottom number), add the two numerators (top numbers), and keep the denominators the same.

The numerator shows the number of parts out of the whole and the denominator shows how many equal parts the whole is divided into.

The equation is taking \, \cfrac{1}{8} \, away from \, \cfrac{4}{8} \, .

Since the denominators are the same, the parts are the same size.

You subtract to see how many parts are left: 4-1 = 3.

There are 3 parts and the size is still eighths, so the denominator stays the same.

When fractions have unlike denominators, create equivalent fractions with common denominators to solve.

The parts are NOT the same size, since the denominators are different.

Use equivalent fractions to create a common denominator of 10.

Multiply the numerator and denominator of \, \cfrac{2}{5} \, by 2.

\cfrac{2 \, \times \, 2}{5 \, \times \, 2}=\cfrac{4}{10}

Add to find how many parts there are in all: 2 + 4 = 6.

There are 6 parts and the size is still tenths, so the denominator stays the same.

The sum could also be written as the equivalent fraction \, \cfrac{3}{5} \, .

Step-by-step guide: Adding fractions

Step-by-step guide: Subtracting fractions

Step-by-step guide: Adding and subtracting fractions

Multiplying and dividing fractions

Multiplying and dividing fractions means using multiplication and division to calculate with fractions. Fraction multiplication and division can be solved using models or an algorithm.

Using models:

In the model, \, \cfrac{2}{3} \, is yellow and \, \cfrac{1}{2} \, is blue.

The product is where the fractions overlap in green.

The model shows \, \cfrac{2}{3} \, of \, \cfrac{1}{2}, \, so \, \cfrac{1}{2} \times \cfrac{2}{3} = \cfrac{2}{6} \, .

Using the algorithm:

To multiply fractions , you multiply the numerators together, and multiply the denominators together:

\cfrac{1}{2} \, \times \, \cfrac{2}{3}=\cfrac{2}{6} \, .

You can also divide fractions with a model or an algorithm.

Think of this equation as how many \, \cfrac{1}{4} \, fit into \, \cfrac{1}{2} \, .

In the model, \, \cfrac{1}{2} \, is orange and \, \cfrac{1}{4} \, is yellow.

To divide into equal groups, use the equivalent fraction \, \cfrac{2}{4} \, .

The quotient is the final fraction formed when \, \cfrac{2}{4} \, is put into a group of \, \cfrac{1}{4} \, .

Two groups of \cfrac{1}{4} can be made, so \cfrac{1}{2} \div \cfrac{1}{4}=2.

KEEP the first fraction, FLIP the second fraction, CHANGE to multiplication.

\cfrac{1}{2} \div \cfrac{1}{4}

Keep the dividend (first fraction): \, \cfrac{1}{2}

Take the reciprocal of the divisor (flip the second fraction): \, \cfrac{1}{4} \rightarrow \cfrac{4}{1}

Change to multiplication: \, \cfrac{1}{2} \times \cfrac{4}{1}

Multiply the fractions: \, \cfrac{1}{2} \times \cfrac{4}{1}=\cfrac{4}{2} \, which simplifies to 2.

\cfrac{1}{2} \div \cfrac{1}{4}=2

Since \, \cfrac{1}{2} \, is larger than \, \cfrac{1}{4} \, , the answer makes sense.

A larger number divided by a smaller number, will have a quotient of greater than 1.

Notice that it is not necessary to create a common denominator to multiply and divide fractions when using the algorithm, like it is to add and subtract fractions.

Step-by-step guide: Multiplying fractions

Step-by-step guide: Dividing fractions

Step-by-step guide: Multiplying and dividing fractions

The algorithm for dividing fractions involves using the reciprocal .

When two numbers are multiplied by something other than 1, and have a product of 1, they are reciprocals.

This is also known as the multiplicative inverse.

The reciprocal of all numbers can be found by writing the number as a fraction and then flipping it so that the numerator becomes the denominator and the denominator becomes the numerator.

Step-by-step guide: Reciprocal

Step-by-step guide: Multiplicative inverse

Common Core State Standards

How does this relate to 4th grade math, 5th grade math, and 6th grade math?

• Grade 4 – Number and Operations – Fractions (4.NF.B.3a) Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
• Grade 4 – Number and Operations – Fractions (4.NF.B.3c) Add and subtract mixed numbers with like denominators, for example, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
• Grade 4 – Number and Operations – Fractions (4.NF.B.4b) ​​Understand a multiple of \, \cfrac{a}{b} \, as a multiple of \, \cfrac{1}{b} \, , and use this understanding to multiply a fraction by a whole number.
• Grade 5 – Number and Operations – Fractions (5.NF.A.1) Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, \, \cfrac{2}{3} + \cfrac{5}{4} = \cfrac{8}{12} + \cfrac{15}{12} = \cfrac{23}{12} \, . \; ( In general, \, \cfrac{a}{b} + \cfrac{c}{d} = \cfrac{(ad \, + \, bc)}{bd} \, . )
• Grade 5 – Number and Operations – Fractions (5.NF.B.4b) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
• Grade 6 – Number System (6.NS.A.1) Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

How to use fractions operations

There are a lot of ways to use fractions operations. For more specific step-by-step guides, check out the fraction pages linked in the “What are fractions operations?” section above or read through the examples below.

Fractions operations examples

Example 1: adding fractions with like denominators.

Solve \, \cfrac{5}{8}+\cfrac{7}{8} \, .

Add or subtract the numerators (top numbers).

Since the denominators are the same, the parts are the same size. You add to see how many parts there are in total: 5 + 7 = 12.

2 Write your answer as a fraction.

There are 12 parts, and the size is still eighths, so the denominator stays the same.

\cfrac{12}{8} \, is an improper fraction and converts to the mixed number 1 \, \cfrac{4}{8} \, .

\cfrac{5}{8}+\cfrac{7}{8}=1 \cfrac{4}{8}

You can also write this answer as the equivalent mixed number \, 1 \cfrac{1}{2} \, .

Example 2: subtracting fractions with unlike denominators

Solve \cfrac{6}{10}-\cfrac{1}{3} \, .

Create common denominators (bottom numbers).

Since \, \cfrac{6}{10} \, and \, \cfrac{1}{3} \, do not have like denominators, the parts are NOT the same size.

Multiply the numerator and denominator by the opposite denominator to create equivalent fractions with common denominators.

\cfrac{6 \, \times \, 3}{10 \, \times \, 3}=\cfrac{18}{30} \quad and \quad \cfrac{1 \, \times \, 10}{3 \, \times \, 10}=\cfrac{10}{30}

Now use the equivalent fractions to solve: \, \cfrac{18}{30}-\cfrac{10}{30} \, .

Since the denominators are the same, the parts are the same size. You subtract to see how many parts are left: 18-10 = 8.

Write your answer as a fraction.

There are 8 parts and the size is still thirtieths, so the denominator stays the same.

\cfrac{18}{30}-\cfrac{10}{30}=\cfrac{8}{30}

You can also write this answer as the equivalent fraction \, \cfrac{4}{15} \, .

Example 3: multiplying a mixed number by a fraction with the algorithm

Solve 1 \, \cfrac{11}{12} \times \cfrac{3}{4} \, .

Convert whole numbers and mixed numbers to improper fractions.

Convert the mixed number to an improper fraction.

Multiply the numerators together.

\cfrac{23}{12} \times \cfrac{3}{4}=\cfrac{69}{}

Multiply the denominators together.

\cfrac{23}{12} \times \cfrac{3}{4}=\cfrac{69}{48}

If possible, simplify or convert to a mixed number.

The numerator is greater than the denominator, so the improper fraction can be converted to a mixed number.

\cfrac{69}{48}=1 \, \cfrac{21}{48}

The product can be simplified. 21 and 48 have a common factor of 3.

\cfrac{21 \, \div \, 3}{48 \, \div \, 3}=\cfrac{7}{16}

So, \, \cfrac{23}{12} \times \cfrac{3}{4}=\cfrac{69}{48} \, or 1 \, \cfrac{7}{16} \, .

Example 4: dividing a fraction by a fraction

Divide the numbers \, \cfrac{1}{12} \div \cfrac{1}{4} \, .

Take the reciprocal (flip) of the divisor (second fraction).

\cfrac{1}{4} \, → \, \cfrac{4}{1}

Change the division sign to a multiplication sign.

\cfrac{1}{12} \, \times \, \cfrac{4}{1}

Multiply the fractions together.

\cfrac{1}{12} \, \times \, \cfrac{4}{1}=\cfrac{4}{12}

\cfrac{4}{12}=\cfrac{1}{3}

This can also be solved with a model.

You can think of this equation as how many \, \cfrac{1}{4} \, fit into \, \cfrac{1}{12} \, .

In the model, \, \cfrac{1}{12} \, is yellow and \, \cfrac{1}{4} \, is orange.

To divide into equal groups, the fractional pieces need to be the same size.

Use \, \cfrac{1}{12} \, and \, \cfrac{3}{12} \, to solve.

The quotient is the final fraction formed when \, \cfrac{1}{12} \, is put into groups of \, \cfrac{3}{12} \, .

One out of the three parts are filled, so \, \cfrac{1}{12} \div \cfrac{3}{12}=\cfrac{1}{3} \, .

Example 5: adding mixed numbers with unlike denominators

There are 2 \, \cfrac{1}{3} \, pounds of red apples and 4 \, \cfrac{1}{6} \, pounds of green apples.

How many pounds of apples are there in all?

Create an equation to model the problem.

2 \cfrac{1}{3}+4 \cfrac{1}{6}= \, ?

Add or subtract the whole numbers.

Since \, \cfrac{1}{3} \, and \, \cfrac{1}{6} \, do not have like denominators, the parts are NOT the same size.

Use equivalent fractions to create a common denominator.

A common denominator of 6 can be used.

Multiply the numerator and denominator of \, \cfrac{1}{3} \, by 2 to create an equivalent fraction.

\cfrac{1}{3}=\cfrac{1 \, \times \, 2}{3 \, \times \, 2}=\cfrac{2}{6} \quad and \quad \cfrac{1}{6}

Add or subtract the fractions.

Since the denominators are the same, the parts are the same size. You add to see how many parts there are in total: 2 + 1 = 3.

There are 3 parts, and the size is still sixths, so the denominator stays the same.

Write your answer as a mixed number.

Add the whole number and fraction together.

You can also write this answer as the equivalent mixed number 6 \, \cfrac{1}{2} \, .

There are 6 \, \cfrac{1}{2} \, pounds of apples in all.

Example 6: word problem dividing with fractions

Each seed needs \, \cfrac{1}{5} \, cup of soil. How many seeds can be planted with 11 cups of soil?

11 \div \cfrac{1}{5}= \, ?

Change any mixed numbers to an improper fraction.

Change 11 to an improper fraction.

11=\cfrac{11}{1}

Take the reciprocal (flip) of the divisor (second fractions).

\cfrac{1}{5} \, → \, \cfrac{5}{1}

\cfrac{11}{1} \times \cfrac{5}{1}

\cfrac{11}{1} \times \cfrac{5}{1}=\cfrac{55}{1}

If possible, simplify or convert to a mixed number (mixed fraction).

\cfrac{55}{1}=55

55 seeds can be planted with 11 cups of soil.

Teaching tips for fractions operations

• Fraction work in lower grades emphasizes understanding through models, including area models and number lines. To support students in upper grades, always have digital or physical models available for students to use as they work with fractions operations.
• Fraction worksheets can be useful when students are developing understanding around basic operations with fractions. However, when students have successful strategies and can flexibly operate, make the practice more engaging by using math games or real world projects that allow students to use fractions in a variety of situations.
• Highlight patterns within and between the operations as students are learning and encourage them to look for patterns on their own. This will help students make sense of the algorithms used to operate with fractions and minimize conceptual errors.
• Let students find reciprocal numbers on their own by consistently asking questions such as, “What number multiplied by 7 will have a product of 1 ?” Each time this is discussed, write these equations on an anchor chart and students will begin to see a pattern over time. Although worksheets can serve a purpose and help with skill and test prep practice, having students discover and make sense of mathematical concepts is more meaningful for building long lasting understanding.

Easy mistakes to make

• Forgetting how to find the reciprocal of a whole number Whole numbers can be written as an improper fraction and then the numerator and denominator of the improper fraction can be flipped to find the reciprocal of the whole number. For example, 16 can be written as \, \cfrac{16}{1} \, and the reciprocal is \, \cfrac{1}{16} \, .

Practice fractions operations questions

1. Solve \, \cfrac{5}{9}+\cfrac{2}{9} \, .

Since the denominators are the same, the parts are the same size. You add to see how many parts there are in total: 5 + 2 = 7.

There are 7 parts and the size is still ninths, so the denominator stays the same.

\cfrac{5}{9}+\cfrac{2}{9}=\cfrac{7}{9}

2. Solve \, 2 \, \cfrac{3}{10}-1 \, \cfrac{4}{5} \, .

The equation is taking \, 1 \cfrac{4}{5} \, away from \, 2 \cfrac{3}{10} \, .

Start with the fractions. Since \, \cfrac{3}{10} \, and \, \cfrac{4}{5} \, do not have like denominators, the parts are NOT the same size.

Use equivalent fractions to create a common denominator. Both denominators are multiples of 10.

\cfrac{3}{10} \quad and \quad \cfrac{4 \, \times \, 2}{5 \, \times \, 2}=\cfrac{8}{10}

Now use the equivalent fraction to solve: 2 \, \cfrac{3}{10}-1 \, \cfrac{8}{10}

However, there are not enough parts to take 8 away from 3.

You can break one of the wholes into \cfrac{10}{10} \, …

Now you can solve 1 \, \cfrac{13}{10}-1 \, \cfrac{8}{10}.

You subtract to see how many parts are left: 13-8 = 5.

There are 5 parts and the size is still tenths, so the denominator stays the same.

\cfrac{13}{10}-\cfrac{8}{10}=\cfrac{5}{10}

Subtract the whole numbers.

1 \, \cfrac{13}{10}-1 \, \cfrac{8}{10}=\cfrac{5}{10}

You can also write this answer as the equivalent fraction \, \cfrac{1}{2} \, .

3. Solve \, \cfrac{1}{4} \times \cfrac{2}{5} \, .

To solve using a model, draw a rectangle. Divide one side into fourths.

Divide the other side into fifths.

Shade in \, \cfrac{1}{4} \, with yellow and \, \cfrac{2}{5} with blue.

The model shows \, \cfrac{2}{5} \, of \, \cfrac{1}{4} \, , so \, \cfrac{1}{4} \times \cfrac{2}{5}=\cfrac{2}{20} \, , because there are 2 green squares and the whole has 20 squares in total.

The product can be simplified. Both 2 and 20 have a factor of 2, so they can be divided by 2 :

\, \cfrac{2 \, \div \, 2}{20 \, \div \, 2}=\cfrac{1}{10} \, .

So, \, \cfrac{1}{4} \times \cfrac{2}{5}=\cfrac{2}{20} \; or \; \cfrac{1}{10}

4. Solve \, 2 \, \cfrac{1}{6} \div 1 \, \cfrac{2}{3} \, . Write the quotient in lowest terms.

Change the mixed numbers to improper fractions:

Keep the dividend (first fraction): \, \cfrac{13}{6}

Take the reciprocal of the divisor (flip the second fraction): \, \cfrac{5}{3} → \cfrac{3}{5}

Change to multiplication: \, \cfrac{13}{6} \times \cfrac{3}{5}

Multiply the fractions: \, \cfrac{13}{6} \times \cfrac{3}{5}=\cfrac{39}{30}

Change back into a mixed number: \, \cfrac{39}{30}=1 \, \cfrac{9}{30}

Simplify: \, \cfrac{9 \, \div \, 3}{30 \, \div \, 3}=\cfrac{3}{10} \, , so the answer in lowest terms is \, 1 \, \cfrac{3}{10} \, .

5. Rashad is cutting a 12 \, ft rope into smaller \, \cfrac{2}{3} \, ft pieces. How many smaller pieces of rope will he have?

8 smaller pieces of rope

12 smaller pieces of rope

18 smaller pieces of rope

\cfrac{24}{3} smaller pieces of rope

Use the equation \, 12 \div \cfrac{2}{3}= \, ?

Draw 12 wholes and break them up into thirds.

Create groups of \, \cfrac{2}{3} \, .

There are 18 groups of \, \cfrac{2}{3} \, .

Rashad will have 18 pieces of smaller rope.

6. A recipe calls for 3 \, \cfrac{1}{4} \, cups of strawberries. If Tyler has 5 \, \cfrac{5}{8} \, cups of strawberries, how many will he have left after he makes 1 recipe?

2 \, \cfrac{3}{8} cups

2 \, \cfrac{4}{4} cups

8 \, \cfrac{7}{8} cups

8 \, \cfrac{6}{12} cups

Use the equation 5 \cfrac{5}{8}-3 \cfrac{1}{4}= \, ?

Start with the fraction.

Since \, \cfrac{5}{8} \, and \, \cfrac{1}{4} \, do not have like denominators, the parts are NOT the same size.

A common denominator of 8 can be used.

Multiply the numerator and denominator of \, \cfrac{1}{4} \, by 2 to create an equivalent fraction.

\cfrac{5}{8} \quad and \quad \cfrac{1}{4}=\cfrac{1 \, \times \, 2}{4 \, \times \, 2}=\cfrac{2}{8}

You subtract to see how many parts there are in total: 5-2 = 3.

There are 2 parts and the size is still eighths, so the denominator stays the same.

There will be \, 2 \cfrac{3}{8} \, cups of strawberries left.

Fractions operations FAQs

No, although using these operations will create different denominators and numerators, as long as they are multiplied or divided by the same thing, the value of the fraction will remain the same.

No, unless the question specifies the lowest terms, it is valid to answer without using the least common denominator (LCD). However, as students progress in their understanding of fractions, it is a good idea to encourage them to practice this skill. Also be mindful of standard expectations, as they may vary from state to state.

Yes, just like any other type of number, to solve multistep problems correctly, the order of operations must be followed.

The multiplicative inverse of a number is the reciprocal. For any integer, that is the number written as the numerator over a denominator of 1. For any rational number, that is switching the numerator and denominator.

The next lessons are

• Algebraic expression
• Converting fractions decimals and percents
• Interpret fractions as division
• Fraction word problems

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Word Problems on Fractions: Types & Solved Examples

Word Problems on Fractions: A fraction is a mathematical expression for a portion of a whole. Each portion acquired when we divide the entire whole into parts is referred to as a fraction. When we divide a pizza into parts, for example, each slice represents a fraction of the whole pizza. Fractions are subjected to a variety of operations, including addition, subtraction, multiplication, and division. Fractions are used in many real-life situations.

This article will outline how to construct and solve fraction word problems. Students will come across fraction word problems with answers, fraction problem solving and dividing fractions word problems. It is advisable to practice all the problems thoroughly before attempting the exam. Keep reading to know more about word problems on fractions,, definition, types, solved examples and many more

Definition of Fractions

A fraction is a number that is used to expresses a part per whole. Each part obtained when we divide the whole into several parts is called the fraction.

Example: When we cut an apple into two-part, then each part represents the fraction \(\left(\frac{1}{2}\right)\) of the apple.

A fraction consists mainly of two parts, one is the numerator, and the other one is the denominator. The upper part or topmost part of the fraction is called the numerator, and the bottom part or below part is called the denominator.

We have mainly three types of fractions: proper fractions, improper fractions, and mixed fractions. They are categorised by the relationship between the numerator and denominator of the fractions.

Word Problems on Fractions

The fraction problem solving consist of a few sentences describing a real-life scenario where a mathematical calculation of fraction formulas are used to solve a problem.

Example: Keerthi took one piece of pizza, which is cut into a total of four pieces. Find the fraction of the pizza taken by Keerthi? The fraction of pizza taken by Keerthi \(=\frac{1}{4}\)

Some of the word problems on fractions that uses fraction formula are listed below:

• Word problems on simplification of fractions
• Word problems on addition and subtraction of fractions
• Word problems on multiplication of fractions
• Word problems on dividing fractions
• Word problems on fractions, percentages, decimals.

Word Problems on Simplifications of Fractions

A fraction in which the numerator and the denominator have no common factor other than “one” is said to be the simplest form of fractions.

Example: Divya took \(8\) apples from the bucket of \(24\) apples. Find the fraction of apples taken by the Divya? The fraction of apples taken by Divya \(=\frac{8}{24}\) and its simplest form is \(\frac{1}{3}\)

Word Problems on Addition of Fractions

To add the like fractions (Fractions with the same denominators), keep the denominator the same and add the numerator values of the given fractions.

To add the unlike fractions (fractions with different denominators), convert the denominators of the given fractions equal to L.C.M of their denominators. Now add the numerator value and take the denominator of the resultant as L.C.M.

Example: Sahana bought \(\frac{1}{4} \mathrm{~kg}\) of apples and \(\frac{1}{2} \mathrm{~kg}\) of oranges from the shop. Total how many fruits she bought? The total fruits bought by Sahana \(=\frac{1}{2}+\frac{1}{4}=\frac{1 \times 2+1}{4}=\frac{3}{4} \mathrm{~kg}\)

Word Problems on Subtraction of Fractions

To subtract the like fractions (Fractions with the same denominators), keep the denominator the same and find the difference of the numerator values of the given fractions.

To subtract the unlike fractions (fractions with different denominators), convert the denominators of the given fractions equal to L.C.M of their denominators. Now find the difference of the numerator value and take the denominator of the resultant as L.C.M.

Example: Keerthi travelled \(\frac{2}{5} \mathrm{~km}\) to school. While returning home, she stopped at her friend’s house at a distance of \(\frac{1}{3} \mathrm{~km}\). Find the remaining distance? The remaining distance needs to be travelled \(=\frac{2}{5}-\frac{1}{3}=\frac{(2 \times 3)-(1 \times 5)}{5 \times 3}=\frac{6-5}{15}=\frac{1}{15} \mathrm{~km}\)

Word Problems on Multiplication of Fractions

To multiply the two or more fractions, find the product of numerators of the given fractions and the product of the denominators of the given fractions separately.

Example: Keerthi had \(Rs.10000\), and she had donated \(\frac{1}{10}\) of the money to the Oldage home. How much amount did she donate? The amount Keerthi donated \(=\frac{1}{10} \times Rs.10000= Rs. 1000\)

Word Problems on Division of Fractions

The division of fractions is nothing but multiplying the first fraction with the reciprocal of the second fraction. The reciprocal of the fraction is a fraction obtained by interchanging the numerator and denominator.

Example: The area of the rectangle is \(\frac{15}{4} \mathrm{~cm}^{2}\), whose length is \(\frac{5}{2} \mathrm{~cm}\). Find the width of the rectangle? We know that area of rectangle \(= \text {length} \times \text {bredath}\) And, breadth \(=\frac{\text { area }}{\text { length }}=\frac{15}{\frac{4}{2}}=\frac{15}{4} \times \frac{2}{5}=\frac{3}{2} \mathrm{~cm}\).

Word Problems on Conversion of Fractions to Percentage

We know that percentages are also fractions with the denominator equals to hundred. To convert the given fraction to a percentage, multiply it with hundred and to convert any percentage value to a fraction, divide with hundred.

Example: Keerthi ate \(\frac{2}{5}\) of the pizza. How much percentage of pizza is eaten by Keerthi? The percentage of pizza ate by Keerthi \(=\frac{2}{5} \times 100 \%=40 \%\).

Word Problems on Conversion of Fractions to Decimals

Decimal numbers are the numbers (quotient) obtained by dividing the fraction’s numerator with the given fraction’s denominator. To convert the given decimal to the fractional value by writing the given number without decimals and making the denominator equal to \(1\) followed by the zeroes and number of zeroes equal to the number of decimal places.

Example: Keerthi got \(\frac{1}{10}\) of the price of a T.V. as a discount. Find the discount in decimal. The part of the discount received by a Keerthi as a discount \(=\frac{1}{10}=0.1\)

Solved Examples – Word Problems on Fractions

Q.1. In February \(2021\) , a school was working only three-fourths of the total number of days in the month and the remaining number of days given as holidays. How many days did the school work in the month of February? Ans: The year \(2021\) is a non-leap year. We know that a non-leap has \(28\) days in February month. So, the total number of days \(=28\). Given, the school was working only three-fourths of the total number of days in the month. The number of days school working in February month \(=\frac{3}{4}\) of \(28\). \(=\frac{3}{4} \times 28=21\) days Hence, the school working for \(21\) days in the month of February for the year \(2021\).

Q.2. Keerthi needs \(1 \frac{1}{2}\) cups of sugar for baking a cake. She decided to make \(6\) cakes for her friends. How many cups of sugar did she need for making the \(6\) cakes? Ans: Given, Keerthi needs \(1 \frac{1}{2}\) cup of sugar to make a cake. The total cups of sugar required to make 6 cakes is calculated by multiplying the sugar needed for one cake with the number of cakes that needs to be prepared by Keerthi and is given by \(1 \frac{1}{2} \times 6\) Convert the above-mixed fraction to an improper fraction by multiplying the denominator with the whole and add to the numerator keeping the same denominator as \(1 \frac{1}{2}=\frac{(\text { whole×denominator })+\text { numerator })}{\text { denominator }}=\frac{(1 \times 2)+1}{2}=\frac{3}{2}\) The total cups of sugar needed for making \(6\) cakes \(=\frac{3}{2} \times 6=9\) Hence, Keerthi needs \(9\) cups of sugar to make \(6\) cakes.

Q.3. An oil container contains \(7 \frac{1}{2}\) litres of oil which are poured into \(2 \frac{1}{2}\) litres bottles. How many bottles are needed to fill \(7 \frac{1}{2}\) litres of oil? Ans: Given, a container holds total oil of \(7 \frac{1}{2}\) litres, and the total amount held by each bottle is \(2 \frac{1}{2}\) litres. Consider the number of bottles required is \(x\). From the given question, the total oil in the container is equal to the product of oil in each bottle and the number of bottles required. \(\Rightarrow 7 \frac{1}{2}=x \times 2 \frac{1}{2}\) \(\Rightarrow \frac{15}{2}=x \times \frac{5}{2}\) \(\Rightarrow 15=5 x\) \(\Rightarrow x=\frac{15}{5}=3\) Therefore, \(3\) bottles are required to fill the total oil in the container.

Q.4. A square garden has the area \(\frac{36}{25} \,\text {sq.ft}\). Find the side of the square garden. Ans: Given the area of the square garden is \(\frac{36}{25} \,\text {sq.ft}\). Let the length of the side of the square garden is \(a\) fts. We know that area of the square \( = {\rm{side}} \times {\rm{side}} = {a^2}\) Thus, \(a^{2}=\frac{36}{25}\) \(\Rightarrow a=\sqrt{\frac{36}{25}}=\frac{\sqrt{36}}{\sqrt{25}}=\frac{6}{5}\) feet. Hence, the length of the side of the square garden is \(\frac{6}{5}\) feet.

Q.5. At a party, total \(280\) ice-creams are prepared. Four-seventh of them is eaten by the children. Find the ice-creams eaten by the children. Ans: Total ice-creams prepared \(=280\) Number of ice-creams eaten by children \(=\frac{4}{7}\) of \(280=\frac{4}{7} \times 280=160\) Hence, children ate \(160\) ice-creams.

In mathematics, a fraction is used to represent a piece of something larger. It depicts the whole’s equal pieces. The numerator and denominator are the two elements of a fraction. The numerator is the number at the top, while the denominator is the number at the bottom. The numerator specifies the number of equal parts taken, whereas the denominator specifies the total number of equal parts in the total.

In this article, we have studied the definitions of fractions,  different types of fractions. We also studied the word problems on fractions and their operations. This article gives the word problems on fractions, addition and subtraction of fractions, multiplication of fractions, division of fractions, the simplest form of fractions, conversion of fractions to percentage, decimals etc., with the help of solved examples.

FAQs on Word Problems on Fractions

Here are some of most commonly asked questions on word problems on fractions.

Q.1: How do you solve word problems with fractions?

Ans: To solve word problems with fractions, first, read and write the given data. Write the mathematical form by given data and perform the operations on fractions according to the data.

Q.2: How do you write a fraction division in word problems? 

Ans: The fraction division can be written as keeping the first fraction as it is and multiplying it with the reciprocal of the second fraction.

Q.3: How do you know when to divide or multiply fractions in a word problem?

Ans: To find the product, we need to multiply and to find any one of the quantities, we need to divide.

Q.4: What is an example of a fraction word problem?

Ans: Keerthi ate 40% of the pizza. How much is part of the pizza eaten by Keerthi.

Q.5: What is a fraction?

Ans: A fraction is a number that is used to express a part per whole.

Learn About Conversion Of Fractions

We hope this detailed article on Word Problem on Fractions helps you in your preparation. If you get stuck do let us know in the comments section below and we will get back to you at the earliest.

Stay tuned to Embibe to learn more important concepts

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Fractions Questions

Fractions questions are given here will help the students to understand how to perform arithmetic operations on fractions. We know that fractions is one of the most important concepts of Class 7 Maths. In this article, you will get the questions on fractions, along with their solutions, based on the latest NCERT curriculum.

What are Fractions?

In maths, a fraction is defined as a part of the whole thing, and it can be written in the form a/b, where a and b are whole numbers, also, b ≠ 0. Based on the numerical values of numerator and denominator, we can define different types of fractions .

Proper fraction: A proper fraction is a number representing a part of a whole. This whole may be a single object or a group of objects.

Improper fraction: An improper fraction is a number in which the numerator is greater than the denominator.

Mixed fraction: A mixed fraction is a combination of a whole number and a proper fraction.

Learn more about fractions here.

Fractions Questions and Answers

1. How many 2/3 kg pieces can be cut from a cake of weight 4 kg?

Let p be the number 2/3 kg pieces that are cut from a 4 kg cake.

So, p × (2/3) = 4

p = 4 × (3/2)

Therefore, six 2/3 kg pieces can be cut from a cake of weight 4 kg.

2. What is the product of 5/129 and its reciprocal?

Given fraction: 5/129

Here, numerator = 5

Denominator = 129

Reciprocal of 5/129 = 129/5

The product of 5/129 and its reciprocal = (5/129) × (129/5) = 1.

3. Sunita and Rehana want to make dresses for their dolls. Sunita has 3/4 m of cloth, and she gave 1/3 of it to Rehana. How much did Rehana have?

Length of cloth Sunita has = 3/4 m

According to the given,

Sunita has 3/4 m of cloth, and she gave 1/3 of it to Rehana.

Therefore, the length of cloth Rehana has

= 1/3 of 3/4 m

= (1/3) x (3/4) m

4. Anuradha can do a piece of work in 6 hours. What part of the work can she do in 1 hour, in 5 hours, in 6 hours?

Let m be the whole work to be done.

The part of work done by Anuradha in 6 hours = m

Thus, the part of work done by her in 1 hour = m/6

The part of work done by her in 5 hours = (m/6) x 5 = 5m/6

The part of work done by her in 6 hours = (m/6) x 6 = m

Therefore, Anuradha can do 1/6 part of work in 1 hour, 5/6 part of work in 5 hours and the complete work in 6 hours.

5. Multiply the following fractions.

(i) (⅖) × 5 ¼

(ii) 2 ⅗ × 3

Here, 5 ¼ is a mixed fraction.

Let us convert this mixed fraction into an improper fraction.

5 ¼ = [(5 × 4) + 1]/4 = 21/4

Thus, (⅖) × 5 ¼ = (⅖) × (21/4) = 21/10

Here, 2 ⅗ is a mixed fraction.

2 ⅗ = [(2 × 5) + 3]/5 = 13/5

Therefore, 2 ⅗ × 3 = (13/5) × 3 = 39/5

6. Divide 3/10 by (1/4 of 3/5).

1/4 od 3/5 = (1/4) × (3/5) = 3/(4 × 5) = 3/20

3/10 ÷ (1/4 of 3/5)

= 3/10 ÷ 3/20

= (3/10) × (20/3)

\(\begin{array}{l}\text{7. Find the value of }\frac{1}{4\frac{2}{7}}+\frac{1}{3\frac{11}{13}}\frac{1}{\frac{5}{9}}.\end{array} \)

First, simplify the denominators.

= (7/30) + (13/50) + (9/5)

= (35 + 39 + 270)/150 {since the LCM of 30, 50 and 5 is 150}

8. Evaluate the following:

(i) 3 ½ ÷ 4

(ii) 4 ⅓ ÷ 3

Here, 3 ½ is a mixed fraction.

3 ½ = (3 × 2 + 1)/2 = 7/2

3 ½ ÷ 4 = 7/2 ÷ 4 = (7/2) × (¼) = 7/8

Here, 4 ⅓ is a mixed fraction.

4 ⅓ = (4 × 3 + 1)/3 = 13/3

4 ⅓ ÷ 3 = 13/3 ÷ 3 = (13/3) × (⅓) = 13/9

9. 1/8 of a number equals 2/5 ÷ 1/20. What is the number?

Let p be the number.

(1/8) × p = 2/5 ÷ 1/20

p/8 = (2/5) × (20/1)

p/8 = 2 × 4

Hence, 64 is the required number.

10. Raj travels 360 km on three-fifths of his petrol tank. How far would he travel at the same rate with a full tank of petrol?

Distance travelled by Raj with three-fifths (i.e. ⅗) of petrol tank = 360 km

Distance travelled by him with a full petrol tank = (360 ÷ 3/5) km

= (360 x 5)/3 km

= 120 x 5 km

Video Lesson on Fractions

Practice Questions on Fractions

1. The weight of an object on the moon is 1/6 its weight on the Earth. If an object weighs 5 3/5 kg on the Earth, how much would it weigh on the moon?

2. Lipika reads a book for 1 ¾ hour every day. She reads the entire book in 6 days. How many hours in all were required by her to read the book?

3. Multiply and reduce to the lowest form (if possible).

• 11/2 × 3/10

4.  Arrange the following in descending order:

• 2/9, 2/3, 8/21
• 1/5, 3/7, 7/10

5. Write five equivalent fractions of 8/11.

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Word Problems on Fraction with Solutions | Fraction Word Problems with Answers

Are you feeling difficulty in solving the word problems on fractions? Here you will get plenty of information on how to solve word problems and the method used to solve them. You can apply this related knowledge to the problems you encounter on fractions. By going through the article you can also check the solved examples for a better understanding of the concept.

• Simplification of Fractions
• Worksheet on Simplification of Fractions
• Types of Fractions

What are Fractions?

A fractional number is considered as the ratio between two numbers. Fractions are defined by \(\frac {a}{b} \) a is called the numerator which means the equal number of parts that are counted. b is called the denominator which means a number of parts in the whole.

Fraction Word Problems with Answers

Problem 1:  Mickey has read three-fifth of his 75 pages book. How many more pages he needs to read to complete his book? Solution: Let us write the given information, Mickey has read \(\frac {3}{5} \) of a 75 page book. Which can be written as \(\frac {3}{5} \) * 75 \(\frac {3}{5} \) * 75 = 45 So, Mickey has completed reading 45 pages from his book. Now to find the number of pages he needs to read to complete his book Total number of pages = 75 Number of pages Mickey has completed reading = 45 Number of pages he needs to read to complete his book = (75 – 45) = 30pages Number of pages mickey needs to read to complete his book = 30 pages.

Problem 2: Minnie has Rs. 675. She gave \(\frac {13}{15} \) of the amount to Daisy. Then Daisy spent \(\frac {9}{15} \) of the amount given to her. How much amount is Daisy left with? Solution: Amount Minnie gave to Daisy = \(\frac {13}{15} \) of 675 Which can be written as \(\frac {13}{15} \) * 675 \(\frac {13}{15} \) * 675 = Rs.585 Amount Daisy spent = \(\frac {9}{15} \) of 585 Which can be written as \(\frac {9}{15} \) * 585 \(\frac {9}{15} \) * 585 = 351 Amount Daisy is left with = Amount Minnie gave to Daisy – Amount Daisy spent Rs 585 – Rs 351 = Rs 234 Amount left with Daisy left = Rs 234

Problem 3: Tom bought \(\frac {1}{5} \)L milk on Monday and \(\frac {2}{5} \)L on Tuesday. How much milk did he buy in two days? Solution: Milk bought on Monday = \(\frac {1}{5} \)L Milk bought on Tuesday = \(\frac {2}{5} \)L Total milk he bought = \(\frac {1}{5} \)L + \(\frac {2}{5} \)L \(\frac {1}{5} \)L + \(\frac {2}{5} \)L = \(\frac {1 + 2}{5} \)L = \(\frac {3}{5} \)L Milk bought by Tom in two days = \(\frac {3}{5} \)L

Problem 4:  Jerry bought \(\frac {5}{7} \)Kg of cheese and used \(\frac {1}{7} \)Kg.  How much cheese is left? Solution: Cheese bought = \(\frac {5}{7} \)Kg Cheese used = \(\frac {1}{7} \)Kg Cheese left = Cheese bought  – Cheese used \(\frac {5}{7} \)Kg – \(\frac {1}{7} \)Kg = \(\frac {5 – 1}{7} \)Kg \(\frac {4}{7} \)Kg Cheese left with Jerry = \(\frac {4}{7} \)Kg

Problem 5: Jaggu bought \(\frac {4}{7} \)Kg banana on Monday and \(\frac {2}{7} \)Kg of apple on Tuesday. What is the total quantity of fruits Jaggu bought? Solution: Quantity of bananas bought by Jaggu on Monday = \(\frac {4}{7} \)Kg Quantity of apples bought by Jaggu on Tuesday = \(\frac {2}{7} \)Kg The total quantity of fruits Jaggu bought = Quantity of bananas + Quantity of apples \(\frac {4}{7} \)Kg + \(\frac {2}{7} \)Kg = \(\frac {4 + 2}{7} \)Kg \(\frac {6}{7} \)Kg The total quantity of fruits Jaggu bought = \(\frac {6}{7} \)Kg

Problem 6: Ben bought \(\frac {4}{7} \)m cloth at the rate of Rs 140 per meter. How much amount did he pay? Solution: Cost per meter = Rs 140 Length of cloth ben bought =\(\frac {4}{7} \)m Amount Ben paid = Length of cloth ben bought * Cost per meter \(\frac {4}{7} \)m * Rs 140 = \(\frac {4 * 140}{7} \) \(\frac {4 * 140}{7} \) = \(\frac {560}{7} \) = Rs 80 Amount paid by Ben = Rs 80

Problem 7: What is the difference between \(\frac {3}{5} \) of 5000 and \(\frac {5}{8} \) of 4000 Solution: First, we need to find what is \(\frac {3}{5} \) of 5000 and \(\frac {5}{8} \) of 4000 \(\frac {3}{5} \) of 5000 = \(\frac {3}{5} \) * 5000 = 3000 \(\frac {5}{8} \) of 4000 = \(\frac {5}{8} \) * 4000 = 2500 Now, difference between \(\frac {3}{5} \) of 5000 and \(\frac {5}{8} \) of 4000 = (3000 – 2500) = 500 The difference between \(\frac {3}{5} \) of 5000 and \(\frac {5}{8} \) of 4000 = 500

Problem 8: Jane spent \(\frac {1}{5} \) of her pockey money on food and \(\frac {3}{4} \) on books, how much did she spend alltogether? Solution: Amount spent on food = \(\frac {1}{5} \) Amount spent on books = \(\frac {3}{4} \) Total amount spent = Amount spent on food + Amount spent on books \(\frac {1}{5} \) + \(\frac {3}{4} \) = ( \(\frac {1}{5} \) * \(\frac {4}{4} \) ) + ( \(\frac {3}{4} \) + \(\frac {5}{5} \) ) = \(\frac {4}{20} \) + \(\frac {15}{20} \) = \(\frac {19}{20} \) Amount spent by Jane = \(\frac {19}{20} \)

Problem 9: In a high school contest, Ross jumped 3\(\frac {8}{9} \)m and Joye jumped 4\(\frac {1}{3} \)m. Who jumped more height and by how much more? Solution: Height Ross jumped = 3\(\frac {8}{9} \)m Height Joey jumped = 4\(\frac {1}{3} \)m The given numbers are mixed fractional numbers let’s convert them to improper fractional numbers So, 3\(\frac {8}{9} \)m = \(\frac {35}{9} \)m 4\(\frac {1}{3} \)m = \(\frac {13}{3} \)m This means, Ross jumed \(\frac {35}{9} \)m and Joey jumped \(\frac {13}{3} \)m Now to know who jumped more height we need to compare these numbers by cross multiplication \(\frac {35}{9} \) * \(\frac {13}{3} \) = \(\frac {35 * 3}{9 * 13} \) = \(\frac {105}{117} \) We know 117 > 105 so, \(\frac {13}{3} \) > \(\frac {35}{9} \) This means Joey jumped more height To know by how more Joey jumped than Ross we need to subtract \(\frac {13}{3} \) from \(\frac {35}{9} \) LCM is 9 So,( \(\frac {13}{3} \) * \(\frac {3}{3} \) ) – \(\frac {35}{9} \) = \(\frac {39}{9} \) – \(\frac {35}{9} \) = \(\frac {39 – 35}{9} \) = \(\frac {4}{9} \) Joey jumed \(\frac {4}{9} \) more than Ross.

Problem 10: Bunny bought 2\(\frac {2}{5} \)kg of strawberry, 2kg of blackberry and 1\(\frac {2}{5} \)kg of blueberry. What is the total weight of berries Bunny bought? Solution: Weight of strawberry = 2\(\frac {2}{5} \)kg Weight of blackberry = 2kg Weight of blueberry = 1\(\frac {2}{5} \)kg We can see that weights of berries are in mixed fractional form and whole number form Now, let’s convert them to fractional numbers so that we can add them and find the weight of the berries 2\(\frac {2}{5} \)kg =\(\frac {12}{5} \)kg 2kg = \(\frac {2}{1} \)kg 1\(\frac {2}{5} \)kg = \(\frac {7}{5} \)kg Total weight of berries = Sum of (strawberry + blackberry + blueberry) = \(\frac {12}{5} \) + \(\frac {2}{1} \) + \(\frac {7}{5} \) LCM is 5 = \(\frac {12}{5} \) + (\(\frac {2}{1} \) + \(\frac {5}{5} \)) + \(\frac {7}{5} \) = \(\frac {12}{5} \) + \(\frac {10}{5} \) + \(\frac {7}{5} \) = \(\frac {12 + 10 + 7}{5} \) = \(\frac {29}{5} \) \(\frac {12}{5} \) is a improper fractional number so let us convert it in to mixed fractional number \(\frac {29}{5} \)  = 5\(\frac {4}{5} \) The total weight of berries = 5\(\frac {4}{5} \)kg

Problem 11: Mickey bought \(\frac {7}{8} \)kg of noddels and Minnie bought \(\frac {6}{8} \)kg of noddels. What is the total quantity of noddels they have? Solution: Weight of noddles Mickey bought = \(\frac {7}{8} \)kg Weight of noddels Minnie bought = \(\frac {6}{8} \)kg Total weight of noddels = Weight of noddles Mickey bought +Weight of noddels Minnie bought = \(\frac {7}{8} \)kg + \(\frac {6}{8} \)kg = \(\frac {7 +6}{8} \)kg = \(\frac {13}{8} \)kg This is an improper fractional number so it can be converted to a mixed fractional number \(\frac {13}{8} \)kg = 1\(\frac {5}{8} \)kg The total quantity of noddles Mickey and Minnie have = 1\(\frac {5}{8} \)kg

Problem 12: Kitty’s mother bought 1\(\frac {3}{4} \)kg of cookies and her father bought 1\(\frac {1}{2} \)kg of cookies. What is the total weight of cookies that Kitty has? Solution: Weight of cookies bought by Kitty’s mother = 1\(\frac {3}{4} \)kg Weight of cookies bought by Kitty’s father = 1\(\frac {1}{2} \)kg To know the total weight of cookies we have to add them We can’t add mixed fractional numbers so let us convert them into improper fractional numbers 1\(\frac {3}{4} \)kg = \(\frac {7}{4} \)kg 1\(\frac {1}{2} \)kg = \(\frac {3}{2} \)kg Now we can add these two fractional numbers \(\frac {7}{4} \)kg + \(\frac {3}{2} \)kg LCM= 4 = \(\frac {1*7 + 2*3}{4} \) = \(\frac {7 + 6}{4} \) = \(\frac {13}{4} \) \(\frac {13}{4} \)  is an improper fractional number So we have to convert it into a mixed fractional number \(\frac {13}{4} \) = 3\(\frac {1}{4} \) The total quantity of cookies Kitty have = 3\(\frac {1}{4} \)kg

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Fraction Word Problems (Difficult)

Here are some examples of more difficult fraction word problems. We will illustrate how block models (tape diagrams) can be used to help you to visualize the fraction word problems in terms of the information given and the data that needs to be found.

Related Pages Fraction Word Problems Singapore Math Lessons Fraction Problems Using Algebra Algebra Word Problems

Block modeling (also known as tape diagrams or bar models) are widely used in Singapore Math and the Common Core to help students visualize and understand math word problems.

Example: 2/9 of the people on a restaurant are adults. If there are 95 more children than adults, how many children are there in the restaurant?

Solution: Draw a diagram with 9 equal parts: 2 parts to represent the adults and 7 parts to represent the children.

5 units = 95 1 unit = 95 ÷ 5 = 19 7 units = 7 × 19 = 133

Answer: There are 133 children in the restaurant.

Example: Gary and Henry brought an equal amount of money for shopping. Gary spent $95 and Henry spent $350. After that Henry had 4/7 of what Gary had left. How much money did Gary have left after shopping?

350 – 95 = 255 3 units = 255 1 unit = 255 ÷ 3 = 85 7 units = 85 × 7 = 595

Answer: Gary has $595 after shopping.

Example: 1/9 of the shirts sold at Peter’s shop are striped. 5/8 of the remainder are printed. The rest of the shirts are plain colored shirts. If Peter’s shop has 81 plain colored shirts, how many more printed shirts than plain colored shirts does the shop have?

Solution: Draw a diagram with 9 parts. One part represents striped shirts. Out of the remaining 8 parts: 5 parts represent the printed shirts and 3 parts represent plain colored shirts.

3 units = 81 1 unit = 81 ÷ 3 = 27 Printed shirts have 2 parts more than plain shirts. 2 units = 27 × 2 = 54

Answer: Peter’s shop has 54 more printed colored shirts than plain shirts.

Solve a problem involving fractions of fractions and fractions of remaining parts

Example: 1/4 of my trail mix recipe is raisins and the rest is nuts. 3/5 of the nuts are peanuts and the rest are almonds. What fraction of my trail mix is almonds?

How to solve fraction word problem that involves addition, subtraction and multiplication using a tape diagram or block model

Example: Jenny’s mom says she has an hour before it’s bedtime. Jenny spends 3/5 of the hour texting a friend and 3/8 of the remaining time brushing her teeth and putting on her pajamas. She spends the rest of the time reading her book. How long did Jenny read?

How to solve a four step fraction word problem using tape diagrams?

Example: In an auditorium, 1/6 of the students are fifth graders, 1/3 are fourth graders, and 1/4 of the remaining students are second graders. If there are 96 students in the auditorium, how many second graders are there?

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Free Mathematics Tutorials

Fractions and mixed numbers- grade 7 math questions and problems with answers.

Grade 7 maths multiple choice questions on fractions and mixed numbers with answers are presented. The questions tests both the skills and concepts related to fractions and mixed numbers with some challenging questions. Solutions and explanations are included.

• F1 = 1/6 , F2 = 1/6
• F1 = 6/6 , F2 = 2/6
• F1 = 5/6 , F2 = 5/6
• F1 = 5/6 , F2 = 1/6
• 3 1/2 , 3 11/20 , 3 4/7 , 3 3/5
• 3 1/2 , 3 3/5 , 3 11/20 , 3 4/7
• 3 1/2 , 3 3/5 , 3 4/7 , 3 11/20
• 3 3/5 , 3 1/2 , 3 11/20 , 3 4/7
• 2.66 , 2 7/8 , 25/8 , 262%
• 25/8 , 2 7/8 , 2.66 , 262%
• 25/8 , 2.66 , 2 7/8 , 262%
• 262% , 2.66 , 2 7/8 , 25/8

Answers to the Above Questions

Links and references, popular pages.

• Grade 7 Math word Problems With Answers
• Middle School Math (Grades 6, 7, 8, 9) - Free Questions and Problems With Answers
• Interactive Tutorial on Fractions
• Free Algebra Questions and Problems with Answers
• Computation and Properties of the Derivative in Calculus

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