Dividing Whole Numbers by Fractions and Mixed Numbers (2024)

Division of a whole number by a fraction and a mixed number

Whole number division exercises with fractions and mixed numbers are easy and not intimidating if you just follow the steps.

How do we solve whole number division by a fraction?

The first step –

Let's turn the whole number into an improper fraction.
How do we do that?
In the numerator, we write the number itself (the whole number) and in the denominator, we always write $1$1.

For example:

Convert the number $8$8 to a fraction:
In the numerator, write $8$8 and in the denominator, write $1$1.
We get:
$8 \over 1$18​

Convert the number $1$1 to a fraction:
In the numerator, we write $1$1 (because this is our whole number) and in the denominator, we also write $1$1 because that is the rule.
We get:
$1 \over 1$11​

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The second step -

After converting the whole number to an improper fraction and having only fractions in the exercise, we replace the division operation with multiplication and switch the positions of the numerator and the denominator in the second fraction.

For example:

Let's perform the second step in the exercise –
$\frac{4}{1}:\frac{2}{3}=$14​:32​=

We will turn the division operation into multiplication and do not forget to switch the positions of the numerator and the denominator in the second fraction. We get:
$\frac{4}{1}*\frac{3}{2}=$14​∗23​=

The third step –

$\frac{12}{2} = 6$212​=6

And now let's practice!
Here is the exercise:

$5:\frac{4}{5}=$5:54​=

Solution:

Let's solve it step by step. First, we will convert the whole number $5$5 into an improper fraction.
In the numerator, we write $5$5 and in the denominator $1$1. We get:

$\frac{5}{1}:\frac{4}{5}=$15​:54​=

Now we move on to the second step and turn the exercise into a multiplication exercise without forgetting to switch the positions of the numerator and the denominator in the second fraction. We get:

$\frac{5}{1}\cdot\frac{5}{4}=$15​⋅45​=

We will solve by multiplying fractions – numerator times numerator and denominator times denominator, and we get:

$\frac{25}{4}= 6\frac{1}{4}$425​=641​

How do we solve the division of a whole number by a mixed number?

First, let's recall the difference between an improper fraction and a mixed number:
Improper fraction – a fraction that consists only of a numerator and a denominator.
Mixed number – a number that consists of both whole numbers and a fraction.

The first step:

Convert the whole number to an improper fraction.
In the numerator, write the whole number and in the denominator, write the number 1 (just as we learned at the beginning of the article)

The second step:

Convert the mixed number to an improper fraction

How do you convert a mixed number to an improper fraction?

Important tip!
Before converting the mixed fraction to an improper fraction, check if it can be simplified and only then convert it to an improper fraction.
For example:
Convert the mixed number $5 \frac{2}{6}$562​ to a fraction.

Solution:

It seems that we can simplify $2 \over 6$62​ to $1 \over 3$31​
Therefore, we rewrite the mixed number as $5 \frac{1}{3}$531​ and convert it to an improper fraction.
We multiply the whole number $5$5 by the denominator $3$3 and add the numerator $1$1
$5*3+1=16$5∗3+1=16

The third step:

After converting the whole number to an improper fraction and the mixed number to an improper fraction, and we only have fractions in the exercise, we will replace the division operation with a multiplication operation and switch the positions of the numerator and the denominator in the second fraction. (As we learned at the beginning of the article).

Let's practice!

Here is the exercise –
$7:2\frac{1}{3}=$7:231​=

Solution:

We will invert the numerator and the denominator in the second fraction and change the division to multiplication. We get:

$\frac{7}{1}\cdot\frac{3}{7}=$17​⋅73​=

We will solve by multiplying fractions:

$\frac{21}{7} = 3$721​=3