problem solving involving multiplication and division of fractions

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Teaching with Jennifer Findley

Upper Elementary Teaching Blog

Fraction Word Problems | Multiplying and Dividing Fractions

Word problems + fractions = a lot of struggle for many students. Especially when you throw in new concepts like multiplying and dividing fractions. Those fraction word problems are always pretty tricky for my students. The first year that I taught multiplying and dividing fractions, I really had to spend some time breaking down the concepts myself in order to best help my students. On this post, I will share an anchor chart and a free word problem sort that helps my students solve these types of fraction word problems and see the difference/connection between the two.

Note: This is based on 5th grade standards and focuses only on multiplying fractions less than 1 and dividing with unit fractions and whole numbers. Click here to grab some free printables to help your students with solving word problems involving multiplying mixed numbers.

Teach Multiplying and Dividing Fractions with Models and a Context

Before even beginning with word problems, I always introduce multiplying and dividing fractions (separately) with a context/situation. And then we work through the situation and solve the problem/ answer the question using models . This really helps the students conceptually understand the operations. When students are only exposed to algorithms, they may not fully understand the operation. As a result, they will struggle with choosing the correct operations when solving word problems.

Here are my go-to introductory word problems for when I first introduce multiplying and dividing fractions (again I introduce each one separately). I prefer to use fudge for all of my introductory word problems because I love fudge, my students love it, the contexts make sense and are relatable, and it is almost an inside joke between us by the middle of the year. I also use student names or teacher names in the problems whenever possible and friendly fractions for easy modeling and visualizing.

Multiplying Fractions Introductory Word Problem: While shopping at a bakery, Ms. Findley purchased 1/2 of a pound of chocolate fudge. After dinner that night, she ate 1/4 of the chocolate fudge that she bought. How much of a pound of fudge did Ms. Findley eat?

Dividing Fractions Introductory Word Problem: Jamal’s mother made 1/3 of a pound of his favorite fudge, peanut butter caramel fudge. She divided the fudge into 4 equal containers. How much fudge did she put in each container?

How I Use the Introductory Word Problems: I write the problem on an anchor chart, gather my students at our mini-lesson area (around a large rug) and follow these steps:

• Read the word problem once (myself or a student).
• Read it again, if needed (based on the level of my students)
• Have the students retell the problem with partners in their own words.
• Have a few students share their retellings with the class.
• Focus on what the question is asking by writing the question in a sentence.
• Use models to demonstrate the situation in the problem (since these are new concepts for them, this part is heavily teacher driven, but typically I prefer student driven). The students practice with models as well. This can be paper folding models, visual representation drawings, or both — my favorite is both in the beginning.
• Translate the visual into a labeled equation ( read more about labeled equations here )  and answer the question.
• Discuss the answer and determine if it makes sense.
• Practice similar/same situations but with different numbers.

Reminder : I teach both of these concepts separately for about a week each.

Fraction Word Problems: Do I Divide or Multiply?

Once my students have “mastered” multiplying and dividing fractions and have seen each in a variety of contexts (through the word problems I use), they are ready to tackle both and see the connections and differences between the two. To do this, I use this anchor chart to show some of the situations and contexts that require multiplication and division of fractions. We discuss each one and how it relates back to multiplication and division.

Since it is impossible to expose students to every type of situation and context, the blurb at the end of the chart is key. The students really need to make a habit of checking to see if their answers make sense. This will help them if they choose the wrong operation.

FREE Multiplying and Dividing Fractions Word Problem Sort

In addition to the above anchor chart, we also do a word problem sort. The word problems were specifically written to match the contexts from the chart so this is a great extension of the lesson involving the anchor chart. The students read the word problems, check the chart, and then sort them accordingly. I do this activity with partners or small groups (pulling a group to work with me that may struggle based on previous assessments using exit slips ), but this could also be done as a math center activity.

My Go-To Resource for Teaching Multiplying and Dividing Fractions

The anchor chart and the sort are used after I have introduced, and we have practiced both operations in isolation. I do this by using resources from my Multiplying and Dividing Fractions resource.

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Multiplying and Dividing Fractions (And Multiplying Mixed Numbers)

This resource includes:

• Teaching Posters
• Practice Printables
• Word Problem Tasks
• and SO much more!

Want More Hands-On Math Activities and Centers?

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4th Grade Math Centers (Digital + Printable)

3rd Grade Math Centers (Digital + Printable)

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More Fraction Resources, Freebies, and Blog Posts:

Free Fraction Mats : I use these free downloadable fraction mats to support my students further as they add and subtract fractions with unlike denominators.

Free Fraction Pacing Guide: This blog post shares an “I Can” checklist for students and shares how I pace my 5th grade fraction skills.

Free Fraction Fun with Snacks Printables: If you can use food in your instruction, your students will love reviewing fraction operations (multiplication and division) using Twizzlers, skittles, and brownies.

4 Ways to Teach Students to Make Common Denominators: Read about the four ways I teach my students to find common denominators and grab a free printable.

Free Fraction Activities: Grab some super easy to prep fraction activities on this post.

Share the Knowledge!

Reader interactions.

January 19, 2019 at 10:34 pm

This is very helpful especially for new teachers. I really appreciate the free printables.

February 12, 2019 at 1:10 am

I am teaching my daughter math and this is super helpful; thank you so much!!

September 22, 2020 at 11:10 am

I like turtles

September 26, 2020 at 2:52 pm

Thank you for the printable Fraction word problem When I read something I am still unsure if you multiply or divide word problems are difficult thanks for your help

December 19, 2020 at 4:12 pm

This is excellent! As an educator sometimes I can notice that a student is still struggling with fractions

June 16, 2022 at 10:16 pm

Tomorrow, I have a math test and I was confused. This really helped me. Thank you so much

December 14, 2022 at 9:01 am

Great activity for my 6th graders! Thank you.

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I’m Jennifer Findley: a teacher, mother, and avid reader. I believe that with the right resources, mindset, and strategies, all students can achieve at high levels and learn to love learning. My goal is to provide resources and strategies to inspire you and help make this belief a reality for your students.

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Multiplying Fractions Word Problems | 10 Real Life Examples | PDF

Table of Contents

Multiplying Fractions Word Problems

I guess maybe some students get it from their parents. After all, I know that I have been known to grumble about things I learned in school, but never used in real life. I’m sure when it comes to word problems for multiplying fractions, that phrase may have passed your lips too.

But, we do multiply fractions in real life and the real world sometimes. For example, recipes! Recipes and adjusting, maybe cutting a recipe in half or doubling it, those are real world examples of multiplying fractions.

Most schools begin introducing fractions around 3rd grade, with multiplying fractions word problems beginning in 6th grade.

Here are 10 multiplying fractions word problems to work on multiplying fractions using real-life examples.

Have you ever heard, “I will never use this”?

It is important for children to see how math is used in everyday life. And word problems are one way to do this.

Multiplying Fractions

Multiplying Fractions seems like a foreign concept to many students, but it is a concept we use.

Have you ever wanted to only make 1/2 of a recipe? If so, you have probably multiplying fractions…..especially if the recipe called for 3/4 a cup of flour.

So today, we are going to finish up our multiplying fraction unit with some word problems. I am doing the activity in the post as well as some of the fraction games and activities below.

Grab my other free multiplying fractions by fractions activities.

• How to Multiply Fractions by Fractions – Step by Step Instructions with Free Printable
• Here is a Multiplying Fractions BINGO Game That’s Perfect for Extra Practice
• 3 Cut and Paste Worksheets For Multiplying Fractions Practice
• Free Printable Fraction Game For Multiplying Fractions
• Many More on my TeachersPayTeachers page for Multiplying Fractions

Preparing the Fractions Real World Problems

These task cards are easy to prepare.

• Print off on copy paper.
• Have children cut them out and glue them in their math journal.
• Finally, provide them pencils, glue, and colored pencils. and you are ready to go.

Multiplying Fractions Word Problems Example

Rachel’s  Famous  Cookies sold  2/3 as many sugar cookies as peanut butter cookies. If they sold 1/4  of a box of peanut butter cookies, how many boxes of sugar cookies did they sell?

The first step is to look at we know. We know that they sold 1/4 a box of peanut butter cookies. But they only sold 2/3 of the 1/4 when it came to the sugar cookies.

So if we want to start with a diagram, we can begin by drawing a box of cookies and coloring in 1/4.

Many students require a multisensory approach to learning. It’s not just enough to talk about something and hear it. They have to see it. This activity works as a visual graphic organizer of sorts, so that the student can visualize what is going on.

Next, we can color in 2/3.

Finally, we look and see what part overlaps, and this is the answer! Two out of the 12 squares overlap, so our answer is 2/12 or 1/6 when the fraction is simplified . But using the squares on the paper and coloring with overlap, we have completed our first multiplying fractions word problem.

Using Fractions in Real Life

I’m a firm believer that children should not be given multiplying fractions word problems that require the same operation each time.

That is not real life, and that does teach them to learn what needs to be done to solve the problem. We need to give them the confidence that they can apply this knowledge to different situations and word problems.

That’s why I am including more than that in the multiplying fractions word problems worksheets.

So even though this printable is for practicing multiplying fractions with word problems there are a few word problems where multiplication is not used. Here is one example.

Luciana gave 1/4 of the cake to one friend, and 1/3 another friend. How much of the cake is left if she started with a whole cake?

This word problem has the children subtracting to figure out the answer.

• We know that Luciana started with a whole cake, which equals one. So we want to begin by drawing a square.
• The next thing we have to figure out is how many parts we need to divide it up into. Since we now we will be subtracting 1/4 and 1/3 we will need to get the Least Common Multiple. The multiples of three and four are…..

4: 4, 8, 12

3: 3, 6, 9, 12

As you can see 12 is the least common multiple. So our square needs to have 12 equal parts.

3. Next, we will need to find equivalent fractions for both of our fractions.

1/4 x 3/3 = 3/12 and 1/3 x 4/4 = 4/12.

4. Now all that is left is to subtract 3 part and then 4 parts.

5. Finally, we can see that there 5/12 of the cake left.

Word Problems are an important part of math instruction, and how we do math in everyday life. Enjoy working through these real life problems with your children.

The printable that accompanies this activity is below. Here you go, your free multiplying fractions word problems PDF. This free printable includes multiplying fractions word problems with answers.

You’ve Got This!

Get more fractions activities by ordering a workbook (but hey, nothing beats a free printable!)

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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.

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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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Word Problems with Division of Fractions

Today we are going to look at problems involving the division of fractions. 

Are you ready to begin? Well, the first thing that we must remember is that in a problem with fractions we should follow all the necessary steps to solve any problem , only we have to add a step for the simplification of the result:

• Read the problem carefully.
• Think about what it asks us.
• Think about the details we need.
• Carry out the operation. In this case, you should know how to divide fractions
• Simplify the results, if possible.
• Think about whether the result makes sense.

Now that we have already recalled what is fundamental for solving a problem with fractions, we can move on to review word problems with division of fractions . We will look at a problem where it is necessary to divide fractions to solve.

Let’s look at an example:

Priscilla bought cheese that weighs ¾ pounds. If she divides it into portions that are each 1/8 pound, how many portions can she make?

The first thing we should do are steps 1, 2, and 3: read carefully, understand the question, and think about the relevant details.

Priscilla bought cheese that weighs ¾ of a pound. If she divides it into portions that are each 1/8 of a pound, how many portions can she make?

That is to say…

If she divided ¾ of a pound into equal portions of 1/8 of a pound, how many portions did she make?

We already know that the operation is division. We are going to move on to steps 4 and 5 (solve and simplify).

We divide by taking the reciprocal of the second fraction and multiplying:

Then we simplify:

She made 6 portions.

Now, all we have left is to check that the solution makes sense, and we have solved the problem!

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Dividing fractions word problems

Dividing fractions word problems arise in numerous situations. We will show you some examples. I recommend that you review the lesson about division of fractions before starting this lesson.

Dividing fractions word problems: a few examples

3 friends share 4/5 of a pizza. what fraction of pizza does each person get?

The amount to share is 4/5

Since the amount will be shared between 3 friends, the amount must be divided between 3 people.

So each person must get 4/5 divided by 3

(4 / 5) / 3 = (4 / 5) / (3 / 1) = 4 / 5 × 1 / 3 = (4 × 1) / (5 × 3)= 4 / 15

Each person will eat 4/15.

Indeed, 4 / 15 + 4 / 15 + 4 / 15 = 12 / 15 = 4/5 (divide 12 and 15 by 3 to get 4 / 5)

On June 21st, there were 9/10 of a billion stars visible to the naked eye.

On December 21st, there were 4/5 of a billion stars out visible to the naked eye.

How many times more stars were there visible on June 21st than December 21st?

9/10 divided by 4/5 = ?

Find the reciprocal of the divisor.

9/10 × 5/4 = ?

9/10 × 5/4 = 9/2 × 1/4

Solve 9/2 × 1/4 = 9/8

Simplify again

Did you have a hard time understanding the problems above? Did you not understand them at all? Take a look at this figure !

Do you need to master fractions once and for all? Check out my book about fractions .

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Mathematics 5 Quarter 1 – Module 17: Solving Problems Involving Division of Fractions

Good day, Mathletes!

In this module, you are going to learn to solve word problems involving division of fractions by following the four-step plan: understand, plan, solve, and check. By doing the steps, you will solve word problems in a systematic and logical way.

At the end of this module, you are expected to:

• define and solve word problems using any operations and strategies; and

• solve routine or non-routine problems involving division without or with any of the other operations of fractions and whole numbers using appropriate problem-solving strategies and tools. M5NS-Ij-97.1

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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.

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Fractions: mixed operations

Fraction word problems with the 4 operations.

These word problems involve the 4 basic operations ( addition, subtraction, multiplication and division ) on fractions .  Mixing word problems encourages students to read and think about the questions, rather than simply recognizing a pattern to the solutions.  

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Multiplying Fractions Words Problems

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37 Math Problems For 3rd Graders: Answers With Worked Examples

Michele Bell

3rd grade math problems formally introduce 3rd graders to math skills such as multiplication, division, and fractions. They build on learners’ conceptual understanding of partitioning shapes and using repeated addition with concrete models, drawings, and expressions, learned in previous grades, to make connections using symbols, letters for unknown numbers, and equations.

In this blog, we look closely at the essential math skills a third grader needs to know and provide math problems, worked examples, and teaching tips, to help teachers and educators support their third-grade students in mathematics.

What are math problems for 3rd graders?

3rd grade math problems are specific math problems suitable for 8-9 year olds. They include the following math concepts: 

• Subtraction
• Multiplication
• Place Value
• Measurement and Data
• Geometrical Shapes

16 Fun Math Games and Activities Pack for 3rd Grade

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Benefits of math problems for 3rd graders

3rd graders can use these math problems to build on their prior knowledge of addition and subtraction developed in Kindergarten, 1st  and 2nd grade. 

The math concept of repeated addition, learned in 2nd grade, directly links to their understanding of multiplication through models learned in the 3rd grade such as equal groups and arrays. 

Many 3rd grade math concepts they focus on strengthen their foundation in fraction concepts and set them up for success with fraction operations explored in 4th grade and 5th grade .  

Word problems help students make connections between representations and develop students understanding of the relationship between addition and subtraction or multiplication and division.

Multiplication word problems are just one example of word problems used to deepen students’ understanding of each operation. Educators should incorporate word problems through all phases of teaching each concept, not just near the end of a unit when learners appear ready to “apply” their learning. 

3rd grade math curriculum 

The topics focused on in third-grade math include: 

• Addition within 1,000
• Subtraction within 1,000
• Whole number multiplication
• Whole number division
• Understanding fractions
• Rounding to the nearest 10 or 100
• Elapsed time
• Representing and Interpreting Data
• Describing Quadrilaterals

How the 3rd grade math curriculum fits into learners’ math development 

3rd grade students extend their 2nd grade knowledge of adding and subtracting within 100 to include adding and subtracting within 1,000 using place value strategies and properties of operations. 

Learners continue to build on equal sharing from 1st grade and learn about unit fractions and the meaning of the numerator and denominator. This sets them up for success with fraction operations in 4th and 5th grade.

Common challenges teaching third graders

As 3rd graders use all four operations, a common challenge for some is mixing up which operation to use when problem solving. They may focus on one word in a word problem instead of considering the entire problem. 

Concrete models and representations can help students work through problems by showing the actions happening in a problem situation. However, as they get older, some students may also want to reduce their use of math manipulatives to build concrete models or draw pictures to show their thinking leaving room for error. 

Teach students to visually show their thinking through models or pictures, or express it with words and numbers instead of keeping it in their head. 

Math problems for 3rd graders with answers

Here are 34 math problems for 3rd graders organized by topic, including:

Addition math problems for 3rd graders 

In 3rd grade, students build on addition skills from K-2nd grade and are expected to add fluently within 1,000. This can include one-digit numbers, two-digit numbers and three-digit numbers.

Question 1 

A local charity collected 356 canned food items in September. They collected 419 canned food items in October. How many canned food items did they collect during the two months?

Answer: 775

Students apply strategies based on place value when solving multi-digit addition problems. A place value chart is a great tool to help organize and record their thinking as they work with values that may require regrouping. 

In this problem, students solve an addition problem that involves regrouping in one place, from ten ones to one ten.

Jessica and Caleb were both sharing their baseball card collections with their class. Jessica has 435 baseball cards in her collection and Caleb has 482 baseball cards in his collection. How many total baseball cards did they both collect?  

Answer: 917

An open number line is another valuable tool that students can draw on anytime. They can use multiple addition strategies on a number line. For example, they might start with an amount and then add on the hundreds, tens and ones of the second number. 

Another strategy is adding the hundreds from both addends, then the tens, and the ones. No matter the strategy, number lines are great visuals for students to record their thinking and refer back to it in their explanations.

Sabrina had 267 beads to use for making bracelets. Her mom bought her a new pack of 135 beads. How many beads does Sabrina have now?

Answer: 402 beads

This problem requires regrouping of ones to tens, and tens to hundreds. Students should have experience regrouping in one or more places when adding within 1,000. 

The partial sum strategy helps set the foundation for using an algorithm in fourth grade to add greater multi-digit numbers.

Subtraction math problems for 3rd graders

As with addition, students build on their subtraction knowledge from K-2nd grade and use single-digit subtraction and subtracting 2-digit numbers within 100 to develop fluency in subtracting within 1,000. This can include up to 3-digit numbers. 

Although students have used subtraction since Kindergarten, it can still be difficult for many students. Providing students with multiple strategies and methods for solving with subtraction allows them to choose the most efficient method move towards fluency, which includes: 

• Efficiency 

283 guests were waiting to ride a ferry boat to get to the entrance of a theme park across the lake.  Only 155 guests can ride the ferry boat at a time. How many guests will have to wait for the next ferry boat to arrive?

Answer: 128 guests

When completing subtraction word problems, make connections between strategies students use to add within 1,000 and subtract within 1,000. This strengthens their understanding of the relationship between addition and subtraction, and place value. 

Similarly to addition, students can use a place value chart to help them with regrouping when subtracting 2 or 3-digit numbers. In this problem, students need to regroup 1 ten for 10 ones.

Andrew and his family drove 607 miles to get to their hotel. They made one stop after driving for 312 miles. How many more miles did they have to drive to get to the hotel?

Answer: 295

Using a number line to subtract, or count back, may confuse some students. Remind students to use strategies that make sense to them. They may start with one number and subtract the hundreds, tens, and then ones of the second number. 

Some students prefer to subtract using place value, while others subtract until they get to a multiple of 10 and continue subtracting from there.

Josie had $168 at the beginning of the week. She spent $27 at the mall on Tuesday. She worked on Thursday and earned some money. She ended the week with $195. How much money did she earn on Thursday?

Answer: $54

This problem includes both addition and subtraction and provides an opportunity for students to write an equation using a letter as the unknown value. Students can use the relationship between addition and subtraction to determine what the letter represents.

168 – 27 + s = 195

141 + s = 195

195 – 141 = s

Multiplication math problems for 3rd graders

Many third-grade standards group multiplication and division together. When students are officially introduced to both operations, typically multiplication is first. 

Learners develop an understanding of multiplication using concrete models, pictures, and equations when solving word problems. 

In 3rd grade, they solve word problems that lend themselves to making equal groups, arrays, or finding the area as a measurement. 

Other multiplication concepts that 3rd grade students will explore include:

• Properties of operations 
• Finding an unknown product 
• Solving one or two-step word problems that involve more than one operation

There are 8 dry-erase markers in one pack. How many dry-erase markers are in 3 packs?  

3rd graders explore equal groups. They can do this using an array. Students must understand that the one factor is the number of groups and the other is the number in each group.  

For example, 3 x 8 can be represented using the following array: 

Find the product of 5 x 3 x 4

Learners explore associative property in 3rd grade as well as commutative property and distributive property.

When evaluating multiplication expressions with three or more factors, students learn that the way they group the factors to multiply does not change the value of the product. 

Encourage students to start with the two factors that seem the friendliest to multiply, but to also keep in mind how confident they will feel when multiplying the product of those two factors with the next factor in the expression.

Other properties of multiplication that students will explore in 3rd grade include the:

• commutative property
• distributive property
• identity property
• zero property

Find the product of 7 x 40.

Answer: 280

7 x 40 = 7 x 4 tens 

7 x 4 tens = 28 tens 

28 tens = 280

7 x 40 = 280

Question 10

The school music teacher set up his classroom for an after-school chorus rehearsal. He formed 3 rows with 12 chairs in each row. How many chairs are in the classroom in total?

Answer: 36 chairs

Allow students to choose their method, whether it’s using manipulatives or drawing pictures to represent the information in word problems. 

Ask them where they see each value in their concrete model or picture.

Division math problems for 3rd graders

Many multiplication strategies are closely related to division problem strategies. Third graders must understand the relationship between multiplication and division to use it as a strategy for problem-solving. This helps with math problems that involve finding an unknown. 

Third graders learn to write a blank, question mark, or letter when there is an unknown product, quotient, or factor. This aids them when writing a related equation using a known math fact with an operation they are comfortable with. 

Question 11

Zoe has 42 stickers. She wants to give 7 stickers to each of her friends at her birthday party. How many friends are at her birthday party?

Answer: 6 friends

Once students begin working with division, they tend to focus on specific keywords such as “each” and think that the problem represents multiplication. Students must model the actions of what is happening in the problem. Giving the same amount out multiple times will highlight the division and sharing equal amounts. 

Encourage students to build and draw models to show their thinking. Ask them to explain their strategy to you, a partner, or the class for solving division word problems such as this one. 

Question 12

There are 3 boxes on each shelf in the backroom of a bookstore. 36 new boxes were delivered and must be placed on the 4 shelves. How many total boxes are on each shelf? 

Extend students’ understanding of multiplication and division by pairing multiplication and division together, or with addition or subtraction. This enables students to solve two-step problems represented as an expression or equation. 

Follow-up discussions to help students understand which operation they should solve first to set them up for success with the order of operations in fifth grade and beyond.

Question 13

George ran 63 miles last week. If he ran every day last week, how many miles did he run each day?

Answer: 9 miles

Writing an equation to represent math word problems supports learners’ understanding of the relationship between multiplication and division. 

When learners write a division equation using a letter or question mark for the unknown number, they can rewrite the expression as a multiplication expression if they aren’t confident with division facts. 

A familiar multiplication equation may lead third graders to use mental math once they’re fluent with multiplication facts.

Question 14

Determine what the ? represents in the equation. 48 6 = ?

48 ➗ 6 = ? 

6 x ? = 48 

6 x 8 = 48 

Rounding math problems for 3rd graders 

The third place value concept covered in third grade is rounding. Third-grade math requires students to use their place value understanding to round whole numbers to the nearest 10 or 100. 

Understanding the value of digits in a number is important when rounding because it helps to determine which 10 or 100 a whole number is closest to. 

Question 15

Round 27 to the nearest 10.

Using a number line with a midpoint and two endpoints helps students visualize which tens or hundreds a whole number falls between. 

Although number lines are not required to be used as a strategy in 3rd grade, they can be used to help students develop their rounding skills conceptually.

Question 16

Round 639 to the nearest 100

Answer: 600

Question 17

Round 450 to the nearest 100

Answer: 500

In some instances, a value is directly in the middle of the tens or hundreds. However, learners should know that if the digit being rounded is 5 or larger, then it must round up. 4 or less and the digit rounds down. 

Fraction math problems for 3rd graders

Students build on their fraction knowledge form 1st and 2nd grade, including: 

• Partitioning shapes into equal shares by exploring unit fractions 
• The meaning of the numerator and the denominator

3rd graders should have plenty of opportunities to represent fractions by building concrete models and drawing pictures before they are required to write fraction notations. 

Using fraction vocabulary such as halves, thirds, fourths, parts and parts of a whole helps students make sense of fractions as part of a number before writing the numerator above the denominator with a fraction bar in between. 

Facilitate discussions involving unit fractions and how the non-unit fractions are the sum of multiple unit fractions.

Question 18

Represent the fraction \frac{3}{4} by drawing a model.

Question 19

Count the parts and label each tick mark on the number line: 

\frac{1}{8} , \frac{2}{8} , \frac{3}{8} , \frac{4}{8} , \frac{5}{8} , \frac{6}{8} , \frac{7}{8} , \frac{8}{8}

Discuss with students that the intervals or spaces between the tick marks represent the distance from one tick mark to the next tick mark or a unit fraction such as \frac{1}{8} . 

The distance from zero to that point or tick mark is a different value labeled with a specific fractional value, such as \frac{5}{8} .

Fraction problems for 3rd graders

Question 20.

Select the equivalent models.

Answer: C and E

Equivalent fractions in third grade focus on visual models preparing them to explore finding equivalent fractions through operations in the fourth grade.

Question 21

Which is greater, \frac{4}{8} or \frac{4}{6} ? Write a comparison statement using the symbols >, =, or <.

Answer: \frac{4}{8} < \frac{4}{6}

Time math problems for 3rd graders

In third-grade math, students learn to tell time to the nearest minute on digital and analog clocks. 

They use their understanding of time to determine an elapsed time when given a start and stop time for an event or sequence of activities. 

Students explore using number lines to help them understand elapsed time word problems . These can include:

• Start and stop time given, elapsed time unknown
• Start and elapsed time given, stop time unknown
• Elapsed time and stop time given, start time unknown

Question 22

Represent the time shown on the digital clock by drawing on the analog clock. 

Answer: 

Question 23

It is 10:50 a.m. and lunch begins in 15 minutes. What time will it be? Use the number line to show the time.

Answer: 11:05 a.m.

Students should use the number line to determine time in a way that makes sense. 

Question 24

On Saturday, Angela left the park at 2:45 p.m. where she attended soccer practice for 75 minutes. What time did Soccer practice begin?

Answer: 1:30 p.m.

Working backwards to determine a time may seem challenging for some students. They may use a number line to subtract whole numbers. 

Pay attention to how students maneuver counting back in time from the 1 o’clock hour into the 12 o’clock or morning time.

Data math problems for 3rd graders

Third-grade math develops the concept of collecting and representing data from previous grades. Students must: 

• Ask and answer questions
• Ceate tally charts
• Draw picture graphs and bar graphs
• Learn about line plots

In third grade, students use larger values and scales to represent their data than in previous grades. They also answer one and two-step word problems about information presented in graphs.

Question 25 

 How many more cloudy days were there than rainy days in March?

Answer: 5 days

In grade 3, students create and read graphs with scales greater than 1. If they struggle to interpret the information on a bar or picture graph, they can add tick marks between the intervals to count accurately.

Question 26

The students in Mrs. Campbell’s class voted on which animal should be their class mascot. The votes are shown on the graph. 

How many fewer students voted for an animal that lives in the ocean than an animal that lives on land? 

Answer: 4 students

(8 + 6) – 10= 4

Provide students with opportunities to solve one and two-step problems involving a picture or bar graph. 

Problems should relate directly to “How many more?” and “How many less?” questions.

Question 27 

What is the length of the pencil measured to the nearest half or quarter of an inch?

Answer: 6 \frac{1}{2} inches

3rd grade students explore measuring objects with a ruler marked with halves and fourths of an inch. Examples like this bring math into real-life scenarios for working with fraction values.  Students can see and hear how the terms fourths and quarters are used interchangeably regarding measurement.

Question 28 

Create a line graph to display the collected data.

Students are introduced to line plots with whole number units in the 2nd grade. In the 3rd grade, students measure units to the nearest half or fourth and record the measurement of objects on line plots. 

They extend their understanding of representing information on a line plot in 4th and 5th grade where they solve problems involving fraction operations.

Area math problems for 3rd graders

Students apply their understanding of multiplication and division while exploring the area of two-dimensional shapes. Area is an attribute of 2-D shapes and multiple strategies can be used to find it. 

Question 29

Find the area of the rectangle.

Answer: 48 square units

Question 30

Jillian has a new painting to hang in her bedroom. The side lengths of the painting are 7 in. and 4 in. What is the area of the painting?

Answer: 28 square inches 

Students must understand that counting the number of tiles arranged as an array is the same as multiplying two of the given side lengths for a rectangle.

Question 31

Find the total area of the figure.

Answer: 10 square inches

(2 x 3) + (4 x 1)

Learners apply their understanding of area to determine the area of rectilinear figures: figures composed of more than one rectangle. 

A common misconception for some students is to multiply all of the side lengths. This is a great opportunity to relate the area to the distributive property by decomposing the figure into two separate rectangles. Then they can determine the area of each rectangle and add the two values together to find the total area. 

Perimeter math problems for 3rd graders

3rd graders explore the perimeter of shape, how to work it out and how it differs from the area. 

A common misconception for third graders, that sometimes carries on into fourth grade and fifth grade, is mixing up area and perimeter. Take the time to allow students to explore and discuss examples and non-examples of area and perimeter in the real world and around the classroom.

Question 32

Find the perimeter of the bulletin board.

Answer: 160 inches

Students need to add all of the side lengths together: 

45 + 45 + 35 +35 = 160

Question 33

The school garden has one side length of 13 feet. The perimeter of the garden is 40 feet. How long is the other side length?

Answer: 7 feet

13 + 13 + s + s = 40  

(2 x 13) + (2 x s ) = 40  

26 + (2 x s ) = 40 

40 – 26 = 2 x s   

Question 34

• Which rectangles have the same perimeters but different areas? 
• Which rectangles have the same area but different perimeters?

• Rectangles 3 and 4 have the same perimeters and different areas. 
• Rectangles 2 and 3 have the same area and different perimeters.

Reminder students the perimeter is the distance around the outside of a shape or object and the area is the number of square units needed to cover the space of the shape or object.

Rectangle 1 : side length = 2, side length = 12 

Perimeter: 12 + 12 + 2 + 2 = 28

Area : 2 x 12 = 24

Rectangle 2: side length = 6, side length = 6

Perimeter: 6 + 6 + 6 + 6 = 24

Area : 6 x 6 = 36

Rectangle 3: side length = 4, side length = 9

Perimeter: 9 + 9 + 4 + 4 = 26

Area : 4 x 9 = 36

Rectangle 4: side length = 6, side length = 7

Perimeter: 6 + 6 + 7 + 7 = 26

Area : 6 x 7 = 42

Geometry problems for 3rd graders

Describing, analyzing, and comparing properties of 2D shapes is one of the main concepts of geometry in third-grade math. 

3rd graders must determine whether shapes are considered quadrilaterals from the number of their sides. They describe and draw examples of specific quadrilaterals such as a rectangle and a rhombus and sort shapes according to their sides, angles, and other characteristics. 

This sets a foundation for further investigation of quadrilaterals and triangles in fourth grade and fifth grade where they learn about the hierarchy of quadrilaterals.

Question 35

How many of the shapes are quadrilaterals?

Answer: 5 are quadrilaterals

Provide printouts of the shapes and allow students to cut and sort the shapes into groups such as quadrilaterals or non-quadrilaterals. 

Students may also draw a circle around shapes with four sides.

Question 36

Count and record the number of quadrilaterals with:

• 0 pairs of parallel sides

1 pair of parallel sides

2 pairs of parallel sides

0 parallel sides 

Question 37

Draw the following 2D shapes: 

• A quadrilateral that is not a parallelogram or trapezoids.

Possible extension: ask students to explain why the shape they have drawn is an example of that specific shape.

3 top tips for teaching math problems to 3rd graders

• When exploring multiplication and division concepts, provide multiple opportunities for students to make connections between models, representations, and equations.  Present learners with real-life word problems. Have students use math manipulatives to build concrete models and draw pictures that represent their model and the word problem. Next, ask them to write an equation representing the word problem and their models. Last, prompt students to explain how all three pieces of their work represent the word problem and how they used each to solve the problem.
• Remember the CRA model: Concrete, Representation, Abstract. Understanding multiplication, division, and fractions starts at the concrete phase in 3rd grade, moves into the representation phase, and has many opportunities for the abstract phase. Other skills such as fluently adding and subtracting within 1,000 focus on the representation and abstract phases. There may be some students who need more time in the concrete phase, using manipulatives while others may be more comfortable with drawing pictures and number lines or using the relationship between addition and subtraction as their strategies. Students should always use strategies and models that make sense to them.
• Teach multiplication facts using positive experiences. Avoid focusing on memorization drill worksheets and multiplication tables. Instead provide opportunities to practice in meaningful ways using games, real-world problems, partner and group discussions, and reasoning with manipulatives.

How can Third Space Learning help with 3rd grade math?

STEM-specialist tutors help close learning gaps and address misconceptions for struggling 3rd grade math students. One-on-one online math tutoring sessions help students deepen their understanding of the math curriculum and keep up with difficult math concepts.

Each student works with a private tutor who adapts instruction and math lesson content in real-time according to the student’s needs to accelerate learning.

3rd grade math worksheets and resources 

Looking for more resources? Check out our math games and selection of second grade addition and subtraction worksheets, posters and activities covering the key 3rd grade math topics and more:

• 3rd Grade Fractions Error Analysis  
• 3rd Grade Addition And Subtraction Code Crackers
• 3rd Grade Place Value and Rounding Word Problems
• 3rd Grade CCSS Practice Test 

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