How to Divide Fractions (With Steps, Tips, and Examples)

By Indeed Editorial Team

Published June 17, 2022

The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.

Having the ability to solve common math problems and perform basic mathematical calculations is an important life skill. Fractions are a common aspect of math that you might use throughout your career. Learning more about dividing fractions can help you perform quick and correct division calculations and help you be more effective in your role. In this article, we discover how to divide fractions, review the steps you can take to divide fractions, explore ways to divide fractions with different types of numbers, examine some tips, and provide examples of dividing fractions.

What is a fraction?

A fraction is a part or portion of a whole number. It has two parts, namely a numerator and a denominator. The numerator is the number of parts you're counting, and the denominator is the total number of equal parts or portions that makes up the whole. For example, 4/5 is a fraction, where 4 is the numerator, and 5 is the denominator. To conceptualize it, it means to calculate four parts out of five.

How to divide fractions

To learn how to divide fractions, here's a list of steps you can follow:

1. Use the cross multiplication method

In the cross-multiplication method, you multiply the first fraction's numerator by the second fraction's denominator and the second fraction's numerator with the first fraction's denominator.

Example:

(4/5) / (8/15)

The first step is multiplying the numerator of the first fraction, which is 4, by the second fraction's denominator, which is 15. The numerator of the resulting fraction becomes:

4 × 15 = 60

Next, multiply the first fraction's denominator with the second fraction's numerator.

The new denominator becomes:

5 × 8 = 40

The answer is 60/40.

The last step involves simplifying the fraction. To do this, divide both the numerator and denominator by 20 to get a simplified value of 3/2.

2. Utilize the inverse multiplication method

The inverse of any number (n) is 1/n. In this method, you inverse the second fraction and multiply the numbers rather than divide them. By doing so, the numerator becomes the denominator while the denominator becomes the numerator. To use this method, follow these steps:

  • Find the inverse of the second fraction by switching the numerator and denominator, then change the divide symbol to a multiplying symbol.

  • Multiply the first fraction's numerator with the second fraction's numerator.

  • Multiply the second fraction's denominator with the second fraction's denominator.

Here's how you can demonstrate this method as a formula:

(x/y) / (p/q) = (x/y) × (q/p) = xq/yp

Example:

(3/8) / (6/7)

In the first step, switch the numerator and denominator of the second fraction and change the divide symbol to the multiply symbol.

3/8 × 7/6

Now, multiply the numerator of both fractions and the denominator of both the fractions.

3 × 7 = 21
8 × 6 = 48

The answer is 21/48.

Now, divide the numerator and denominator by 3 to simplify the fraction.

(21/48) / (3/3) = 7/16

Dividing fractions with a whole number

For dividing a fraction by a whole number, use the inverse multiplication method. If x/y is the fraction and p is the whole number, here's the formula you can use:

(x/y) / p = x/y × 1/p = x/yp

Example:

(3/10) / 9

The first step is converting the whole number to a fraction. To represent 9 as a fraction, you can write 9/1. Next, inverse this value or find the reciprocal of 9/1. Its reciprocal is 1/9. Then, change the division to a multiplication symbol:

(3/10) / 9 = 3/10 × 1/9

Next, multiply the first fraction's numerator by the second fraction's numerator and the first fraction's denominator by the second fraction's denominator.

3/10 × 1/9 = 3/90

After dividing the numerator and denominator by 3, the simplified fraction is 1/30.

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Dividing fractions with decimals

Decimals are numbers that are a fraction of the base 10. To divide a fraction with a decimal, convert the decimal to a fraction and then perform the division calculation.

Example:

(7/20) /0.2

First, convert the decimal to a fraction with base 10.

0.2 = 2/10

Now, calculate the equation using the inverse multiplication method.

(7/20) / (2/10) = (7/20) x (10/2) = 70/40

Next, simplify the fraction by dividing the numerator and denominator by 10.

(70/40) / (10/10) = 7/4

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Dividing fractions with the same denominator

When you have two fractions with the same denominator, it's not necessary to find the reciprocal. Instead, you can divide the numerator of both the fractions to get the final answer. The denominator cancels each other, and you get one.

Example:

(6/7) / (8/7)

Instead of finding the reciprocal, and multiplying the numerator with numerator and denominator with denominator, divide the fractions' numerators.

(6/7) / (8/7) = 6/8

Now, simplify the fraction to get your answer as 3/4.

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Tips to remember when dividing fractions

Here are a few tips you can use when dividing fractions:

Know the answer you require

When finishing an assignment for school or using fractions in real life, ensure you read the problem carefully. It helps you understand the format of the desired answer you require. For instance, you might require the answer in decimal, mixed fraction, whole number, or percentage format.

Double-check your work

When dividing fractions, it's essential to double-check your answer to help ensure you're correct. One way to check your work is by performing the same calculation again. If you calculate the same answer twice, you can assume your calculation is correct. If you get a different answer on the second try, consider dividing the fraction again.

Practise division problems

It's essential to practise calculations to develop your skills and become experienced at calculating the division of fractions. You can use online resources to practise problems that challenge and develop your math skills. Also, you can play online math games that help you master your division skills with different types of fractions.

Examples of dividing fractions

Here are a few examples of dividing fractions to help you learn more about this concept:

(3/4) / (8/5)

You can divide these fractions using the following method:

In the first step, switch the numerator and denominator of the second fraction and change the divide symbol to the multiplication symbol.

(3/4) / (8/5) = 3/4 × 5/8

Now, multiply the numerator of both fractions and the denominator of both fractions.

3 × 5 = 15
4 × 8 = 32

Your answer is 15/32.

(9/5) / (11/5)

You can divide these fractions using the following method:

Here, the denominator of both the fraction is the same, so it's unnecessary to find the reciprocal of the second fraction. Instead, you can divide the numerator of both the fractions to get your answer.

(9/5) / (11/5) = 9/11

As this fraction is in the simplest form, your answer is 9/11.

(4/15) / 0.5

You can divide a fraction by a number with a decimal using the following method:

First, convert the decimal to a fraction with base 10.

0.5 = 5/10

Now, calculate (4/15) / (5/10) using the inverse multiplication method.

4/15 × 10/5= 40/75

Next, simplify the fraction by dividing the numerator and denominator both by 5.

(70/40) / (5/5) = 8/15

Your answer is 8/15.

(25/8) /15

You can divide a fraction by a whole number using the following method:

The first step is converting the whole number to a fraction. To represent 15 as a fraction, you can write 15/1. Next, inverse this value to get 1/15. Then, change the division to a multiplication symbol, and the fraction becomes:

(25/8) /15 = 25/8 × 1/15

Next, multiply the first fraction's numerator by the second fraction's numerator and the first fraction's denominator by the second fraction's denominator.

25/8 × 1/15 = 25/120

After dividing the numerator and denominator by 5, the simplified fraction becomes 5/24.

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