Division of Fractions

🏆Practice division of fractions

Dividing fractions is easy

We will solve fraction divisions in the following way:
First step
Let's look at the exercise.

• If there is any mixed number - we will convert it into a fraction
• If there is any whole number - we will convert it into a fraction

Second step
We will convert the division into multiplication
Also, we will swap the numerator and denominator in the second fraction.
Third step
We will solve by multiplying numerator by numerator and denominator by denominator.

Test yourself on division of fractions!

Complete the following exercise:

$$\frac{1}{2}:\frac{1}{2}=\text{?}$$

How to Divide Fractions

Fraction division is a pleasant and simple topic, especially if you already know how to solve fraction multiplications.
In this article, you will learn how to operate to divide fractions and discover how easy it is to do it with this method.

We will solve fraction divisions in the following way:
First step
Let's look at the exercise.

• In case there is any mixed number - we will convert it into a fraction
• In case there is any whole number - we will convert it into a fraction

Second step
We will convert the division into multiplication
Also, we will swap between the numerator and the denominator in the second fraction.
Third step
We will solve by multiplying numerator by numerator and denominator by denominator.

It's worth remembering

How are fractions multiplied?
Numerator by numerator and denominator by denominator.

How is a mixed number converted to a fraction?
Multiply the denominator by the whole number and add the numerator.
Write the result in the numerator. The denominator remains unchanged.

How is a whole number converted to a fraction?
Write the whole number in the numerator
and in the denominator write $1$.

Let's practice and see all the possible cases we might encounter:

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Simple Fraction Division Exercises –> Fraction Divided by Fraction

Here is an exercise:

$\frac{4}{5}:\frac{3}{2}=$

Solution:
We will change the division operation to a multiplication and swap the numerator and denominator in the second fraction.

We will obtain:

$\frac{2}{3} \times \frac{4}{5}=$

We will solve the exercise as it is done in fraction multiplication - Numerator by numerator and denominator by denominator.

We will obtain:
$8 \over 15$

Now let's move on to a slightly more complex example:

Division of a Fraction by a Mixed Number

$\frac{4}{6}:5\frac{1}{2}=$

Solution:
Upon examining the exercise, we will realize that there is a mixed number -> $5\frac{1}{2}$
We will convert it to a fraction:
$\frac{11}{2}$

Pay attention! After obtaining another fraction, the exercise looks as follows:
$\frac{4}{6}:\frac{11}{2}=$

Clearly, it remains a division exercise, now we must operate as is done to solve a division exercise:
We will change the division operation to multiplication and swap between the numerator and the denominator in the second fraction.
We will obtain:

$\frac{4}{6} \times \frac{11}{2}=$

Upon solving we will obtain:

$​​\frac{4}{33}=\frac{8}{66}$

Do you know what the answer is?

Division of an integer by a fraction

Here is an exercise:
$3:\frac{1}{2}=$

Solution:
First, we will convert the whole number to a fraction: $3=\frac{3}{1}$
Let's copy the new exercise:
$\frac{3}{1}:\frac{1}{2}=$
We will operate according to the rules of fraction division, we will obtain:
$\frac{2}{1} \times \frac{3}{1}=$
$\frac{6}{1}=6$

Word Problems with Division of Fractions

Sometimes you will come across word problems from which you must extract the appropriate division exercise.

For example

A seamstress has $30$ meters of fabric. The seamstress uses $1\frac{3}{4}$ m. to sew each shirt.

How many shirts can the seamstress make with the amount of fabric she has?
The solution may include a number that is not an integer.

Solution:
To find out how many shirts the seamstress can make with $30$ meters of fabric, we must divide $30$ (the amount of fabric she has) by the amount of fabric she uses for each shirt -> $1\frac{3}{4}$
The division exercise will be: $30:1\frac{3}{4}=$

We will convert the mixed number to a fraction:  $1\frac{3}{4}=\frac{7}{4}$
And the whole number $30$ to a fraction: $30=\frac{30}{1}$
Let's rewrite the exercise:
$\frac{30}{1}:\frac{7}{4}=$
Let's convert to multiplication and swap between the numerator and the denominator in the second fraction.
We will obtain:
$\frac{4}{7} \times \frac{30}{1}=$
Upon solving, we will obtain:
$\frac{120}{7}=17\frac{1}{7}$
The seamstress can make $17\frac{1}{7}$ shirts with the fabric she has.

Examples and exercises with solutions for fraction division

Exercise #1

$1\times\frac{1}{2}:2$

Step-by-Step Solution

According to the order of operations rules, we will solve the exercise from left to right since there are only multiplication and division operations:

$1\times\frac{1}{2}=\frac{1}{2}$

$\frac{1}{2}:2=\frac{1}{4}$

1/4

Exercise #2

$\frac{0.5}{2}=$

Step-by-Step Solution

Let's convert the decimal fraction to a simple fraction:

$0.5=\frac{5}{10}$

We'll write the division problem as follows:

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

Let's convert the division problem to a multiplication problem.

We'll multiply $\frac{5}{10}$ by the reciprocal of $2$ as follows:

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

We'll solve it this way:

$\frac{5\times1}{10\times2}=\frac{5}{20}$

We'll reduce both the numerator and denominator by 5 and get:

$\frac{5:5}{20:5}=\frac{1}{4}$

$\frac{1}{4}$

Exercise #3

$\frac{0.5}{4}=$

Step-by-Step Solution

Let's convert the decimal fraction to a simple fraction:

$\frac{0.5}{4}=\frac{\frac{1}{2}}{4}$

Let's convert the division problem to a multiplication problem.

We'll multiply $\frac{1}{2}$ by the reciprocal of 4 as follows:

$\frac{1}{2}\times\frac{1}{4}$

We'll solve it as follows:

$\frac{1\times1}{2\times4}=\frac{1}{8}$

$\frac{1}{8}$

Exercise #4

$\frac{0.3}{0.5}=$

Step-by-Step Solution

Let's convert the decimal fractions to simple fractions:

$0.3=\frac{3}{10}$

$0.5=\frac{5}{10}$

We'll write the division problem as follows:

$\frac{\frac{3}{10}}{\frac{5}{10}}$

Let's convert the division problem to a multiplication problem.

We'll multiply $\frac{3}{10}$ by the reciprocal of $\frac{5}{10}$ as follows:

$\frac{3}{10}\times\frac{10}{5}$

We'll solve it this way:

$\frac{3\times10}{10\times5}$

We'll cancel out the 10 in the numerator with the 10 in the denominator and get:

$\frac{3}{5}$

$\frac{3}{5}$

Exercise #5

Complete the following exercise:

$\frac{1}{2}:\frac{1}{2}=\text{?}$

Video Solution

$1$