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Dividing Fractions Worksheets

Welcome to our Dividing Fractions Worksheets page. Here you will find a range of free printable sheets and support to help your child learn to divide fractions by other fractions.

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• Dividing Fractions Calculator
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• Dividing Fractions by Whole Numbers
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Dividing Fractions Online Quiz

Divding fractions calculator.

We have a calculator to help you to divide a fraction by another fraction.

You can divide mixed fractions or divide a fraction by an integer too.

All the working out is shown step-by-step so you can see how it is worked out.

• Divide Fractions Calculator

How to Divide Fractions Support

This support page will help you find out all about how to divide fractions.

There are several worked examples and a printable support sheet.

Formula for dividing two fractions

\[{a \over b} \div {c \over d} = {ad \over bc} \]

• How to Divide Fractions

About our Dividing Fractions Worksheets

Here you will find a selection of Fraction worksheets designed to help your child understand how to divide a fraction by another fraction, or to divide a fraction by a whole number.

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

Before your child tackles dividing fractions, they should first be confident with multiplying fractions .

Using these sheets will help your child to:

• divide a fraction by another fraction;
• apply their understanding of simplest form;
• convert between mixed fractions and improper fractions.

To divide mixed fractions, use the link below!

Sheet 1 is supported and has examples and instructions to follow.

Sheet 2 has less support - also the fractions do not need to be simplified.

Sheets 3 and 4 have no support and the fractions need to be simplified.

Sheet 5 is similar to sheets 3 & 4, but the fractions also need to be converted to mixed fraction answers.

• Dividing Fractions Sheet 1
• PDF version
• Dividing Fractions Sheet 2
• Dividing Fractions Sheet 3
• Dividing Fractions Sheet 4
• Dividing Fractions Sheet 5

Dividing Fractions Walkthrough Video

This short video walkthrough shows several problems from our Dividing Fractions Worksheet 1 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, please check out the video below!

Multiplying and Dividing Fractions Worksheets

We also have some multiplying and dividing fractions worksheets.

Often when you have taught both of these concepts, it is important to muddle them up and practice them both to develop confidence.

The sheets below are practice sheets for students who are already fairly confident multiplying and dividing fractions.

Sheets 1 & 2 have 24 questions. The fractions need simplifying, but can be left as improper fractions.

Sheet 3 has just 12 questions. The fractions need simplifying and converting to mixed fractions.

• Multiplying and Dividing Fractions 1
• Multiplying and Dividing Fractions 2
• Multiplying and Dividing Fractions 3

More Recommended Math Worksheets

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

Multiplying and Dividing Fractions Support

We have a number of support pages designed to help you understand how to multiply and divide fractions.

On each support page, there are some worked examples to show you what to do.

We also have some math videos on some support pages to help explain what to do.

• Dividing Fractions by whole numbers
• Divide Whole numbers by Fractions

• How do you Multiply Fractions support

• How to Multiply Mixed Fractions support page
• How to Divide Fractions support page
• How to Divide Mixed Numbers support page

We have more worksheets to help your child learn and practice multiplying and dividing fractions.

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How to Convert Improper Fractions

This support page shows how to convert improper fractions to mixed numbers, and how to convert mixed numbers to improper fractions.

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• Convert Improper Fractions Support

Simplifying Fractions

This is also sometimes called reducing fractions to their simplest form.

This involves dividing both the numerator and denominator by a common factor to reduce the fraction to the equivalent fraction with the smallest possible numerator and denominator.

The printable fraction page below contains more support, examples and practice about simplifying fractions.

• How to Simplify Fractions support page
• Simplify Fractions Practice Zone

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

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Dividing Fractions – Definition with Examples

What do we mean by dividing fractions, steps to divide fractions, properties of dividing fractions, practice problems.

• Frequently Asked Questions

By dividing fractions we mean the division involves at least one fraction. For example, 

• $\frac{3}{4} \div \frac{1}{2}$
• $7 \div \frac{1}{2}$
• $\frac{3}{4} \div 6$

The quotient of such multiplication could be a fraction or a whole number.

Let’s consider some examples to see what it means to divide fractions through visual models.

• Whole Number ÷ Fraction

• Fraction ÷ Whole

• Fraction ÷ Fraction

Visualising Fraction Division that Involves Remainder

Example 1: 

Example 2: 

• Fraction by Fraction

To divide a fraction by another fraction, multiply the dividend fraction by the reciprocal of the divisor fraction. The reciprocal of a fraction can be found by interchanging its numerator and denominator. For example, $\frac{3}{4}$ is reciprocal of $\frac{4}{3}$ and vice-versa.

There is a quick way to remember the steps to divide fractions: Keep >> Change >> Flip. 

Follow these steps to divide a fraction by fraction (either proper or improper):

STEP 1: 

Keep the dividend the same.

Change the division sign to multiply

Flip the divisor by writing its reciprocal.

STEP 2: Multiply the fractions

STEP 3: Simplify the result, if needed. 

Quick Tip : In case the dividend and/or divisor are mixed numbers, we first convert them into improper fractions and then follow the steps mentioned above.

• Fraction by Whole Number

Recall that the reciprocal of a whole number ‘ a ’ is the unit fraction $\frac{1}{a}$ because we can write a whole in fraction form with denominator equal to 1, that is, $\frac{a}{1}$. Let’s understand how to divide when divisor is a whole number through an example:

Why do we flip the divisor after changing the division sign?

When we divide one number by another, let’s say, a is the dividend and b is the divisor, then we can write it as $\frac{a}{b}$. Also, we can write $\frac{a}{b}$ as the product of a and $\frac{1}{b}$. That is, 

$a \div b = \frac{a}{b} = a \times \frac{1}{b}$

We can also understand it like this:

Division is the inverse operation of multiplication. So, dividing by a number is the same as multiplying by its reciprocal.

Related Worksheets

The properties of division with whole numbers hold true for fractions as well. Let’s check!

• Property 1: When a fraction is divided by 1, the quotient is the fraction itself. $\frac{3}{4} \div 1 = \frac{3}{4}$
• Property 2: When zero is divided by a non-zero fraction, then the quotient is always 0.  $0 \div \frac{3}{4} = 0$ 
• Property 3: When a non-zero fraction is divided by itself, then the quotient is 1.  $\frac{3}{4} \div \frac{3}{4} = 1$
• Property 4: Division by 0 is not possible and the result is not defined. $\frac{3}{4}\div 0 =$ Not Defined

Solved Examples

Example 1: Divide: ​​$\frac{1}{5} \div \frac{1}{10}$.

Keep $\frac{1}{5}$ as it is; change ÷ to × and flip $\frac{1}{10}$ and write it as $\frac{10}{1}$. 

$\frac{1}{5} \div \frac{1}{10} = \frac{1}{5} \times \frac{10}{1} = \frac{10}{5} = \frac{2}{1} = 2$ 

Example 2: Divide: ​​$1 \frac{2}{3} \div \frac{5}{7}$

Solution: Change 1 23 to improper fraction and then follow the steps to divide fractions.

$1\frac{2}{3} \div \frac{5}{7} = \frac{5}{3} \div \frac{5}{7} = \frac{5}{3} \times \frac{7}{5} = \frac{7}{3} = 2\frac{1}{3}$

Example 3 : Max is painting toy cars. He has $2\frac{1}{4}$ L of paint. If each car requires $\frac{7}{3}$ L of paint, how many cars can Max paint?

Quantity of paint with Max $= 2\frac{1}{4}$ L $= \frac{9}{4}$ L

Quantity of paint required to paint 1 car $= \frac{3}{8}$ L

Numbers of toy cars that Max can paint $= \frac{9}{4} \div \frac{3}{8}$

$= \frac{9}{4} \times \frac{8}{3}$

$= \frac{72}{12} = 6$

So, Max can paint 6 toys with  $2\frac{1}{4}$ L of paint.

Example 4 : Melvin sang a medley of songs for 10 minutes. If one song was $2\frac{1}{2}$ minutes long, how many songs did Melvin sing?

Duration for which Melvin sang $= 10$ minutes

Length of one song $= 2\frac{1}{2}$ minutes

Numbers of songs that Melvin sing $= 10 \div 2\frac{1}{2}$

$= 10 \div \frac{5}{2}$

$= 10 \times \frac{2}{5}$

$= \frac{20}{5} = 4$

So, Melvin sang 4 songs in 10 minutes. 

Dividing Fractions

Attend this Quiz & Test your knowledge.

Divide: ​​$\frac{7}{8} \div \frac{3}{9}$

Divide: ​​$\frac{4}{8}\div 9$, divide: $1\frac{1}{7}\div \frac{3}{5}$, divide: $\frac{3}{7}\div\frac{3}{7}$, f requently asked questions.

What does division of fractions mean?

The division of fractions means dividing a fraction into further equal parts. For example, If you have three-fourth of a pizza left and you divided each slice into 2 parts you would get a total of six slices but this would represent six-eighths of the total pizza. 

What is the method of dividing fractions?

The first step for dividing fractions is to reciprocate the second fraction, that is, exchange its numerator and denominator. Next, multiply the first fraction with this reciprocal using standard method of fracton multiplication and convert the answer into simplest form.

How does one divide a fraction by a whole number?

To divide a fraction by a whole number, convert the whole number into a fraction with denominator 1 and then follow the standard steps of dividing fractions i.e., Flip the second fraction and multiply this with the first fraction.

How do you divide fractions by mixed number?

To divide a fraction by a mixed number (or vice versa), convert the mixed number into an improper fraction and then follow the standard steps of dividing fractions.

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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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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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4.9: Dividing Fractions- Problems

• Last updated
• Save as PDF
• Page ID 10584

• Michelle Manes
• University of Hawaii

We’ve spent the last couple of chapters talking about dividing fractions: how to make sense of the operation, how to picture what’s going on, and how to do the computations. But all of this kind of begs the question: When would you ever want to divide fractions, anyway? How does that even come up?

It’s important that teachers are able to come up with situations and problems that model particular operations, which means you have to really understand what the operations mean and when they are used.

Think / Pair / Share

• Use one of our methods (draw a picture, rectangles, common denominator, missing factor) to compute \(1 \frac{3}{4} \div \frac{1}{2}\).
• Come up with a situation where you would want to compute \(1 \frac{3}{4} \div \frac{1}{2}\). (That is, write a word problem that would require you to do this computation to solve it.)

When to Multiply, When to Divide?

A common answer to

Come up with a situation where you would want to compute \(1 \frac{3}{4} \div \frac{1}{2}\).

Is something like this:

My recipe calls for \(1 \frac{3}{4} \div \frac{1}{2}\) cups of flour, but I only want to make half a recipe. How much flour should I use?

But that problem doesn’t ask you to divide fractions. It asks you to cut your recipe in half, which means dividing by 2 or multiplying by \(\frac{1}{2}\).

Why is it so hard to come up with division problems that use fractions? Maybe it’s because fractions are already the answer to a division problem, so you’re dividing and then dividing some more. Maybe it’s because they just make it look so complicated. In any case, it’s worth spending some time thinking about division problems that involve fractions and how to recognize and solve them.

One handy trick: Write a problem that involves division of whole numbers, and then see if you can change the numbers to fractions in a sensible way.

Example \(\PageIndex{1}\):

Here are some division problems involving whole numbers:

• I have 10 feet of ribbon. How many 2-inch pieces can I cut from it?
• I have a fancy old clock that rings once every 15 minutes. How many times will it ring over the course of 2 hours (120 minutes)?
• My fish tank needs 6 gallons of water, and my bucket holds 3 gallons. How many times will I need to fill my bucket in order to fill the tank?
• A recipe calls for 6 cups of flour, and my largest scoop measures exactly 2 cups. How many times should I use it?
• I ran 12 miles and went around the the same route 3 times. How long was the route?

Here are some very similar problems, rewritten to use fractions instead:

• I have \(1 \frac{3}{4}\) feet of ribbon. How many 6-inch (that’s \(\frac{1}{2}\) a foot) pieces can I cut from it?
• My watch alarm goes off every half hour, and I don’t know how to shut it off. How many times will it go off during the \(1 \frac{3}{4}\) hour movie?
• My fish tank needs \(1 \frac{3}{4}\) gallons of water, and my bucket holds \(\frac{1}{2}\) gallon. How many times will I need to fill my bucket in order to fill the tank?
• I want to measure \(1 \frac{3}{4}\) cups of flour for a recipe, but I only have a \(\frac{1}{2}\) cup measuring cup. How many times should I fill it?
• I ran \(1 \frac{3}{4}\) miles before I twisted my ankle. I only finished half the race. How long was the race course?

For each one of the fraction division questions, we can understand why it’s a division problem:

• I have \(1 \frac{3}{4}\) feet of ribbon. How many 6-inch (that’s \(\frac{1}{2}\) a foot) pieces can I cut from it? This means making equal groups of \(\frac{1}{2}\) foot each and asking how many groups. That’s quotative division.
• My watch alarm goes off every half hour, and I don’t know how to shut it off. How many times will it go off during the \(1 \frac{3}{4}\) hour movie? Again, we’re making equal groups of \(\frac{1}{2}\) hour each, and asking how many groups. Quotative division.
• My fish tank needs \(1 \frac{3}{4}\) gallons of water, and my bucket holds \(\frac{1}{2}\) gallon. How many times will I need to fill my bucket in order to fill the tank? Once again: we’re making equal groups of \(\frac{1}{2}\) gallon each, and asking how many groups (buckets).
• I want to measure \(1 \frac{3}{4}\) cups of flour for a recipe, but I only have a \(\frac{1}{2}\) cup measuring cup. How many times should I fill it? This is making equal groups of \(\frac{1}{2}\) cup and asking how many groups.
• I ran \(1 \frac{3}{4}\) miles before I twisted my ankle. I only finished half the race. How long was the race course? This one is a little different. This one is a little different. It’s the fraction version of partitive division.

Recall what partitive division asks: For \(20 \div 4\), we ask 20 is 4 groups of what size?

So for \(1 \frac{3}{4} \div \frac{1}{2}\), we ask: \(1 \frac{3}{4}\) is half a group of what size?

You try it.

• First write five different division word problems that use whole numbers. (Try to write at least a couple each of partitive and quotative division problems.)
• Then change the problems so that they are fraction division problems instead. You might need to rewrite the problem a bit so that it makes sense.
• Solve your problems!

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• What is a mixed number?
• A mixed number is a combination of a whole number and a fraction.
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• To add or subtract fractions with different denominators, convert the fractions to have a common denominator. Then you can add or subtract the numerators of the fractions, leaving the denominator unchanged.

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

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

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Division with unit fractions

Unit fractions word problems.

Unit fractions are fractions with 1 as the numerator. Below are word problems involving the division of whole numbers by unit fractions, or vice versa. 

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Course: 5th grade   >   Unit 7

• Fraction division in context
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Divide fractions and whole numbers word problems

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• an integer, like 6 ‍  
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Math Day at the Beach 2024

On March 23, 2024, the 23rd Math Day at the Beach event was hosted on the California State University, Long Beach campus. Math Day at the Beach is a problem-solving festival for Southern California high school students who want to have fun with mathematics and enjoy a day of camaraderie with university mathematics students and professors.

A total of 34 teams of six high school students each participated in this event, 5 teams in Division A and the others in Division B.

This year's event was hosted on the campus and it was an unequivocal success. There were several parts to this event: an individual round, team round, relay, presentation by an invited speaker, teachers face-off round, and the face-off round to determine individual winners. The problems were designed by the Mathematics and Statistics Department faculty and were selected from algebra, geometry, trigonometry, number theory, combinatorics, and probability.

2024 Winners

Here is a list of the teams and individuals who placed during the competition.

Winning Teams in Division A:

• 1st Place - University High School
• 2nd Place - Sierra Canyon School
• 3rd Place - North Hollywood High School

Winning Teams in Division B:

• 1st Place - La Canada High School, Team 1
• 2nd Place - University High School, Team 1
• 3rd Place - San Marino High School
• 4th Place - Santa Fe Christian Schools, Team 1
• 5th Place - Palos Verdes Peninsula High School, Team 1

Individual Winners:

• 1st Place - Evan Li, San Marino High School
• 2nd Place - Natalie Song, Sage Hill School
• 3rd Place - Neal Frankenberg, La Canada High School
• 4th Place - Timi Fang, University High School
• 5th Place - Justin Kchao, Palos Verdes Peninsula High School

Top New Team:

• Valencia High School

Top Young Team:

• Santa Fe Christian Schools, Team 2

Invitation to 2025

An invitation to participate in the 2025 event will go out to schools in October of 2024. If your school is interested in trying its hand at tackling those math problems, email Dr. Olga Korosteleva at [email protected]  to request practice tests.

Division A schools for 2024 (in alphabetical order):

• La Canada High School
• North Hollywood High School
• Palos Verdes Peninsula High School
• San Marino High School
• Santa Fe Christian Schools
• Sierra Canyon School
• University High School

About Math Day at the Beach

This annual event was started in 2000 by the Department of Mathematics and Statistics under the directorship of Dr. Kent Merryfield, a charismatic leader with unparalleled expertise in high-school math competitions, and ran uninterrupted until Dr. Merryfield's untimely death in November of 2018.

In March 2019, the 20th Math Day at the Beach took place under the new directorship of Dr. Olga Korosteleva. Then the pandemic placed this event on hold for two years. The event returned on March 12, 2022, and has been held since.

Math Day at the Beach is completely free, thanks to our generous sponsors, the Jerry Cassaday Family and LBS Financial Credit Union.

Learn more about Math Day at the Beach.