dividing fractions by whole numbers problem solving

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Dividing Fractions Word Problems Worksheets

Toss off solutions to our pdf worksheets on dividing fractions word problems to foster a sense of excellence in identifying the dividend and the divisor and solving word problems on fraction division. Equipped with answer key, our worksheets get children in grade 5, grade 6, and grade 7 rattling their way through the division of fractions and mixed numbers in regular and themed problems. A flurry of everyday scenarios, our free worksheet for dividing fractions word problems is worth a shot!

Dividing Fractions and Whole Numbers Word Problems

Prepare the child through and through so they divide fractions and whole numbers with word problems. Let them take the reciprocal of the divisor and multiply it with the dividend, and they’re good to go!

• Download the set

Dividing Fractions by Cross Cancelling Word Problems

Exceed every learning expectation with our dividing fractions word problems worksheets! Apply cross cancellation after inverting the divisor, find products of what's left, and do write the correct units.

Dividing Mixed Numbers Word Problems

Give 5th grade and 6th grade students a good round of practice to hone their skills in fraction division. Convert mixed numbers into improper fractions, and proceed to divide them as usual.

Dividing Mixed Numbers and Fractions Word Problems

The road to mastery in word problems on dividing mixed numbers and fractions is made smooth with our printable worksheets. Read the problems, identify the dividends and divisors, and find the answers.

Themed Fraction Division Word Problems

If grade 6 and grade 7 learners are bent on proving they're real gifted at tackling fraction division, nothing can stop them! With our themed word problems pdfs, problem-solving is at its most exciting.

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» Adding Fractions Word Problems

» Subtracting Fractions Word Problems

» Multiplying Fractions Word Problems

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Dividing Fractions By Whole Numbers

To divide a fraction by a whole number:.

• Step 1. Multiply the bottom number of the fraction by the whole number
• Step 2. Simplify the fraction (if needed)

1 2   ÷  3

Step 1. Multiply the bottom of the fraction by the whole number:

1 2 × 3

Which equals:

Step 2. Fraction is already as simple as possible, so no need for step 2.

1 2   ÷  3  =   1 6

With Pen and Paper

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

Does it make sense?

Does   1 2   ÷  3 really equal   1 6   ?

Well look at the pizzas below ...

When half a pizza is divided into 3 equal parts, each person gets one sixth of a whole pizza.

Another example:

2 5 × 4   =   2 20

Step 2. Simplify the fraction:

2 20   =   1 10

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Divide Whole Numbers by Fractions

Welcome to our support page to help you learn How to Divide Whole Numbers by Fractions page.

On this page, we have a range of free printable sheets to help your child learn to divide integers (or whole numbers) by fractions.

Take a look at our worked examples or have a go at our practice sheets!

We also have a calculator which will not only give you the answer, but also show you all the working out along the way!

If you need support to divide fractions by other fractions, use the link below.

• How to Divide fractions page

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• Dividing Whole Numbers By Fractions Introduction
• Dividing Fraction Calculator
• Dividing Whole Numbers by Unit Fractions
• Dividing Whole Numbers By Fractions Worksheets
• Dividing Fractions (by Fractions) Worksheets
• Dividing Mixed Fractions
• More Recommended Resources
• Dividing Whole Numbers By Fractions Quiz

Dividing Whole Numbers by Fractions

On this page, you will learn how to divide a whole number by a fraction, and also some practice worksheets designed to help your master this skill.

The sheets are carefully graded so that the easiest sheets come first, and the most difficult sheet is the last one.

We have split the sheets into two main sections:

• Dividing Whole Numbers by Non-unit Fractions

Before your child tackles dividing whole numbers by fractions, they should be confident with multiplying fractions, and also converting mixed fractions to improper fractions and reducing fractions to simplest form.

Using these sheets will help your child to:

• divide a whole number by a fraction;
• apply their understanding of simplest form;
• convert an improper fraction to a mixed number.

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Dividing Fractions Calculator

If you want to divide any fractions, you can use our Free Divide Fractions calculator.

The calculator will help you dividing whole numbers by fractions, or fractions by other fractions or mixed numbers.

The best thing about the calculator is that it also shows you all the working out along the way.

• Divide Fractions Calculator

Divide Whole Numbers by Fractions Support

Frazer says "To divide a whole number by a fraction, follow these 4 easy steps."

Change the whole number to a fraction by putting it over a denominator of 1.

If any of the fractions are mixed fractions (or mixed numbers), then convert them into improper fractions.

Swap the numerator and denominator of the dividend fraction (the fraction after the ÷ sign) and change the operator to a 'x' instead of a '÷ '

Multiply the numerators of the fractions together, and the denominators of the fractions together. This will give you the answer.

Simplify the fraction.

For those of you who like to see the algebra:

Formula for dividing a whole number by a fraction.

\[a \div {b \over c} \; = \; {a \over 1} \times {c \over b} \; = \; {a \times c \over 1 \times b} \; = \; {ac \over b} \]

Examples of Dividing Whole Numbers by Fractions

Example 1) work out: \[ 6 \div {3 \over 4} \].

Put the integer over a denominator of 1.

So this gives us: \[ 6 \div {3 \over 4} \; = \; {6 \over 1} \div {3 \over 4} \]

Invert the dividend fraction and change the operation to multiplication.

So we now have \[ {6 \over 1} \div {3 \over 4} \; = \; {6 \over 1} \times {4 \over 3}\]

Now multiply the fractions:

\[{6 \over 1} \times {4 \over 3} \; = \; {6 \times 4 \over 1 \times 3} \; = \; {24 \over 3} \]

Simplify the answer.

\[ {24 \over 3} \; = \; 8 \]

Final answer: \[ 6 \div {3 \over 4} \; = \; 8 \]

Example 2) Work out: \[ 4 \div {5 \over 9} \]

So this gives us: \[ 4 \div {5 \over 9} \; = \; {4 \over 1} \div {5 \over 9} \]

So we now have \[{4 \over 1} \div {5 \over 9} \; = \; {4 \over 1} \times {9 \over 5} \]

\[{4 \over 1} \times {9 \over 5} \; = \; {4 \times 9 \over 1 \times 5} \; = \; {36 \over 5} \]

This fraction is already in simplest form, but we can convert it to a mixed number.

\[ {36 \over 5} \; = \; 7 {1 \over 5} \]

Final answer: \[ 4 \div {5 \over 9} \; = \; {36 \over 5} \; or \; 7 {1 \over 5} \]

Example 3) Work out: \[ 10 \div 2 {2 \over 3} \]

Convert the mixed number to an improper fraction and put the integer over a denominator of 1.

As an improper fraction: \[ 2 {2 \over 3} \; = \; {8 \over 3} \]

So this gives us: \[ 10 \div 2 {2 \over 3} \; = \; {10 \over 1} \div {8 \over 3} \]

So we now have \[{10 \over 1} \div {8 \over 3} \; = \; {10 \over 1} \times {3 \over 8} \]

\[{10 \over 1} \times {3 \over 8} \; = \; {10 \times 3 \over 1 \times 8} \; = \; {30 \over 8} \]

This fraction needs to be simplified and can also be written as a mixed number.

\[ {30 \over 8} \; = \; {15 \over 4} \; = \; 3 {3 \over 4} \]

Final answer: \[10 \div 2 {2 \over 3} \; = \; {15 \over 4} \; or \; 3 {3 \over 4} \]

• How to Divide Whole Numbers by Fractions Support Page

We have created a support page to help you understand how to divide whole numbers by fractions with some examples.

It is quick and easy to print, and has all the information on one page.

• PDF version

Dividing Whole Number by Unit Fractions

A unit fraction is a fraction which has a numerator of 1.

Dividing whole numbers by unit fractions is a Common Core objective for 5th grade.

Our sheets are carefully graded and get gradually harder.

Our first two worksheets have been designed to introduce this concept, and include using visual models to aid understanding.

Sheet 3 is for children who are confident with this process and need some practice.

Sheet 4 is trickier and involves finding the missing number or fraction in the equation.

Sheet 5 consists of a series of challenges which involve using the skill of dividing whole numbers by unit fractions.

Dividing Whole Numbers by Unit Fractions Worksheets

• Dividing Whole Numbers by Unit Fractions 1
• Dividing Whole Numbers by Unit Fractions 2
• Dividing Whole Numbers by Unit Fractions 3
• Dividing Whole Numbers by Unit Fractions 4
• Dividing Whole Numbers by Unit Fractions 5

Dividing Whole Numbers by Fractions Worksheets

Dividing whole numbers by fractions worksheets using models.

These fraction sheets have fraction strips to help you find the number of times the fraction goes into the whole number.

• Divide Whole Numbers by Fractions using Models Sheet 1
• Divide Whole Numbers by Fractions using Models Sheet 2

Dividing Whole Numbers by Fractions Worksheets without Models

The first 3 sheets involve dividing whole numbers by proper fractions.

Sheets 4 & 5 involve dividing whole numbers by mixed numbers.

Use these sheets to practice your division of whole by fractions.

• Divide Whole Numbers by Fractions 1
• Divide Whole Numbers by Fractions 2
• Divide Whole Numbers by Fractions 3
• Divide Whole Numbers by Fractions 4
• Divide Whole Numbers by Fractions 5

Dividing by Whole Numbers and Fractions

These sheets involve both dividing whole numbers by fractions and also dividing fractions by whole numbers.

The first two sheets involve dividing by proper and improper fractions.

Sheet 3 involves dividing by mixed numbers.

Use these sheets to practice your division of whole by fractions and also division of fractions by whole numbers.

• Dividing by Whole Numbers and Fractions 1
• Dividing by Whole Numbers and Fractions 2
• Dividing by Whole Numbers and Fractions 3

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Multiplying and Dividing Fractions Support Pages

The links below will take you to our support pages for multiplying and dividing fractions.

All the support pages contain detailed explanations and some worked examples.

• Dividing Fractions by Whole numbers

• How do you Multiply Fractions Support

• How to Divide Fractions Support
• How to Divide Mixed Numbers

Multiplying and Dividing Fractions Worksheets

The links below will take you to our worksheets for multiplying and dividing fractions.

The worksheets are all carefully graded and have different levels of support for students.

• Multiplying Fractions Worksheets (not mixed)
• Multiplying Mixed Fractions Worksheets
• Dividing Fractions Worksheets
• Dividing Mixed Fractions Worksheets

Converting Improper Fractions

Here you will find a selection of Fraction worksheets designed to help your child understand how to convert an improper fraction to a mixed number.

• convert an improper fraction to a mixed number;
• convert a mixed number to an improper fraction.

• Convert Improper Fractions

How to Convert to Simplest Form

Here you will find a selection of Fraction worksheets designed to help your child understand how to convert a fraction to its simplest form.

• develop an understanding of equivalent fractions;
• know when a fraction is in its simplest form;
• convert a fraction to its simplest form.
• How to Simplify Fractions support page

Fractions Adding and Subtracting Generated Sheets

We have created a random generator for making your own adding and subtracting fractions worksheets.

You can change your fraction values, choose whether you want like or unlike denominators or change from proper to improper fractions.

• Fractions Adding and Subtracting Worksheets (randomly generated)

Dividing Whole Numbers by Fractions Online Quiz

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

We do not collect any personal data from our quizzes, except in the 'First Name' and 'Group/Class' fields which are both optional and only used for teachers to identify students within their educational setting.

We also collect the results from the quizzes which we use to help us to develop our resources and give us insight into future resources to create.

For more information on the information we collect, please take a look at our Privacy Policy

We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick quiz tests your understanding and skill at dividing whole numbers by fractions.

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Dividing Fractions with Whole Numbers

Dividing fractions with whole numbers is done by multiplying the whole number with the denominator of the given fraction. In the general form, it can be understood as, x/y ÷ a = x/ya, where x/y is the fraction and 'a' is any whole number. Let us learn about dividing fractions with whole numbers in this article along with interesting games, worksheets, and examples.

Steps of Dividing Fractions with Whole Numbers

Dividing fractions with whole numbers results in a value less than the given fraction . It is because we are dividing it into smaller equal parts and the quotient obtained will be the value of one part out of those. For example, if we say that divide 2/3 into 4 equal parts. It means we are breaking 2/3 into 4 equal parts and the answer will be the value of one such part. So, 2/3 ÷ 4 = 2/3 × 1/4 = 2/12 = 1/6. Here, you can observe that 1/6 < 2/3.

How to Divide Fractions by Whole Numbers?

To divide fractions by whole numbers, one should be aware of the concept of reciprocal. For dividing fractions with whole numbers, follow the steps given below:

• Step 1: Write the division fact as dividend ÷ divisor, where the given fraction will be the dividend and the given whole number will be the divisor .
• Step 2: Change the division sign into multiplication and write the reciprocal of the divisor (whole number).
• Step 3: Find the product by multiplying numerator with numerator and denominator with denominator. That will be the required answer.

For example, let us divide 11/8 by 2.

Step 1: 11/8 ÷ 2

Step 2: 11/8 × 1/2 (as the reciprocal of 2 is 1/2)

Step 3: 11/8 × 1/2 = 11/16.

Therefore, 11/8 ÷ 2 = 11/16.

Another way to understand this method of dividing fractions with whole numbers is that we can simply multiply the given whole number to the denominator of the fraction. In the above example, we are actually doing the same in step 2. We multiply 2 to 8, and then the denominator of the answer becomes 2 × 8 = 16.

Look at the image given below to understand the division of fractions by whole numbers in a better way.

Dividing Fractions with Whole Numbers Games

There are a number of games and activities for learning dividing fractions with whole numbers in an easy way. Some of the games are given below:

• Ask learners to take two strips of paper of equal length. Ask them to cut one of the strips into 3 equal parts. This way they will be left with 1/3 part of the strip. Now, ask them to cut that 1/3 part into 4 equal parts. Finally, they will be left with some portion. Ask learners to compare that part with the other strip. This way they will find that it is 1/12th part of the original which is nothing but the answer of the division fact of 1/3 ÷ 4.
• The other game can be around activity cards of the division of fractions with whole numbers. Write a division fact (for example, 8/5 ÷ 3) in some cards (a different question in each of the cards, obviously!) and distribute it among learners. Draw an image of a blank strip or a circle along with the division fact to make it more visually attractive.

Division of Whole Number by Fraction

Now, let us learn how to do the division of whole numbers by fractions. To divide a whole number by a fraction, follow the steps mentioned below:

• Step 1: Find the reciprocal of the given fraction.
• Step 2: Multiply the reciprocal with the given whole number. The product will be required answer.

For example, to divide 3 by 2/5, we just need to multiply 3 by 5/2 (reciprocal of 2/5). This implies, 3 × 5/2 = 15/2.

► Also Check:

• Division of Fractions
• Whole Numbers
• Multiplication of Fractions

Dividing Fractions with Whole Numbers Examples

Example 1: Divide 1/9 by 7.

Solution: To divide 1/9 by 7, we will use the steps for dividing fractions with whole numbers. First, we will write it as a division fact 1/9 ÷ 7. Now change the division sign with the multiplication sign and replace 7 by its reciprocal. The reciprocal of 7 is 1/7. So we get 1/9 × 1/7 = 1/63. Therefore, 1/9 ÷ 7 = 1/63.

Example 2: Sergio wants to cut the 5/3rd portion of a strip into 8 equal parts. What will be the fraction of each piece after this division?

Solution: If Sergio will cut 5/3 portion into 8, it means we need to divide 5/3 by 8. The concept of dividing fractions with whole numbers needs to be applied.

Therefore, the fraction of each piece will be 5/24.

Example 3: What will be the value obtained when 20 is divided by 1/20?

Solution: For the division of a whole number by a fraction, we need to multiply the reciprocal of the fraction by the whole number. The reciprocal of 1/20 is 20. This implies, 20 × 20 = 400. Therefore, 20 ÷ 1/20 = 400.

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FAQs on Dividing Fractions with Whole Numbers

What is dividing fractions with whole numbers.

While learning about the division of fractions , one may find questions based on a special case which is dividing fractions with whole numbers. In dividing fractions by whole numbers, we need to multiply the fraction with the reciprocal of the whole number. That product will be the answer to the division.

What is the Rule for Dividing Fractions with Whole Numbers?

The rule for dividing fractions by whole numbers is that we need to multiply the reciprocal of the whole number to the given fraction. By this simple rule, we can solve any problem based on this concept.

How do you Divide Fractions with Whole Numbers?

To divide fractions with whole numbers, follow the steps listed below:

• Find the reciprocal of the whole number. The reciprocal of x is 1/x.
• Multiply the reciprocal value to the fraction.
• That product will be the required answer.

How to Solve Dividing Fractions with Whole Numbers?

In order to solve dividing fractions with whole numbers, we need to multiply the given whole number to the denominator of the fraction. It always results in a number less than the value of the fraction given.

How do you Divide a Whole Number by a Fraction 5th Grade?

For dividing whole numbers with fractions, we need to multiply the reciprocal of the fraction with the whole number. In mathematics, this concept is generally learnt in grade 5 when learners get to know about the division of fractions.

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1.  Color each person’s share with a different color, and write a division sentence.

2. Write a division sentence for each problem and solve it. 

Each person gets 1/15. To see that, divide each fifth (colored and uncolored) into three new parts.

3. Split the unit fraction equally among the people. Write a division sentence. Write a multiplication     sentence to check your division.

b. Divide between two people.

c. Divide between two people.

d. Divide between two people.

e. Divide among five people.

5. Three children share 1/4 lb of chocolate equally.

    a. How much does each one get, in pounds?

    b. In ounces?

6. A half a liter of juice is poured evenly into five glasses.

    a. How much juice is in each glass, measured in liters?

    b. How many milliliters of juice is in each glass?

7. There are 12 beakers with various amounts of oil in them. The line plot shows how much oil     each beaker has, in cups.

    If all the oil in the beakers was poured together, and then distributed evenly into the 12 beakers,     how much oil would be in each beaker?

9. Solve the opposite problem: if each person got this much pie, how much was there originally?

10. Write a story problem to match each division, and solve.

11. One morning, Joshua's gasoline container was only 1/8 full.       He poured half of it into his lawnmower.

      a. How full is the gasoline container now?  

      b. If the container holds 3 gallons, what is the amount of gasoline left, in gallons?

          (Challenge) In quarts?

12. The leftover pie is divided equally. How much does each person get? Write a division sentence.

b. Divide 2/3 among three people.     First, split each piece into 3 new ones.

e. Divide 2/5 among three people.     First, split each piece into 3.

f. Divide 4/5 among three people.  

Math Mammoth Fractions 2

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How to Divide a Whole Number by a Fraction

Last Updated: April 7, 2024 Fact Checked

This article was reviewed by Grace Imson, MA . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. There are 7 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 293,835 times.

When dividing a whole number by a fraction, you are finding how many groups of the fraction you can fit in the whole. The standard way of dividing a whole number by a fraction is to multiply the whole number by the reciprocal of the fraction. You can also draw a diagram to help you visualize the process.

Multiplying by the Reciprocal

Joseph Meyer

Simplifying a fraction just changes the way the fraction is written. To simplify a fraction, you can cancel out the greatest common factor from the numerator and denominator or convert an improper fraction to a mixed number. This doesn't change the inherent value of the fraction.

Drawing a Diagram

Solving Sample Problems

• Draw 9 circles representing the 9 cans.
• Count the number of complete groups. There should be 13.

Community Q&A

You Might Also Like

• ↑ http://www.virtualnerd.com/pre-algebra/rational-numbers/definitions-basics/convert-decimals-fractions/integer-to-fraction-conversion
• ↑ https://www.mathsisfun.com/reciprocal-fraction.html
• ↑ https://www.varsitytutors.com/hotmath/hotmath_help/topics/dividing-fractions
• ↑ https://www.calculatorsoup.com/calculators/math/fractionssimplify.php
• ↑ https://www.khanacademy.org/math/mappers/number-and-operations-213-219/x261c2cc7:dividing-fractions-and-whole-numbers-word-problems/v/dividing-a-whole-number-by-a-fraction-word-problem
• ↑ http://illinois.pbslearningmedia.org/resource/mgbh.math.nf.divfrac/dividing-a-whole-number-by-a-unit-fraction/
• ↑ https://www.mathsisfun.com/numbers/fractions-division-whole-numbers.html

About This Article

To divide a whole number with a fraction, make the whole number into a fraction by putting it over a denominator of 1. Next, reverse the numerator and denominator of the fraction you’re dividing the whole number with. Multiply this new fraction and the whole number. To do this, multiply both of the numerators, then both of the denominators. If you need to, simplify the new result. Keep reading to learn how to divide a whole number into fractions by drawing a diagram! Did this summary help you? Yes No

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Usagi Tsukino

Nov 2, 2017

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Dividing Fractions with Whole Numbers

With our Dividing Fractions with Whole Numbers lesson plan, students learn how to solve division problems that include fractions.

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Our Dividing Fractions with Whole Numbers lesson plan teaches students how to solve division problems that include unit fractions. During this lesson, students are asked to work cooperatively with a partner to create four different word problems, two of which must require whole number division by a fraction and the other two of which must require a fraction being divided by a whole number; once completed, they meet with another pair of students who will solve the problems. Students are also asked to solve practice division problems that include fractions.

At the end of the lesson, students will be able to divide unit fractions by whole numbers and whole numbers by unit fractions.

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Division of whole numbers

Fraction word problems.

These grade 5 word problem worksheets have problems involving the division of whole numbers with fractional results, such as sharing 3 pizzas between 10 people. Some answers involve estimating.

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