problem solving with adding fractions

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Fraction Addition Word Problems Worksheets

Let children work on our printable adding fractions word problems worksheets hammer and tongs! Whether it's sharing a meal with your friends or measuring the ingredients for a recipe, adding fractions is at the heart of it all, hence our worksheets. A wealth of real-life scenarios that involve addition of fractions with whole numbers and addition of two like fractions, two unlike fractions, and two mixed numbers, our pdf worksheets are indispensable for grade 3, grade 4, grade 5, and grade 6 students. The free fraction addition word problems worksheet is worth a try!

Adding Fractions with Whole Numbers

Dazzle 3rd grade kids with a gift of lifelike story problems! If you're a novice up against fraction addition, don't miss our pdf adding fractions word problems worksheets using whole numbers and fractions!

• Download the set

Adding Like Fractions Word Problems

Gerald ate 5/9 of an apple, and Garry ate 4/9 of it. How many apples did they eat in all? Good going! They both ate one whole apple. Simply combine the numerators and solve the like fraction word problems here!

Adding Unlike Fractions

A potpourri of word problems that involve adding unlike fractions, these pdfs mean that 4th grade and 5th grade students will breeze through addition of fractions with different denominators in their day-to-day lives.

Adding Mixed Numbers | Same Denominators

See in your mind's eye adding mixed numbers with same denominators riding on the several real-life scenarios in our printable worksheets! Convert the mixed numbers to fractions, and add them as usual.

Adding Mixed Numbers | Different Denominators

Steal a march on your 5th grade and 6th grade peers by getting your act together to power through the real-world situations featured in this set of printable adding mixed numbers word problems worksheets.

Related Worksheets

» Adding Like Fractions

» Adding Unlike Fractions

» Adding Mixed Numbers

» Adding Fractions with Whole Numbers

» Fraction Word Problems

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Fraction word prob.

Fraction word problems

Here you will learn about fraction word problems, including solving math word problems within a real-world context involving adding fractions, subtracting fractions, multiplying fractions, and dividing fractions.

Students will first learn about fraction word problems as part of number and operations—fractions in 4 th grade.

What are fraction word problems?

Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation.

To solve a fraction word problem, you must understand the context of the word problem, what the unknown information is, and what operation is needed to solve it. Fraction word problems may require addition, subtraction, multiplication, or division of fractions.

After determining what operation is needed to solve the problem, you can apply the rules of adding, subtracting, multiplying, or dividing fractions to find the solution.

For example,

Natalie is baking 2 different batches of cookies. One batch needs \cfrac{3}{4} cup of sugar and the other batch needs \cfrac{2}{4} cup of sugar. How much sugar is needed to bake both batches of cookies?

You can follow these steps to solve the problem:

Step-by-step guide: Adding and subtracting fractions

Step-by-step guide: Adding fractions

Step-by-step guide: Subtracting fractions

Step-by-step guide: Multiplying and dividing fractions

Step-by-step guide: Multiplying fractions

Step-by-step guide: Dividing fractions

Common Core State Standards

How does this relate to 4 th grade math to 6 th grade math?

• Grade 4: Number and Operations—Fractions (4.NF.B.3d) Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
• Grade 4: Number and Operations—Fractions (4.NF.B.4c) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat \cfrac{3}{8} of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
• Grade 5: Number and Operations—Fractions (5.NF.A.2) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result \cfrac{2}{5}+\cfrac{1}{2}=\cfrac{3}{7} by observing that \cfrac{3}{7}<\cfrac{1}{2} .
• Grade 5: Number and Operations—Fractions (5.NF.B.6) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
• Grade 5: Number and Operations—Fractions (5.NF.B.7c) Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{1}{3} cup servings are in 2 cups of raisins?
• Grade 6: The Number System (6.NS.A.1) Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for \cfrac{2}{3} \div \cfrac{4}{5} and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that \cfrac{2}{3} \div \cfrac{4}{5}=\cfrac{8}{9} because \cfrac{3}{4} of \cfrac{8}{9} is \cfrac{2}{3}. (In general, \cfrac{a}{b} \div \cfrac{c}{d}=\cfrac{a d}{b c} \, ) How much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{3}{4} cup servings are in \cfrac{2}{3} of a cup of yogurt? How wide is a rectangular strip of land with length \cfrac{3}{4} \: m and area \cfrac{1}{2} \: m^2?

[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!

How to solve fraction word problems

In order to solve fraction word problems:

Determine what operation is needed to solve.

Write an equation.

Solve the equation.

State your answer in a sentence.

Fraction word problem examples

Example 1: adding fractions (like denominators).

Julia ate \cfrac{3}{8} of a pizza and her brother ate \cfrac{2}{8} of the same pizza. How much of the pizza did they eat altogether?

The problem states how much pizza Julia ate and how much her brother ate. You need to find how much pizza Julia and her brother ate altogether , which means you need to add.

2 Write an equation.

3 Solve the equation.

To add fractions with like denominators, add the numerators and keep the denominators the same.

4 State your answer in a sentence.

The last step is to go back to the word problem and write a sentence to clearly say what the solution represents in the context of the problem.

Julia and her brother ate \cfrac{5}{8} of the pizza altogether.

Example 2: adding fractions (unlike denominators)

Tim ran \cfrac{5}{6} of a mile in the morning and \cfrac{1}{3} of a mile in the afternoon. How far did Tim run in total?

The problem states how far Tim ran in the morning and how far he ran in the afternoon. You need to find how far Tim ran in total , which means you need to add.

To add fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before adding.

\cfrac{5}{6}+\cfrac{1}{3}= \, ?

The least common multiple of 6 and 3 is 6, so 6 can be the common denominator.

That means \cfrac{1}{3} will need to be changed so that its denominator is 6. To do this, multiply the numerator and the denominator by 2.

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

Now you can add the fractions and simplify the answer.

\cfrac{5}{6}+\cfrac{2}{6}=\cfrac{7}{6}=1 \cfrac{1}{6}

Tim ran a total of 1 \cfrac{1}{6} miles.

Example 3: subtracting fractions (like denominators)

Pia walked \cfrac{4}{7} of a mile to the park and \cfrac{3}{7} of a mile back home. How much farther did she walk to the park than back home?

The problem states how far Pia walked to the park and how far she walked home. Since you need to find the difference ( how much farther ) between the two distances, you need to subtract.

To subtract fractions with like denominators, subtract the numerators and keep the denominators the same.

\cfrac{4}{7}-\cfrac{3}{7}=\cfrac{1}{7}

Pia walked \cfrac{1}{7} of a mile farther to the park than back home.

Example 4: subtracting fractions (unlike denominators)

Henry bought \cfrac{7}{8} pound of beef from the grocery store. He used \cfrac{1}{3} of a pound of beef to make a hamburger. How much of the beef does he have left?

The problem states how much beef Henry started with and how much he used. Since you need to find how much he has left , you need to subtract.

To subtract fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before subtracting.

\cfrac{7}{8}-\cfrac{1}{3}= \, ?

The least common multiple of 8 and 3 is 24, so 24 can be the common denominator.

That means both fractions will need to be changed so that their denominator is 24.

To do this, multiply the numerator and the denominator of each fraction by the same number so that it results in a denominator of 24. This will give you an equivalent fraction for each fraction in the problem.

\begin{aligned}&\cfrac{7 \times 3}{8 \times 3}=\cfrac{21}{24} \\\\ &\cfrac{1 \times 8}{3 \times 8}=\cfrac{8}{24} \end{aligned}

Now you can subtract the fractions.

\cfrac{21}{24}-\cfrac{8}{24}=\cfrac{13}{24}

Henry has \cfrac{13}{24} of a pound of beef left.

Example 5: multiplying fractions

Andre has \cfrac{3}{4} of a candy bar left. He gives \cfrac{1}{2} of the remaining bit of the candy bar to his sister. What fraction of the whole candy bar does Andre have left now?

It could be challenging to determine the operation needed for this problem; many students may automatically assume it is subtraction since you need to find how much of the candy bar is left.

However, since you know Andre started with a fraction of the candy bar and you need to find a fraction OF a fraction, you need to multiply.

The difference here is that Andre did NOT give his sister \cfrac{1}{2} of the candy bar, but he gave her \cfrac{1}{2} of \cfrac{3}{4} of a candy bar.

To solve the word problem, you can ask, “What is \cfrac{1}{2} of \cfrac{3}{4}? ” and set up the equation accordingly. Think of the multiplication sign as meaning “of.”

\cfrac{1}{2} \times \cfrac{3}{4}= \, ?

To multiply fractions, multiply the numerators and multiply the denominators.

\cfrac{1}{2} \times \cfrac{3}{4}=\cfrac{3}{8}

Andre gave \cfrac{1}{2} of \cfrac{3}{4} of a candy bar to his sister, which means he has \cfrac{1}{2} of \cfrac{3}{4} left. Therefore, Andre has \cfrac{3}{8} of the whole candy bar left.

Example 6: dividing fractions

Nia has \cfrac{7}{8} cup of trail mix. How many \cfrac{1}{4} cup servings can she make?

The problem states the total amount of trail mix Nia has and asks how many servings can be made from it.

To solve, you need to divide the total amount of trail mix (which is \cfrac{7}{8} cup) by the amount in each serving ( \cfrac{1}{4} cup) to find out how many servings she can make.

To divide fractions, multiply the dividend by the reciprocal of the divisor.

\begin{aligned}& \cfrac{7}{8} \div \cfrac{1}{4}= \, ? \\\\ & \downarrow \downarrow \downarrow \\\\ &\cfrac{7}{8} \times \cfrac{4}{1}=\cfrac{28}{8} \end{aligned}

You can simplify \cfrac{28}{8} to \cfrac{7}{2} and then 3 \cfrac{1}{2}.

Nia can make 3 \cfrac{1}{2} cup servings.

Teaching tips for fraction word problems

• Encourage students to look for key words to help determine the operation needed to solve the problem. For example, subtracting fractions word problems might ask students to find “how much is left” or “how much more” one fraction is than another.
• Provide students with an answer key to word problem worksheets to allow them to obtain immediate feedback on their solutions. Encourage students to attempt the problems independently first, then check their answers against the key to identify any mistakes and learn from them. This helps reinforce problem-solving skills and confidence.
• Be sure to incorporate real-world situations into your math lessons. Doing so allows students to better understand the relevance of fractions in everyday life.
• As students progress and build a strong foundational understanding of one-step fraction word problems, provide them with multi-step word problems that involve more than one operation to solve.
• Take note that students will not divide a fraction by a fraction as shown above until 6 th grade (middle school), but they will divide a unit fraction by a whole number and a whole number by a fraction in 5 th grade (elementary school), where the same mathematical rules apply to solving.
• There are many alternatives you can use in place of printable math worksheets to make practicing fraction word problems more engaging. Some examples are online math games and digital workbooks.

Easy mistakes to make

• Misinterpreting the problem Misreading or misunderstanding the word problem can lead to solving for the wrong quantity or using the wrong operation.
• Not finding common denominators When adding or subtracting fractions with unlike denominators, students may forget to find a common denominator, leading to an incorrect answer.
• Forgetting to simplify Unless a problem specifically says not to simplify, fractional answers should always be written in simplest form.

Related fractions operations lessons

• Fractions operations
• Multiplicative inverse
• Reciprocal math
• Fractions as divisions

Practice fraction word problem questions

1. Malia spent \cfrac{5}{6} of an hour studying for a math test. Then she spent \cfrac{1}{3} of an hour reading. How much longer did she spend studying for her math test than reading?

Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.

Malia spent \cfrac{5}{18} of an hour longer studying for her math test than reading.

Malia spent \cfrac{1}{2} of an hour longer reading than studying for her math test.

Malia spent 1 \cfrac{1}{6} of an hour longer studying for her math test than reading.

To find the difference between the amount of time Malia spent studying for her math test than reading, you need to subtract. Since the fractions have unlike denominators, you need to find a common denominator first.

You can use 6 as the common denominator, so \cfrac{1}{3} becomes \cfrac{3}{6}. Then you can subtract.

\cfrac{3}{6} can then be simplified to \cfrac{1}{2}.

Finally, you need to choose the answer that correctly answers the question within the context of the situation. Therefore, the correct answer is “Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.”

2. A square garden is \cfrac{3}{4} of a meter wide and \cfrac{8}{9} of a meter long. What is its area?

The area of the garden is 1\cfrac{23}{36} square meters.

The area of the garden is \cfrac{27}{32} square meters.

The area of the garden is \cfrac{2}{3} square meters.

The perimeter of the garden is \cfrac{2}{3} meters.

To find the area of a square, you multiply the length and width. So to solve, you multiply the fractional lengths by mulitplying the numerators and multiplying the denominators.

\cfrac{24}{36} can be simplified to \cfrac{2}{3}. 

Therefore, the correct answer is “The area of the garden is \cfrac{2}{3} square meters.”

3. Zoe ate \cfrac{3}{8} of a small cake. Liam ate \cfrac{1}{8} of the same cake. How much more of the cake did Zoe eat than Liam?

Zoe ate \cfrac{3}{64} more of the cake than Liam.

Zoe ate \cfrac{1}{4} more of the cake than Liam.

Zoe ate \cfrac{1}{8} more of the cake than Liam.

Liam ate \cfrac{1}{4} more of the cake than Zoe.

To find how much more cake Zoe ate than Liam, you subtract. Since the fractions have the same denominator, you subtract the numerators and keep the denominator the same.

\cfrac{2}{8} can be simplified to \cfrac{1}{4}. 

Therefore, the correct answer is “Zoe ate \cfrac{1}{4} more of the cake than Liam.”

4. Lila poured \cfrac{11}{12} cup of pineapple and \cfrac{2}{3} cup of mango juice in a bottle. How many cups of juice did she pour into the bottle altogether?

Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.

Lila poured \cfrac{1}{4} cups of juice in the bottle altogether.

Lila poured \cfrac{11}{18} cups of juice in the bottle altogether.

Lila poured 1 \cfrac{3}{8} cups of juice in the bottle altogether.

To find the total amount of juice that Lila poured into the bottle, you need to add. Since the fractions have unlike denominators, you need to find a common denominator first.

You can use 12 as the common denominator, so \cfrac{2}{3} becomes \cfrac{8}{12}.  Then you can add.

\cfrac{19}{12} can be simplified to 1 \cfrac{7}{12}. 

Therefore, the correct answer is “Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.”

5. Killian used \cfrac{9}{10} of a gallon of paint to paint his living room and \cfrac{7}{10} of a gallon to paint his bedroom. How much paint did Killian use in all?

Killian used \cfrac{2}{10} gallons of paint in all.

Killian used \cfrac{1}{5} gallons of paint in all.

Killian used \cfrac{63}{100} gallons of paint in all.

Killian used 1 \cfrac{3}{5} gallons of paint in all.

To find the total amount of paint Killian used, you add the amount he used for the living room and the amount he used for the kitchen. Since the fractions have the same denominator, you add the numerators and keep the denominators the same.

\cfrac{16}{10} can be simplified to 1 \cfrac{6}{10} and then further simplified to 1 \cfrac{3}{5}.

Therefore, the correct answer is “Killian used 1 \cfrac{3}{5} gallons of paint in all.”

6. Evan pours \cfrac{4}{5} of a liter of orange juice evenly among some cups.

He put \cfrac{1}{10} of a liter into each cup. How many cups did Evan fill?

Evan filled \cfrac{2}{25} cups.

Evan filled 8 cups.

Evan filled \cfrac{9}{10} cups.

Evan filled 7 cups.

To find the number of cups Evan filled, you need to divide the total amount of orange juice by the amount being poured into each cup. To divide fractions, you mulitply the first fraction (the dividend) by the reciprocal of the second fraction (the divisor).

\cfrac{40}{5} can be simplifed to 8.

Therefore, the correct answer is “Evan filled 8 cups.”

Fraction word problems FAQs

Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation. Fraction word problems may involve addition, subtraction, multiplication, or division of fractions.

To solve fraction word problems, first you need to determine the operation. Then you can write an equation and solve the equation based on the arithmetic rules for that operation.

Fraction word problems and decimal word problems are similar because they both involve solving math problems within real-world contexts. Both types of problems require understanding the problem, determining the operation needed to solve it (addition, subtraction, multiplication, division), and solving it based on the arithmetic rules for that operation.

The next lessons are

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Solving Word Problems by Adding and Subtracting Fractions and Mixed Numbers

Learn how to solve fraction word problems with examples and interactive exercises.

Example 1: Rachel rode her bike for one-fifth of a mile on Monday and two-fifths of a mile on Tuesday. How many miles did she ride altogether?

Analysis: To solve this problem, we will add two fractions with like denominators.

Solution: 

Answer: Rachel rode her bike for three-fifths of a mile altogether.

Analysis: To solve this problem, we will subtract two fractions with unlike denominators.

Answer: Stefanie swam one-third of a lap farther in the morning.

Analysis: To solve this problem, we will add three fractions with unlike denominators. Note that the first is an improper fraction.

Answer: It took Nick three and one-fourth hours to complete his homework altogether.

Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having like denominators.

Answer: Diego and his friends ate six pizzas in all.

Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having like denominators.

Answer: The Cocozzelli family took one-half more days to drive home.

Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having unlike denominators.

Answer: The warehouse has 21 and one-half meters of tape in all.

Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having unlike denominators.

Answer: The electrician needs to cut 13 sixteenths cm of wire.

Analysis: To solve this problem, we will subtract a mixed number from a whole number.

Answer: The carpenter needs to cut four and seven-twelfths feet of wood.

Summary: In this lesson we learned how to solve word problems involving addition and subtraction of fractions and mixed numbers. We used the following skills to solve these problems: 

• Add fractions with like denominators.
• Subtract fractions with like denominators.
• Find the LCD.
• Add fractions with unlike denominators.
• Subtract fractions with unlike denominators.
• Add mixed numbers with like denominators.
• Subtract mixed numbers with like denominators.
• Add mixed numbers with unlike denominators.
• Subtract mixed numbers with unlike denominators.

Directions: Subtract the mixed numbers in each exercise below.  Be sure to simplify your result, if necessary.  Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

Note: To write the fraction three-fourths, enter 3/4 into the form. To write the mixed number four and two-thirds, enter 4, a space, and then 2/3 into the form.

Adding Fractions

A fraction like 3 4 says we have 3 out of the 4 parts the whole is divided into.

To add fractions there are Three Simple Steps:

• Step 1: Make sure the bottom numbers (the denominators ) are the same
• Step 2: Add the top numbers (the numerators ), put that answer over the denominator
• Step 3: Simplify the fraction (if possible)

Step 1 . The bottom numbers (the denominators) are already the same. Go straight to step 2.

Step 2 . Add the top numbers and put the answer over the same denominator:

1 4 + 1 4 = 1 + 1 4 = 2 4

Step 3 . Simplify the fraction:

In picture form it looks like this:

... and do you see how 2 4 is simpler as 1 2 ? (see Equivalent Fractions .)

Step 1 : The bottom numbers are different. See how the slices are different sizes?

We need to make them the same before we can continue, because we can't add them like that.

The number "6" is twice as big as "3", so to make the bottom numbers the same we can multiply the top and bottom of the first fraction by 2 , like this:

Important: you multiply both top and bottom by the same amount, to keep the value of the fraction the same

Now the fractions have the same bottom number ("6"), and our question looks like this:

The bottom numbers are now the same, so we can go to step 2.

Step 2 : Add the top numbers and put them over the same denominator:

2 6 + 1 6 = 2 + 1 6 = 3 6

Step 3 : Simplify the fraction:

In picture form the whole answer looks like this:

With Pen and Paper

And here is how to do it with a pen and paper (press the play button):

A Rhyme To Help You Remember

♫ "If adding or subtracting is your aim, The bottom numbers must be the same! ♫ "Change the bottom using multiply or divide, But the same to the top must be applied, ♫ "And don't forget to simplify, Before its time to say good bye"

Again, the bottom numbers are different (the slices are different sizes)!

But let us try dividing them into smaller sizes that will each be the same :

The first fraction: by multiplying the top and bottom by 5 we ended up with 5 15 :

The second fraction: by multiplying the top and bottom by 3 we ended up with 3 15 :

The bottom numbers are now the same, so we can go ahead and add the top numbers:

The result is already as simple as it can be, so that is the answer: 

1 3 + 1 5 = 8 15

Making the Denominators the Same

In the previous example how did we know to cut them into 1 / 15 ths to make the denominators the same? We simply multiplied the two denominators together (3 × 5 = 15).

Read about the two main ways to make the denominators the same here:

• Common Denominator Method , or the
• Least Common Denominator Method

They both work, use which one you prefer!

Example: Cupcakes

You want to make and sell cupcakes:

• A friend can supply the ingredients, if you give them 1 / 3 of sales
• And a market stall costs 1 / 4 of sales

How much is that altogether?

We need to add 1 / 3 and 1 / 4

First make the bottom numbers (the denominators) the same.

Multiply top and bottom of 1 / 3 by 4 :

And multiply top and bottom of 1 / 4 by 3 :

Now do the calculations:

Answer: 7 12 of sales go in ingredients and market costs.

Adding Mixed Fractions

We have a special (more advanced) page on Adding Mixed Fractions .

Adding Fractions

Learn about adding fractions., adding fractions lesson, how to add fractions.

To add fractions, we follow three simple steps. They are as follows:

• Make the denominators the same if they aren't already.
• Add the numerators, keeping the denominator the same.
• Simplify the resulting fraction.

The same three steps apply for adding mixed fractions (such as 4 1 / 2 + 1 2 / 3 ) except that we will simply add the whole number and fraction components separately.

In this lesson we will go through how to add fractions and show examples of adding fractions with like and unlike denominators.

Adding Fractions with Like Denominators

Let's go through how to add fractions with like denominators first, since it is most simple type of fraction addition. Here's an example of adding fractions with like denominators, using the three steps from earlier.

Find the sum of 3 / 5 + 1 / 5 .

• The denominators are already the same, so we can skip step 1.
• Let's add the numerators. 3 + 1 = 4, so the sum of our numerators is 4. The denominator is still 5, so our result is 4 / 5 .
• 4 / 5 is already in its simplest form, so there is no simplifying needed here.

The solution is 3 / 5 + 1 / 5 = 4 / 5 .

Adding Fractions with Unlike Denominators

Now let's go through another example but this time with unlike denominators. We will use the same exact three steps.

Find the sum of 1 / 4 + 2 / 3 .

• Let's find the lowest common denominator and convert these fractions to like denominators to make them addable. Multiplying the top and bottom of each fraction by the other fraction's denominator gives us 1 / 4  ·  3 / 3 = 3 / 12 and 2 / 3  ·  4 / 4 = 8 / 12 .
• Now let's add the numerators. 3 + 8 = 11, so the sum of our numerators is 11. The denominator is still 12, so our result is 11 / 12 .
• 11 / 12 is already in its simplest form, so there is no simplifying needed here.

The solution is 1 / 4 + 2 / 3 = 11 / 12 .

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Fraction Addition Word Problems Worksheets

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Look to your laurels by answering our pdf fraction addition word problems worksheets, a collage of well-researched real-world word problems. Adding fractions or mixed numbers is not an alien concept. Whether it's cooking recipes; measuring lengths, weights, etc.; or sharing something among many, fraction addition and mixed-number addition are never too far away. Witness adding fractions and mixed numbers with like and unlike denominators leap into life as you solve this collection of word problems! Begin your learning journey with some of our free worksheets!

Adding Like Fractions

Pump up your practice with a pleasant potpourri of everyday situations in these adding fractions word problems worksheets for 3rd grade, 4th grade, and 5th grade. Keep at it, and summing up two like fractions will soon be a cakewalk!

Adding Unlike Fractions

An eclectic collection of word problems centering around fractions with unlike denominators, this pdf resource proves an imperative addition to your repertoire! Find equivalent like fractions and whizz through the problems!

Adding Fractions with Whole Numbers

Are you a novice wondering how to add fractions to whole numbers? Take a look at the real-life scenarios in these pdf worksheets and say goodbye to all your doubts! Put the numbers together as mixed numbers, and that's your sum.

Adding Mixed Numbers | Same Denominators

Natasha brewed a 1 1/2-ounce shot of espresso for latte and another 1 1/2-ounce shot for Americano. How much coffee did Natasha make in all? 3 shots! Keen to be explored in our printable set are a wealth of such situations!

Adding Mixed Numbers | Different Denominators

Evaluate 5th grade and 6th grade students' skills in adding mixed numbers with different denominators in this part of the fraction addition word problems worksheets. Convert to mixed numbers with the same denominators, and press on!

Related Printable Worksheets

▶ Adding Like Fractions

▶ Adding Unlike Fractions

▶ Fraction Word Problems

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• Math Article

Addition of Fractions

The addition of fractions teaches us to add two or more fractions with the same or different denominators. The addition  of fraction depends  on two major conditions: 

• Same denominators
• Different denominators

While adding fractions, if denominators are the same (such fractions are said to be like fractions), then they can be added directly. But if the denominators are different, (such fractions are called unlike fractions) then we need to make the denominators same and then add the fractions. Learn  like or unlike fractions , here.

Addition of Fractions with Same Denominators

If denominators of two or more fractions are same, then we can directly add the numerators, keeping the denominator common. 

Follow the below steps to add the fractions with same denominators:

• Add the numerators together, keeping the denominator common
• Write the simplified fraction

For example: Add the fractions: 5/6 and 7/6.

Since the denominators are same, therefore we can add the numerators directly.

(5/6) + (7/6) = (5 + 7)/6 = 12/6

• Simplify the fraction

Hence, the sum of ⅚ and 7/6 is 2.

Adding fractions with Different Denominators

When two or more fractions with different denominators are added together, then we cannot the numerators directly. 

Follow the below steps to add fractions with different denominators:

• Check the denominators of the fractions.
• Make the denominators of the fractions same, by finding the LCM of denominators and rationalising them
• Add the numerators of the fractions, keeping the denominator common
• Simplify the fraction to get final sum

For example: Add 3/12 + 5/2

Solution: Both the fractions 3/12 and 5/2 have different denominators.

We can write 3/12 = ¼, in a simplified fraction.

Now, ¼ and 5/2 are two fractions.

LCM of 2 and 4 = 4

Multiply 5/2 by 2/2.

5/2 x 2/2 = 10/4

Now add ¼ and 10/4

¼ + 10/4 = (1+10)/4 = 11/4

Hence, the sum of 3/12 and 5/2 is 11/4.

Adding fractions with whole numbers

Add the fraction and a whole number with three simple steps:

• Write the given whole number in the form of a fraction (for example, 3/1)
• Make the denominators same and add the fractions

For example: Add 7/2 + 4

Here, 7/2 is a fraction and 4 is a whole number.

We can write 4 as 4/1.

Now making the denominators same, we get;

7/2 and 4/1 x (2/2) = 8/2

Add 7/2 and 8/2

7/2 + 8/2 = 15/2

Hence, the sum of 7/2 and 4 is 15/2.

Adding Fractions with Co-prime Denominators

Co-prime  denominators : The denominators which do not have common factors, other than 1.

Let us learn how to add fractions with co-prime denominators with the help of the following steps:

• Check the denominators whether they are co-prime
• Multiply the first fraction (numerator and denominator) with the denominator of the other fraction and the second fraction (numerator and denominator) with the denominator of the first fraction.
• Add the resulting fractions and simplify

For example, the addition of fractions 9/7 and 3/4 can be done as follows.

The denominators 7 and 4 are coprime since they have only one highest common factor 1.

So, (9/7) + (3/4) = [(9 × 4) + (3 × 7)]/ (7 × 4)

= (36 + 21)/28

Adding Mixed Fractions

A mixed fraction is a combination of a whole number and a fraction. To add two mixed fractions, we need to convert them first into improper fractions and then add them together.

Follow the below steps to add mixed numbers:

• Convert the given mixed fraction into improper fractions
• Check if denominators are the same or different
• If different denominators, then rationalise them
• Add the fractions and simplify

Let’s understand how to add mixed fractions with an example:

Example: Add : 3 ⅓  + 1 ¾

Step1: Convert the given mixed fractions to improper fractions.

3 ⅓  = 10/3 

Step 2: Make the denominators same by taking the LCM and multiplying the suitables fractions for both.

LCM of 3 and 4 is 12.

So, 10/3 = (10/3) × (4/4) = 40/12

7/4 = (7/4) × (3/3) = 21/12

Step 3: Take the denominator as common and add numerators.  Then, write the final answer.

(40/12) + (21/12) = (40 + 21)/12 = 61/12      

Therefore, 3 ⅓  + 1 ¾ = 61/12 = 5 1/12

Subtraction of Fractions

As we know, addition and subtraction are similar operations in Maths. In addition, we add two or more numbers, whereas, in subtraction, we subtract a number from another. Therefore, subtraction of fractions also follows the same rule as addition of fractions. 

If the denominators are the same for given fractions, then we can directly subtract the numerator, keeping the denominator same.

If the denominators of fractions are different, we need to rationalise them first and then perform subtraction. 

Some examples are:

Example 1: Subtract ⅓ from 8/3.

Solution: We need to find,

8/3 – ⅓ = ?

Since the denominator of two fractions ⅓ and 8/3 is common, therefore, we can directly subtract them:

8/3 – ⅓ = (8-1)/3 = 7/3

Example 2: Subtract ½ from ¾. 

Solution: We need to subtract ½ from ¾, i.e.,

¾ – ½ = ?

Since the denominators of two fractions are different, therefore, we need to rationalise them by taking the LCM.

LCM (4,2) = 4

Now multiply the ½ by 2/2, to get 2/4

¾ – 2/4 = (3-2)/4 = ¼

Hence, ¾ – ½ = ¼

Video Lesson on Fractions

Solved Examples

Let us solve some problems based on adding fractions.

Q. 1: Add 1/2 and 7/2.

Solution: Given fractions: 1/2 and 7/2 Since the denominators are the same, hence we can just add the numerators here, keeping the denominator as it is.

Q. 2: Add 3/5 and 4.

Solution: We can write 4 as 4/1

Now, 3/5 and 4/1 are the two fractions to be added.

Since the denominators here are different, thus we need to simplify the denominators first, before adding the fractions.

Taking LCM of 5 and 1, we get;

LCM(5,1) = 5

Therefore, multiplying the second fraction, 4/1 by 5 both in numerator and denominator, we get;

(4×5)/((1×5) = 20/5

Now 3/5 and 20/5 have a common denominator, i.e. 5, therefore, adding the fractions now;

Addition of Fraction Worksheet

Fraction addition is one of the important topics in classes 6, 7 and 8. We have provided a worksheet for the addition of fractions here. After practising the questions given in this worksheet, you’ll be able to solve ant fraction addition sums easily. Practice from the given addition of fraction worksheet link here and score well in exams.

Practice Questions

• 1(⅓) + 3(5/2) = 
• 2(¾) + ___ = 7
• 3/7 + 2 + 4/3 = ?

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Adding & subtracting fractions word problems

Word problem worksheets: addition & subtraction of fractions.

Below are three versions of our grade 4 math worksheet on adding and subtracting fractions and mixed numbers.  All fractions have like denominators.  Some problems will include irrelevant data so that students have to read and understand the questions, rather than simply recognizing a pattern to the solutions.  These worksheets are pdf files .

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→ → Fractions 1 This worksheet generator produces a variety of worksheets for the four basic operations (addition, subtraction, multiplication, and division) with fractions and mixed numbers, including with negative fractions. You can make the worksheets in both html and PDF formats. You can choose like or unlike fractions, make missing number problems, restrict the problems to use proper fractions or to not to simplify the answers. Further, you can control the values of numerator, denominator, and the whole-number part to make the fractions or mixed numbers as easy or difficult as you like. Each worksheet is randomly generated and thus unique. The and is placed on the second page of the file. You can generate the worksheets — both are easy to print. To get the PDF worksheet, simply push the button titled " " or " ". To get the worksheet in html format, push the button " " or " ". This has the advantage that you can save the worksheet directly from your browser (choose File → Save) and then in Word or other word processing program. Sometimes the generated worksheet is not exactly what you want. Just try again! To get a different worksheet using the same options: Tip: chose value 1 to be a fraction and value 2 to be a mixed number, and then tick the box of "Value 1 - Value 2 random switching" to make problems where either the first or the second number is a mixed number. Just experiment with the options to customize the worksheets as you like! (2 fractions, easy, for 4th grade) (3 fractions, for 4th grade) (for 4th grade) (for 5th grade) (for 6th grade) (for 5th grade) (mixed problems, for 5th grade) (answers are whole numbers, for 5th grade) (mixed problems, for 6th grade) (incl. negative fractions, for 7th-8th grade) (incl. negative fractions, for 7th-8th grade) (negative fractions, for 7th-8th grade) Drag unit fraction pieces (1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/9, 1,10, 1/12, 1,16, and 1/20) onto a square that represents one whole. You can see that, for example, 6 pieces of 1/6 fit into one whole, or that 3 pieces of 1/9 are equal to 1/3, and many other similar relationships. Use the generator below to make customized worksheets for fraction operations.     Min: Max: List: Numerator Denominator Whole number   Min: Max: List: Numerator Denominator Whole number Key to Fractions Workbooks These workbooks by Key Curriculum Press feature a number of exercises to help your child learn about fractions. Book 1 teaches fraction concepts, Book 2 teaches multiplying and dividing, Book 3 teaches adding and subtracting, and Book 4 teaches mixed numbers. Each book has a practice test at the end. 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 15 fun minutes a day Adapts to your child’s level Millions of students since 2009 Recent Posts The Language of Functions and Graphs - 07/01/2024 Educational Technology: The Christodoulou Test - 05/06/2024 Multiplication Activities in Smartick - 04/09/2024 Add a new public comment to the blog: Cancel reply The comments that you write here are moderated and can be seen by other users. For private inquiries please write to [email protected] Your personal details will not be shown publicly. I have read and accepted the Privacy and Cookies Policy It is really great. It helps me a lot. Thank you Get started with computers Learn Microsoft Office Apply for a job Improve my work skills Design nice-looking docs Getting Started Smartphones & Tablets Typing Tutorial Online Learning Basic Internet Skills Online Safety Social Media Zoom Basics Google Docs Google Sheets Career Planning Resume Writing Cover Letters Job Search and Networking Business Communication Entrepreneurship 101 Careers without College Job Hunt for Today 3D Printing Freelancing 101 Personal Finance Sharing Economy Decision-Making Graphic Design Photography Image Editing Learning WordPress Language Learning Critical Thinking For Educators Translations Staff Picks English expand_more expand_less Fractions  - Adding and Subtracting Fractions Fractions  -, adding and subtracting fractions, fractions adding and subtracting fractions. Fractions: Adding and Subtracting Fractions Lesson 3: adding and subtracting fractions. /en/fractions/comparing-and-reducing-fractions/content/ Adding and subtracting fractions In the previous lessons, you learned that a fraction is part of a whole. Fractions show how much you have of something, like 1/2 of a tank of gas or 1/3 of a cup of water. In real life, you might need to add or subtract fractions. For example, have you ever walked 1/2 of a mile to work and then walked another 1/2 mile back? Or drained 1/4 of a quart of gas from a gas tank that had 3/4 of a quart in it? You probably didn't think about it at the time, but these are examples of adding and subtracting fractions. Click through the slideshow to learn how to set up addition and subtraction problems with fractions. Let's imagine that a cake recipe tells you to add 3/5 of a cup of oil to the batter. You also need 1/5 of a cup of oil to grease the pan. To see how much oil you'll need total, you can add these fractions together. When you add fractions, you just add the top numbers, or numerators . That's because the bottom numbers, or denominators , show how many parts would make a whole. We don't want to change how many parts make a whole cup ( 5 ). We just want to find out how many parts we need total. So we only need to add the numerators of our fractions. We can stack the fractions so the numerators are lined up. This will make it easier to add them. And that's all we have to do to set up an addition example with fractions. Our fractions are now ready to be added. We'll do the same thing to set up a subtraction example. Let's say you had 3/4 of a tank of gas when you got to work. If you use 1/4 of a tank to drive home, how much will you have left? We can subtract these fractions to find out. Just like when we added, we'll stack our fractions to keep the numerators lined up. This is because we want to subtract 1 part from 3 parts. Now that our example is set up, we're ready to subtract! Try setting up these addition and subtraction problems with fractions. Don't try solving them yet! You run 4/10 of a mile in the morning. Later, you run for 3/10 of a mile. You had 7/8 of a stick of butter and used 2/8 of the stick while cooking dinner. Your gas tank is 2/5 full, and you put in another 2/5 of a tank. Solving addition problems with fractions Now that we know how to write addition problems with fractions, let's practice solving a few. If you can add whole numbers , you're ready to add fractions. Click through the slideshow to learn how to add fractions. Let's continue with our previous example and add these fractions: 3/5 of cup of oil and 1/5 of a cup of oil. Remember, when we add fractions, we don't add the denominators. This is because we're finding how many parts we need total. The numerators show the parts we need, so we'll add 3 and 1 . 3 plus 1 equals 4 . Make sure to line up the 4 with the numbers you just added. The denominators will stay the same, so we'll write 5 on the bottom of our new fraction. 3/5 plus 1/5 equals 4/5 . So you'll need 4/5 of a cup of oil total to make your cake. Let's try another example: 7/10 plus 2/10 . Just like before, we're only going to add the numerators. In this example, the numerators are 7 and 2 . 7 plus 2 equals 9 , so we'll write that to the right of the numerators. Just like in our earlier example, the denominator stays the same. So 7/10 plus 2/10 equals 9/10 . Try solving some of the addition problems below. Solving subtraction problems with fractions Subtracting fractions is a lot like regular subtraction. If you can subtract whole numbers , you can subtract fractions too! Click through the slideshow to learn how to subtract fractions. Let's use our earlier example and subtract 1/4 of a tank of gas from 3/4 of a tank. Just like in addition, we're not going to change the denominators. We don't want to change how many parts make a whole tank of gas. We just want to know how many parts we'll have left. We'll start by subtracting the numerators. 3 minus 1 equals 2 , so we'll write 2 to the right of the numerators. Just like when we added, the denominator of our answer will be the same as the other denominators. So 3/4 minus 1/4 equals 2/4 . You'll have 2/4 of a tank of gas left when you get home. Let's try solving another problem: 5/6 minus 3/6 . We'll start by subtracting the numerators. 5 minus 3 equals 2 . So we'll put a 2 to the right of the numerators. As usual, the denominator stays the same. So 5/6 minus 3/6 equals 2/6 . Try solving some of the subtraction problems below. After you add or subtract fractions, you may sometimes have a fraction that can be reduced to a simpler fraction. As you learned in Comparing and Reducing Fractions , it's always best to reduce a fraction to its simplest form when you can. For example, 1/4 plus 1/4 equals 2/4 . Because 2 and 4 can both be divided 2 , we can reduce 2/4 to 1/2 . Adding fractions with different denominators On the last page, we learned how to add fractions that have the same denominator, like 1/4 and 3/4 . But what if you needed to add fractions with different denominators? For example, our cake recipe might say to blend 1/4 cup of milk in slowly and then dump in another 1/3 of a cup. In Comparing and Reducing Fractions , we compared fractions with a different bottom number, or denominator. We had to change the fractions so their denominators were the same. To do that, we found the lowest common denominator , or LCD . We can only add or subtract fractions if they have the same denominators. So we'll need to find the lowest common denominator before we add or subtract these fractions. Once the fractions have the same denominator, we can add or subtract as usual. Click through the slideshow to learn how to add fractions with different denominators. Let's add 1/4 and 1/3 . Before we can add these fractions, we'll need to change them so they have the same denominator . To do that, we'll have to find the LCD , or lowest common denominator, of 4 and 3 . It looks like 12 is the smallest number that can be divided by both 3 and 4, so 12 is our LCD . Since 12 is the LCD, it will be the new denominator for our fractions. Now we'll change the numerators of the fractions, just like we changed the denominators. First, let's look at the fraction on the left: 1/4 . To change 4 into 12 , we multiplied it by 3 . Since the denominator was multiplied by 3 , we'll also multiply the numerator by 3 . 1 times 3 equals 3 . 1/4 is equal to 3/12 . Now let's look at the fraction on the right: 1/3 . We changed its denominator to 12 as well. Our old denominator was 3 . We multiplied it by 4 to get 12. We'll also multiply the numerator by 4 . 1 times 4 equals 4 . So 1/3 is equal to 4/12 . Now that our fractions have the same denominator, we can add them like we normally do. 3 plus 4 equals 7 . As usual, the denominator stays the same. So 3/12 plus 4/12 equals 7/12 . Try solving the addition problems below. Subtracting fractions with different denominators We just saw that fractions can only be added when they have the same denominator. The same thing is true when we're subtracting fractions. Before we can subtract, we'll have to change our fractions so they have the same denominator. Click through the slideshow to learn how to subtract fractions with different denominators. Let's try subtracting 1/3 from 3/5 . First, we'll change the denominators of both fractions to be the same by finding the lowest common denominator . It looks like 15 is the smallest number that can be divided evenly by 3 and 5 , so 15 is our LCD. Now we'll change our first fraction. To change the denominator to 15 , we'll multiply the denominator and the numerator by 3 . 5 times 3 equals 15 . So our fraction is now 9/15 . Now let's change the second fraction. To change the denominator to 15 , we'll multiply both numbers by 5 to get 5/15 . Now that our fractions have the same denominator, we can subtract like we normally do. 9 minus 5 equals 4 . As always, the denominator stays the same. So 9/15 minus 5/15 equals 4/15 . Try solving the subtraction problems below. Adding and subtracting mixed numbers Over the last few pages, you've practiced adding and subtracting different kinds of fractions. But some problems will need one extra step. For example, can you add the fractions below? In Introduction to Fractions , you learned about mixed numbers . A mixed number has both a fraction and a whole number . An example is 2 1/2 , or two-and-a-half . Another way to write this would be 5/2 , or five-halves . These two numbers look different, but they're actually the same. 5/2 is an improper fraction . This just means the top number is larger than the bottom number. Even though improper fractions look strange, you can add and subtract them just like normal fractions. Mixed numbers aren't easy to add, so you'll have to convert them into improper fractions first. Let's add these two mixed numbers: 2 3/5 and 1 3/5 . We'll need to convert these mixed numbers to improper fractions. Let's start with 2 3/5 . As you learned in Lesson 2 , we'll multiply the whole number, 2 , by the bottom number, 5 . 2 times 5 equals 10 . Now, let's add 10 to the numerator, 3 . 10 + 3 equals 13 . Just like when you add fractions, the denominator stays the same. Our improper fraction is 13/5 . Now we'll need to convert our second mixed number: 1 3/5 . First, we'll multiply the whole number by the denominator. 1 x 5 = 5 . Next, we'll add 5 to the numerators. 5 + 3 = 8 . Just like last time, the denominator remains the same. So we've changed 1 3/5 to 8/5 . Now that we've changed our mixed numbers to improper fractions, we can add like we normally do. 13 plus 8 equals 21 . As usual, the denominator will stay the same. So 13/5 + 8/5 = 21/5 . Because we started with a mixed number, let's convert this improper fraction back into a mixed number. As you learned in the previous lesson , divide the top number by the bottom number. 21 divided by 5 equals 4, with a remainder of 1 . The answer, 4, will become our whole number. And the remainder , 1, will become the numerator of the fraction. So 2 3/5 + 1 3/5 = 4 1/5 . /en/fractions/multiplying-and-dividing-fractions/content/ Adding Fractions Practice Questions Click here for questions, click here for answers. Addition, Adding GCSE Revision Cards 5-a-day Workbooks Primary Study Cards Privacy Policy Terms and Conditions Corbettmaths © 2012 – 2024 Addition and Subtraction of Fraction: Methods, Examples, Facts, FAQs What is addition and subtraction of fractions, methods of addition and subtraction of fractions, addition and subtraction of mixed numbers, solved examples on addition and subtraction of fractions, practice problems on addition and subtraction of fractions, frequently asked questions on addition and subtraction of fractions. Addition and subtraction of fractions are the fundamental operations on fractions that can be studied easily using two cases: Addition and subtraction of like fractions (fractions with same denominators) Addition and subtraction of unlike fractions (fractions with different denominators) A fraction represents parts of a whole. For example, the fraction 37 represents 3 parts out of 7 equal parts of a whole. Here, 3 is the numerator and it represents the number of parts taken. 7 is the denominator and it represents the total number of parts of the whole. Adding and subtracting fractions is simple and straightforward when it comes to like fractions. In the case of unlike fractions, we first need to make the denominators the same. Let’s take a closer look at both these cases. Recommended Games Before adding and subtracting fractions, we first need to make sure that the fractions have the same denominators.  When the denominators are the same, we simply add the numerators and keep the denominator as it is. To add or subtract unlike fractions, we first need to learn how to make the denominators alike. Let’s learn how to add fractions and how to subtract fractions in both cases. Recommended Worksheets More Worksheets Addition and Subtraction of Like Fractions The rules for adding fractions with the same denominator are really simple and straightforward.  Let’s learn with the help of examples and visual bar models. Addition of Like Fractions Here are the steps to add fractions with the same denominator: Step 1: Add the numerators of the given fractions.  Step 2: Keep the denominator the same.  Step 3: Simplify.           $\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$  …$c \neq 0$ Example 1: Find $\frac{1}{4} + \frac{2}{4}$ . $\frac{1}{4} + \frac{2}{4} = \frac{1 + 2}{4} = \frac{3}{4}$ We can visualize this addition using a bar model: Example 2: $\frac{1}{8} + \frac{3}{8} = \frac{1 + 3}{8} = \frac{4}{8} = \frac{1}{2}$ Subtraction of Like Fractions Here are the steps to subtract fractions with the same denominator: Step 1: Subtract the numerators of the given fractions.  Step 3: Simplify.  $\frac{a}{c}\;-\;\frac{b}{c} = \frac{a \;-\; b}{c}$ …$c \neq 0$ Example 1: Find $\frac{4}{6} \;-\; \frac{1}{6}$. $\frac{4}{6}\;-\;\frac{1}{6} = \frac{4-1}{6} = \frac{3}{6} = \frac{1}{2}$ Addition and Subtraction of Unlike Fractions Addition and subtraction of fractions with unlike denominators can be a little bit tricky since the denominators are not the same. So, we need to first convert the unlike fractions into like fractions. Let’s look at a few ways to do this! Addition of Unlike Fractions We can make the denominators the same by finding the LCM of the two denominators. Once we calculate the LCM, we multiply both the numerator and the denominator with an appropriate number so that we get the LCM value in the denominator.  Example: $\frac{3}{5} + \frac{3}{2}$ Step 1: Find the LCM (Least Common Multiple) of the two denominators. The LCM of 5 and 2 is 10. Step 2: Convert both the fractions into like fractions by making the denominators same.   $\frac{3 \times 2}{5 \times 2} = \frac{6}{10}$   $\frac{3 \times 5}{2 \times 5} = \frac{15}{10}$ Step 3: Add the numerators. The denominator stays the same. $\frac{6}{10} + \frac{15}{10} = \frac{21}{10}$ Step 4: Convert the resultant fraction to its simplest form if the GCF of the numerator and denominator is not 1.  In this case, GCF (21,10) $= 1$ The fraction $\frac{21}{10}$ is already in its simplest form.  Thus, $\frac{3}{5} + \frac{3}{2} = \frac{21}{10}$ Subtraction of Unlike Fractions Let’s learn how to subtract fractions when denominators are not the same. To subtract unlike fractions, we use the LCM method. The process is similar to what we discussed in the previous example. Example: $\frac{5}{6} \;-\; \frac{2}{9}$ Step 1: Find the LCM of the two denominators. LCM of 6 and $9 = 18$ Step 2: Convert both the fractions into like fractions by making the denominators same. $\frac{5 \times 3}{6 \times 3} = \frac{15}{18}$    $\frac{2 \times 2}{9 \times 2} = \frac{4}{18}$ Step 3: Subtract the numerators. The denominator stays the same. $\frac{15}{18} \;-\; \frac{4}{18} = \frac{11}{18}$ In this case, the GCF (11,18) $= 1$ So, it is already in its simplest form.  Thus, $\frac{5}{6}\;-\; 29 = \frac{11}{18}$ A mixed number is a type of fraction that has two parts: a whole number and a proper fraction. It is also known as a mixed fraction. Any mixed number can be written in the form of an improper fraction and vice-versa.  Adding and subtracting mixed fractions is done by converting mixed numbers into improper fractions . Addition and Subtraction of Mixed Fractions with Same Denominators The steps of adding and subtracting mixed numbers with the same denominators are the same. The only difference is the operation. Step 1: Convert the given mixed fractions to improper fractions. Step 2: Add/Subtract the like fractions obtained in step 1. Step 3: Reduce the fraction to its simplest form. Step 4: Convert the resulting fraction into a mixed number. Example 1: $2\frac{1}{5} + 1\frac{3}{5}$ $2\frac{1}{5} = \frac{(5 \times 2) + 1}{5} = \frac{11}{5}$ $1\frac{3}{5} = \frac{(5 \times 1) + 3}{5} = \frac{8}{5}$ Thus, $2\frac{1}{5} + 1\frac{3}{5} = \frac{11}{5} + \frac{8}{5} = \frac{19}{5}$ Converting $\frac{19}{5}$ into a mixed number, we get $\frac{19}{5} = 3\frac{4}{5}$ Example 2: $2\frac{1}{5} + 1\frac{3}{5} = \frac{11}{5} \;-\; \frac{8}{5} = \frac{3}{5}$ Addition and Subtraction of Mixed Fractions with Unlike Denominators Step 2: Convert both the fractions into like fractions by finding the least common denominator. Step 3: Add the fractions. (or subtract the fractions.) Step 4: Reduce the fraction if possible or convert back to a mixed number  Let us understand the addition of mixed numbers with unlike denominators with the help of an example. Example 1: Find the value of $1\frac{3}{5} + 2\frac{1}{2}$. Convert the given mixed fractions to improper fractions. $1\frac{3}{5} = \frac{8}{5}$ and $2\frac{1}{2} = \frac{5}{2}$ Step 2: Convert both the fractions into like fractions by making the denominators the same. Here, LCM of 5 and 2 is 10. Thus, $\frac{8 \times 2}{5 \times 2} = \frac{16}{10}$ and $\frac{5\times 5}{2 \times 5} = \frac{25}{10}$ Step 3: Add the fractions by adding the numerators. $\frac{16}{10} + \frac{25}{10} = \frac{41}{10}$ Step 4: Convert back into a mixed number.  Thus, $\frac{41}{10}$ will become  $4\frac{1}{10}$ Therefore, $1\frac{3}{5} + 2\frac{1}{2} =  4\frac{1}{10}$ Here’s an example for subtraction. It follows the same steps. Example 2 : $6\frac{1}{2} \;-\; 1\frac{3}{4}$ Step 1: Convert the mixed numbers into improper fractions.      $6\frac{1}{2} \;-\; 1\frac{3}{4} = \frac{13}{2} \;-\; \frac{7}{4}$ Step 2: Make the denominators equal. LCM of 2 and 4 is 4.     $\frac{13 \times 2}{2 \times 2} = \frac{26}{4}$  Step 3: Subtract the fractions.         $\frac{26}{4} \;-\;  \frac{7}{4} = \frac{19}{4}$ Step 4: Convert the fraction as a mixed number.             $\frac{19}{4}  = 4\frac{3}{4}$   Thus, $6\frac{1}{2} \;-\; 1\frac{3}{4}  =   4\frac{3}{4}$   Facts about Addition and Subtraction of Fractions We cannot add or subtract fractions without converting them into like fractions. Like fractions are fractions that have the same denominator, and unlike fractions are fractions that have different denominators. Equivalent fractions are two different fractions that represent the same value. The LCD (least common denominator) of two fractions is the LCM of the denominators. In this article, we have learned about addition and subtraction of fractions (like fractions, unlike fractions, mixed fractions), methods of addition and subtraction of these fractions along with the steps. Let’s solve some examples on adding and subtracting fractions to understand the concept better. Solve: $\frac{2}{4} + \frac{1}{4}$ . Solution:  Here, the denominators are the same. Thus, we add the numerators by keeping the denominators as it is. $\frac{2}{4} + \frac{1}{4} = \frac{2 + 1}{4}$  $\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$ 2. Find the sum of the fractions $\frac{3}{5}$ and $\frac{5}{2}$ by using the LCM method. $\frac{3}{5}$ and $\frac{5}{2}$ are unlike fractions. The LCM of 2 and 5 is 10. Thus, we can write $\frac{3}{5} + \frac{5}{2} = \frac{3 \times 2}{5 \times 2} + \frac{5 \times 5}{2 \times 5}$ $= \frac{6}{10} + \frac{25}{10}$             $= \frac{6}{10} + \frac{25}{10}$             $= \frac{31}{10}$ Thus, $\frac{3}{5} + \frac{5}{2} =  \frac{31}{10}$ 3. Find $\frac{4}{16} + \frac{5}{8}$. Solution:   To add two fractions with different denominators, we first need to find the LCM of the denominators. The LCM of 16 and 8 is 16. $\frac{4}{16} + \frac{5}{8} = \frac{4 \times 1}{16\times 1} + \frac{5 \times 2}{8 \times 2}$              $= \frac{10}{16} + \frac{4}{16}$              $= \frac{14}{16}$ $= \frac{7}{8}$ 4. From a rope $12\frac{1}{2}$ ft. long, a $7 \frac{6}{8}\;-$ ft-long piece is cut off. Find the length of the remaining rope. Total length of the rope $= 12\frac{1}{2}$ ft. Length of the rope that was cut off $= 7 \frac{6}{8}$ ft.  The length of the remaining rope $= 12\frac{1}{2} \;-\; 7 \frac{6}{8}$ $12\frac{1}{2} \;-\; 7 \frac{6}{8} = \frac{25}{2} \;-\; \frac{62}{8}$          $= \frac{25 \times 4}{2 \times 4} \;-\; \frac{62 \times 1}{8\times 1}$          $= \frac{100}{8} \;-\; \frac{62}{8}$          $= \frac{38}{8}$          $= \frac{19}{4}$ Converting it into a mixed fraction, $\frac{19}{4}$ becomes $4 \frac{3}{4}$. Thus, the length of the remaining rope is $4\frac{3}{4}$ ft. Attend this quiz & Test your knowledge. Find $\frac{2}{4} + \frac{2}{4}$. $\frac{7}{24} + \frac{5}{16} =$, what is the least common denominator of $\frac{1}{2}$ and $\frac{1}{3}$, $\frac{3}{6} \;-\; \frac{1}{6} =$, what equation does the following figure represent. How do we add and subtract negative fractions? Negative fractions are simply fractions with a negative sign. The steps to add and subtract the negative fractions remain the same. We need to follow the rules for addition/subtraction with negative signs. How can we convert an improper fraction into a mixed number? To convert an improper fraction into a mixed number, we divide the numerator by the denominator. The denominator stays the same. The quotient represents the whole number part. The remainder represents the numerator of the mixed number. Example: $\frac{14}{3} = 4\; \text{R}\; 2$ Quotient $= 4$ Remainder $= 2$ $\frac{14}{3} = 4\frac{2}{3}$ How do we divide two fractions? To divide one fraction by another, we multiply the first fraction by the reciprocal of the second fraction. $\frac{A}{B} \div \frac{C}{D} = \frac{A}{B} \times \frac{D}{C}$ For example, $\frac{1}{2} \div \frac{3}{5} = \frac{1}{2} \times \frac{5}{3} = \frac{5}{6}$ What are the rules of adding and subtracting fractions? Before adding or subtracting, we check if the fractions have the same denominator. If the denominators are equal, then we add/subtract the numerators keeping the common denominator. If the denominators are different, then we make the denominators equal by using the LCM method. Once the fractions have the same denominator, we can add/subtract the numerators keeping the common denominator as it is. How do we add and subtract fractions with whole numbers? Convert the whole number to a fraction. To do this, give the whole number a denominator of 1. Convert to fractions of like denominators.  Add/subtract the numerators. Now that the fractions have the same denominators, you can treat the numerators as a normal addition/subtraction problem. RELATED POSTS Cube Numbers – Definition, Examples, Facts, Practice Problems Volume of Hemisphere: Definition, Formula, Examples CPCTC: Definition, Postulates, Theorem, Proof, Examples Dividend – Definition with Examples Reflexive Property – Definition, Equality, Examples, FAQs Math & ELA | PreK To Grade 5 Kids see fun., you see real learning outcomes.. Make study-time fun with 14,000+ games & activities, 450+ lesson plans, and more—free forever. Parents, Try for Free Teachers, Use for Free International Education Jobs Schools directory Resources Education Jobs Schools directory News Search Adding and Subtracting Fraction Word Problems Subject: Mathematics Age range: 7-11 Resource type: Worksheet/Activity Last updated 16 June 2015 Share through email Share through twitter Share through linkedin Share through facebook Share through pinterest Creative Commons "Sharealike" Your rating is required to reflect your happiness. It's good to leave some feedback. Something went wrong, please try again later. Perfect for my year 7. Thank you for sharing. Empty reply does not make any sense for the end user excellent - just what I was looking for roger_matthews Helpful sheet for practicing wordy fraction questions. Answers can sometimes be simplified further. Report this resource to let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch. Not quite what you were looking for? Search by keyword to find the right resource: Worksheet on Add and Subtract Fractions Recall the topic carefully and practice the questions given in the math worksheet on add and subtract fractions. The question mainly covers addition with the help of a fraction number line, subtraction with the help of a fraction number line, add the fractions with the same denominator, subtract the fractions with the same denominator and word problems on add and subtract fractions. I. Addition and Subtraction of Like Fractions: For adding or subtracting like fractions, we follow the following steps. Working Rules for Addition and Subtraction of Like Fractions: Step I:  Add or subtract the numerators of the given fractions and keep the denominator as it is. Step II:  Reduce the fraction of its lowest term. Step III:  If the result is an improper fraction, convert it into a mixed fraction. sum or difference of like fractions                   =  Sum of Difference of Numerators                              Common denominator II: Addition and Subtraction of Unlike Fractions: For adding or subtracting unlike fractions, we follow these steps. Working Rules  for Addition and Subtraction of Like Fractions: Step I: Find the LCM of denominators of the given fractions. Step II: Convert unlike fractions into like fractions by making LCM as their denominator. Step III: Add or subtract the like fractions. 1.   Add with the help of a fraction number line: (a) \(\frac{2}{3}\) + \(\frac{1}{3}\) (b) \(\frac{3}{7}\) + \(\frac{2}{7}\) (c) \(\frac{6}{10}\) + \(\frac{1}{10}\) 2.   Subtract with the help of a fraction number line:   (a) \(\frac{9}{10}\) - \(\frac{3}{10}\) (b) \(\frac{5}{6}\) - \(\frac{2}{6}\) (c) \(\frac{7}{8}\) - \(\frac{4}{8}\) 3. Add:   (a) \(\frac{7}{10}\) + \(\frac{2}{10}\) (b) \(\frac{6}{8}\) + \(\frac{4}{8}\) (c) \(\frac{5}{9}\) + \(\frac{2}{9}\) + \(\frac{1}{9}\) (d) \(\frac{8}{11}\) + \(\frac{2}{11}\) (e) \(\frac{4}{9}\) + \(\frac{7}{9}\) (f) \(\frac{3}{8}\) + \(\frac{5}{8}\) + \(\frac{2}{8}\) (g) \(\frac{4}{6}\) + \(\frac{2}{6}\) + \(\frac{1}{6}\) (h) \(\frac{7}{12}\) + \(\frac{5}{12}\) + \(\frac{6}{12}\) 4. Find the difference. Remember to show the answer in the simplest form: (a) \(\frac{9}{14}\) - \(\frac{4}{14}\) (b) \(\frac{6}{11}\) - \(\frac{3}{11}\) (c) \(\frac{8}{12}\) - \(\frac{4}{12}\) (d) \(\frac{12}{15}\) - \(\frac{9}{15}\) (e) \(\frac{12}{13}\) - \(\frac{9}{13}\) (f) \(\frac{6}{10}\) - \(\frac{2}{10}\) (g) \(\frac{9}{16}\) - \(\frac{5}{16}\) (h) \(\frac{12}{14}\) - \(\frac{8}{14}\) 5. Add the following fractions: (i) \(\frac{4}{7}\) + \(\frac{5}{7}\)  (ii) \(\frac{3}{7}\) + \(\frac{11}{7}\) (iii) \(\frac{3}{23}\) + \(\frac{11}{23}\) + \(\frac{1}{23}\) (iv) \(\frac{2}{5}\) + \(\frac{3}{20}\) (v) \(\frac{2}{7}\) + \(\frac{4}{9}\) (vi) 3\(\frac{7}{9}\) + 2\(\frac{5}{6}\) + 6\(\frac{1}{3}\) (vii) \(\frac{2}{15}\) + \(\frac{5}{12}\) + \(\frac{4}{20}\) (viii) \(\frac{11}{16}\) + \(\frac{3}{10}\) + \(\frac{9}{24}\) (ix) 1\(\frac{3}{8}\) + \(\frac{5}{8}\) (x) 4\(\frac{3}{5}\) + 2\(\frac{7}{20}\) (xi) \(\frac{8}{15}\) + 2\(\frac{1}{15}\) (xii) 3\(\frac{1}{5}\) + 4\(\frac{1}{10}\) + 5\(\frac{1}{15}\) 6. Subtract the following fractions: (i) \(\frac{7}{9}\) - \(\frac{2}{9}\) (ii) \(\frac{3}{4}\) - \(\frac{3}{4}\) (iii) 8\(\frac{2}{9}\) - 2\(\frac{5}{9}\) (iv) \(\frac{11}{20}\) - \(\frac{4}{15}\) (v) \(\frac{8}{15}\) - \(\frac{1}{7}\) (vi) 5\(\frac{1}{40}\) - \(\frac{4}{25}\) (vii) 6\(\frac{2}{16}\) - 3\(\frac{1}{6}\) (viii) 3\(\frac{7}{8}\)  - \(\frac{6}{7}\) (ix) 7\(\frac{3}{21}\) - 6\(\frac{3}{28}\) 7. Simplify the following combination of addition and subtraction of fractions: (i) \(\frac{3}{4}\) + \(\frac{2}{3}\) - \(\frac{1}{2}\) (ii) \(\frac{3}{8}\) + \(\frac{7}{8}\) - \(\frac{1}{8}\) (iii) \(\frac{12}{25}\) - \(\frac{3}{25}\) + \(\frac{9}{25}\) (iv) 2\(\frac{1}{2}\)+ 3\(\frac{3}{5}\) - 1\(\frac{1}{3}\) (v) 11\(\frac{1}{4}\) - 4\(\frac{3}{5}\) + \(\frac{8}{11}\) (vi) \(\frac{7}{18}\) - \(\frac{1}{12}\) + \(\frac{1}{6}\) Worksheet on Word Problems on Addition and Subtraction of Like Fractions: 8. Solve these problems: (a) \(\frac{1}{3}\) of the school garden has vegetable and another \(\frac{1}{3}\) has flowers. What part of the garden is left to grow grass? (b) Sam spent \(\frac{1}{6}\) of his Sunday doing home work and \(\frac{3}{6}\) of the day watching cricket. What part of the day was left to do other things? (c) My mother ate \(\frac{1}{8}\) of the cake and my father \(\frac{3}{8}\). How much of the cake has been eaten and how much is left? (d) Pearl bought \(\frac{2}{3}\) of her school books last week. What part is still left to be bought? (e) Sonia walked \(\frac{3}{8}\) of the distance to school and ran \(\frac{5}{8}\) of the distance. How much more of the distance does she need to cover? (f) Emma likes chocolate. One day she bought a chocolate and ate \(\frac{5}{8}\) of it in the morning and \(\frac{2}{8}\) in the evening. How much part of the chocolate has she eaten? (g) James and  Lucas are eating a pizza.  James ate \(\frac{3}{4}\) of the pizza and  Lucas ate  \(\frac{1}{4}\) of pizza. Who ate more pizza? (h) Sophia completed \(\frac{2}{5}\) of her homework before going out for play. She did \(\frac{1}{5}\) of her homework after the play. How much homework did she complete altogether? (i) David distributed \(\frac{19}{24}\) apples in his class and gave \(\frac{2}{24}\) to his friend Richard. What fraction of apples he gave away in all? (j) Mary read \(\frac{2}{9}\) of her book in the morning and \(\frac{5}{9}\) in the evening. What fraction of the book has she read? (k) A piece of ribbon is \(\frac{12}{15}\) m long. A piece of \(\frac{4}{15}\) m is cut from it. What is the fraction of the remaining ribbon? (l) Nancy saves \(\frac{2}{7}\) of her salary and uses \(\frac{1}{7}\) for paying the house rent. How much salary is she left with? Answers for the worksheet on add and subtract fractions are given below to check the exact answers of the above questions on adding & subtracting fractions.  5.  (i) 1\(\frac{2}{7}\)  (iii) \(\frac{15}{23}\)  (iv) \(\frac{11}{20}\)  (v) \(\frac{46}{63}\)  (vi) 12\(\frac{17}{18}\) (vii) \(\frac{45}{60}\) or, \(\frac{3}{4}\) (viii) 1\(\frac{87}{240}\) (x) 6\(\frac{19}{20}\) (xi) 2\(\frac{9}{15}\) (xii) 12\(\frac{11}{30}\) 6. (i) \(\frac{5}{9}\) (ii) \(\frac{1}{4}\) (iii) 5\(\frac{6}{9}\) or 5\(\frac{2}{3}\) (iv) \(\frac{17}{60}\) (v) \(\frac{41}{105}\) (vi) 4\(\frac{173}{200}\) (vii) 2\(\frac{46}{48}\) or 2\(\frac{23}{24}\) (viii) 3\(\frac{1}{56}\) (ix) 1\(\frac{3}{84}\) or 1\(\frac{1}{28}\) 7.  (i) \(\frac{11}{12}\) (ii) 1\(\frac{1}{8}\) (iii) \(\frac{18}{25}\) (iv) 4\(\frac{23}{30}\) (v) 7\(\frac{83}{220}\) (vi) \(\frac{17}{36}\) You might like these Worksheet on Word Problems on Fractions | Fraction Word Problems | Ans In worksheet on word problems on fractions we will solve different types of word problems on multiplication of fractions, word problems on division of fractions etc... 1. How many one-fifths Worksheet on Fractions | Questions on Fractions | Representation | Ans In worksheet on fractions, all grade students can practice the questions on fractions on a whole number and also on representation of a fraction. This exercise sheet on fractions can be practiced Conversion of Mixed Fractions into Improper Fractions |Solved Examples To convert a mixed number into an improper fraction, we multiply the whole number by the denominator of the proper fraction and then to the product add the numerator of the fraction to get the numerator of the improper fraction. I Verification of Equivalent Fractions | Exploring Equivalent Fractions We will discuss here about verification of equivalent fractions. To verify that two fractions are equivalent or not, we multiply the numerator of one fraction by the denominator of the other fraction. Similarly, we multiply the denominator of one fraction by the numerator Representations of Fractions on a Number Line | Examples | Worksheet In representations of fractions on a number line we can show fractions on a number line. In order to represent 1/2 on the number line, draw the number line and mark a point A to represent 1. Addition and Subtraction of Fractions | Solved Examples | Worksheet Addition and subtraction of fractions are discussed here with examples. To add or subtract two or more fractions, proceed as under: (i) Convert the mixed fractions (if any.) or natural numbers Fractions in Descending Order |Arranging Fractions an Descending Order We will discuss here how to arrange the fractions in descending order. Solved examples for arranging in descending order: 1. Arrange the following fractions 5/6, 7/10, 11/20 in descending order. First we find the L.C.M. of the denominators of the fractions to make the Fractions in Ascending Order | Arranging Fractions | Worksheet |Answer We will discuss here how to arrange the fractions in ascending order. Solved examples for arranging in ascending order: 1. Arrange the following fractions 5/6, 8/9, 2/3 in ascending order. First we find the L.C.M. of the denominators of the fractions to make the denominators 5th Grade Fractions Worksheets | Comparison of Fractions | Addition In 5th Grade Fractions Worksheets we will solve how to compare two fractions, comparing mixed fractions, addition of like fractions, addition of unlike fractions, addition of mixed fractions, word problems on addition of fractions, subtraction of like fractions 5th Grade Fractions | Definition | Examples | Word Problems |Worksheet In 5th Grade Fractions we will discuss about definition of fraction, concept of fractions and different types of examples on fractions. A fraction is a number representing a part of a whole. The whole may be a single object or a group of objects. Word Problems on Fraction | Math Fraction Word Problems |Fraction Math In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers. Comparison of Like Fractions | Comparing Fractions | Like Fractions Any two like fractions can be compared by comparing their numerators. The fraction with larger numerator is greater than the fraction with smaller numerator, for example \(\frac{7}{13}\) > \(\frac{2}{13}\) because 7 > 2. In comparison of like fractions here are some Worksheet on Reducing Fraction | Simplifying Fractions | Lowest Form Practice the questions given in the math worksheet on reducing fraction to the lowest terms by using division. Fractional numbers are given in the questions to reduce to its lowest term. Mental Math on Fractions | Fractions Worksheets | Fraction Mental Math In mental math on fractions we will solve different type of problems on types of fractions, equivalent fractions, fraction in lowest terms, comparison of fractions, fraction in lowest term, types of fractions, addition of fractions, subtraction of fractions and word problems Fraction in Lowest Terms |Reducing Fractions|Fraction in Simplest Form There are two methods to reduce a given fraction to its simplest form, viz., H.C.F. Method and Prime Factorization Method. If numerator and denominator of a fraction have no common factor other than 1(one), then the fraction is said to be in its simple form or in lowest ●   Fractional Numbers - worksheets Worksheet on Equivalent Fractions. Worksheet on Fractions. Worksheet on Comparison of Like Fractions. Worksheet on Conversion of Fractions. Worksheet on Changing Fractions. Worksheet on Types of Fractions. Worksheet on Reducing Fraction. Worksheet on Addition of Fractions having the Same Denominator. Worksheet on Subtraction of Fractions having the Same Denominator. Worksheet on Add and Subtract Fractions. Worksheet on Fractional Numbers. 4th Grade Math Activities From Worksheet on Add and Subtract Fractions to HOME PAGE Didn't find what you were looking for? Or want to know more information about Math Only Math . Use this Google Search to find what you need. New! Comments Share this page: What’s this? 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The printable activities target advanced multi-digit addition and subtraction as well as multiplication, division, fractions, and place value. STW offers free worksheets in all of these 3rd grade topic areas. Multi-Digit Addition & Subtraction Logged in members can use the Super Teacher Worksheets filing cabinet to save their favorite worksheets. Quickly access your most used files AND your custom generated worksheets! Please login to your account or become a member and join our community today to utilize this helpful feature. Multiplication & Division Check out our daily spiral review for 3rd grade math students! Take a look at our daily math word problems for 3rd graders. PDF with answer key: PDF no answer key: Pardon Our Interruption As you were browsing something about your browser made us think you were a bot. There are a few reasons this might happen: You've disabled JavaScript in your web browser. You're a power user moving through this website with super-human speed. You've disabled cookies in your web browser. A third-party browser plugin, such as Ghostery or NoScript, is preventing JavaScript from running. Additional information is available in this support article . To regain access, please make sure that cookies and JavaScript are enabled before reloading the page. 132 IMAGES How To Add Fractions With Lcm Fractions word problems with four operations worksheets Add Fractions: Problem Solving Worksheet for 5th Grade Addition and Subtraction of Similar Fractions How to solve mixed fractions addition Adding Fractions (solutions, examples, videos) VIDEO Problem Solving Involving Fractions Addition of Fraction new method || Fraction easy steps solved || Maths tricks #part 1 || EASIEST WAY to Add Fractions! How to add fraction math antics| Fraction Fractions Adding Fractions with Unlike Denominators COMMENTS Add & subtract fractions word problems Like & unlike denominators. Below are our grade 5 math word problem worksheet on adding and subtracting fractions. The problems include both like and unlike denominators, and may include more than two terms. Worksheet #1 Worksheet #2 Worksheet #3 Worksheet #4. Worksheet #5 Worksheet #6. Adding Fractions Word Problems Solution. This word problem requires addition of fractions. Choosing a common denominator of 4, we get. 1/2 + 3/4 = 2/4 + 3/4 = 5/4. So, John walked a total of 5/4 miles. Example #2: Mary is preparing a final exam. She study 3/2 hours on Friday, 6/4 hours on Saturday, and 2/3 hours on Sunday. How many hours she studied over the weekend. Fraction Addition Word Problems Worksheets A wealth of real-life scenarios that involve addition of fractions with whole numbers and addition of two like fractions, two unlike fractions, and two mixed numbers, our pdf worksheets are indispensable for grade 3, grade 4, grade 5, and grade 6 students. The free fraction addition word problems worksheet is worth a try! Fraction Word Problems 24. To do this, multiply the numerator and the denominator of each fraction by the same number so that it results in a denominator of 24. 24. This will give you an equivalent fraction for each fraction in the problem. 7×3 8×3 = 21 24 1×8 3×8 = 8 248 × 37 × 3 = 2421 3 × 81 × 8 = 248. Now you can subtract the fractions. Solving Word Problems by Adding and Subtracting Fractions and Mixed Solution: Answer: The carpenter needs to cut four and seven-twelfths feet of wood. Summary: In this lesson we learned how to solve word problems involving addition and subtraction of fractions and mixed numbers. We used the following skills to solve these problems: Add fractions with like denominators. Subtract fractions with like denominators. Worksheets for fraction addition Fraction addition worksheets: grades 6-7. In grades 6 and 7, students simply practice addition with fractions that have larger denominators than in grade 5. Add two fractions, select (easier) denominators within 2-25. View in browser Create PDF. Add three fractions, select (easier) denominators within 2-25. Adding and Subtracting Fractions Worksheets Whenever you are adding or subtracting fractions, the key is having both fractions having common denominators. If both fractions share a common denominator, you can simply add/subtract the numerators together, keep the denominator as is, and simplify the result if possible. For example, we could solve the problem: 1/4 + 2/4 as follows: How to Add Fractions in 3 Easy Steps Step Three: Add the numerators and find the sum. The final step is to add the numerators and keep the denominator the same: 2/9 + 4/9 = (2+4)/9 = 6/9. In this case, 6/9 is the correct answer, but this fraction can actually be reduced. Since both 6 and 9 are divisible by 3, 6/9 can be reduced to 2/3. Final Answer: 2/3. Adding Fractions Adding Fractions. A fraction like 3 4 says we have 3 out of the 4 parts the whole is divided into. To add fractions there are Three Simple Steps: Step 1: Make sure the bottom numbers (the denominators) are the same. Step 2: Add the top numbers (the numerators), put that answer over the denominator. Step 3: Simplify the fraction (if possible) Adding Fractions Lesson (Examples + Practice Problems) Here's an example of adding fractions with like denominators, using the three steps from earlier. Find the sum of 3 / 5 + 1 / 5. Solution: The denominators are already the same, so we can skip step 1. Let's add the numerators. 3 + 1 = 4, so the sum of our numerators is 4. The denominator is still 5, so our result is 4 / 5. Fraction Addition Word Problems Worksheets Evaluate 5th grade and 6th grade students' skills in adding mixed numbers with different denominators in this part of the fraction addition word problems worksheets. Convert to mixed numbers with the same denominators, and press on! Grab Worksheet 1. Try our free fraction addition word problems worksheets, replete with refreshing real-world ... Addition of Fractions (Adding like and unlike fractions with Examples) Solved Examples. Let us solve some problems based on adding fractions. Q. 1: Add 1/2 and 7/2. Solution: Given fractions: 1/2 and 7/2 Since the denominators are the same, hence we can just add the numerators here, keeping the denominator as it is. Adding & subtracting fractions word problems Word problem worksheets: Addition & subtraction of fractions. Below are three versions of our grade 4 math worksheet on adding and subtracting fractions and mixed numbers. All fractions have like denominators. Some problems will include irrelevant data so that students have to read and understand the questions, rather than simply recognizing a pattern to the solutions. Free fraction worksheets: addition, subtraction, multiplication, and Multiply fractions and mixed numbers (mixed problems, for 5th grade) Division of fractions, special case (answers are whole numbers, for 5th grade) Divide by fractions (mixed problems, for 6th grade) Add two unlike fractions (incl. negative fractions, for 7th-8th grade) Add three unlike fractions (incl. negative fractions, for 7th-8th grade) Fraction Word Problems: Addition, Subtraction, and Mixed Numbers 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 ... Fractions: Adding and Subtracting Fractions Now that we know how to write addition problems with fractions, let's practice solving a few. If you can add whole numbers, you're ready to add fractions. Click through the slideshow to learn how to add fractions. Let's continue with our previous example and add these fractions: 3/5 of cup of oil and 1/5 of a cup of oil. How to Add Fractions with Different Denominators (Step-by ... Step Two: Add the numerators together and keep the denominator. Now we have a new expression where both fractions share a common denominator: 1/4 + 1/2 → 2/8 + 4/8. Next, we have to add the numerators together and keep the denominator as follows: 2/8 + 4/8 = (2+4)/8 = 6/8. Step Three: Simplify the result if possible. Adding Fractions Practice Questions Next: Dividing Fractions Practice Questions GCSE Revision Cards. 5-a-day Workbooks Word Problems Worksheets Now you are ready to create your Word Problems Worksheet by pressing the Create Button. If You Experience Display Problems with Your Math Worksheet. Click here for More Word Problems Worksheets. This Fractions Word Problems worksheet will produce problems involving adding two fractions. Addition and Subtraction of Fraction: Methods, Facts, Examples Here are the steps to add fractions with the same denominator: Step 1: Add the numerators of the given fractions. Step 2: Keep the denominator the same. Step 3: Simplify. a c + b c = a + b c … c ≠ 0. Example 1: Find 1 4 + 2 4. 1 4 + 2 4 = 1 + 2 4 = 3 4. We can visualize this addition using a bar model: Adding and Subtracting Fraction Word Problems Adding and Subtracting Fraction Word Problems. Subject: Mathematics. Age range: 7-11. Resource type: Worksheet/Activity. File previews. docx, 18.11 KB. Here are some word-based questions for solving problems involving the addition and subtraction of fractions. Feedback greatly appreciated! Fractions Basic Introduction This math video tutorial provides a basic introduction into fractions. It explains how to add, subtract, multiply and divide fractions. It contains plenty ... Worksheet on Add and Subtract Fractions Working Rules for Addition and Subtraction of Like Fractions: Step I: Find the LCM of denominators of the given fractions. Step II: Convert unlike fractions into like fractions by making LCM as their denominator. Step III: Add or subtract the like fractions. 1. Add with the help of a fraction number line: (a) 23 2 3 + 13 1 3. (b) 3 7 3 7 + 27 2 7. 3rd Grade Math Worksheets These third grade math worksheets are perfect to help students understand, learn, and become comfortable using mathematics skills. The printable activities target advanced multi-digit addition and subtraction as well as multiplication, division, fractions, and place value. STW offers free worksheets in all of these 3rd grade topic areas. Basic Math Solution: Subtract the fractions using the same denominator: 2 5 − 1 8 = 16 40 − 5 40 = 11 40 Answer: 11 40 Problem 5) The boss wants 1 4 of the employees to work on Saturday morning and 1 6 of the employees to work on Saturday afternoon. essay homework paper phd project resume review speech thesis