# Division of Fraction by whole number

In this post we will learn how to divide fraction by whole number with simple steps.

After that we will move on to solve some questions related to the concept.

I urge all the students to take out pencil and paper and start learning by writing.

## What happen when fraction is divided by whole number?

Here we will understand what will happen to the fraction when we divide it by a whole number.

Given below is a rectangle which is divided into 2 parts (i.e. fraction \frac{1}{2} )

Now divide the fraction \frac{1}{2} with whole number 3
It means that the half part of rectangle is divided into 3 parts

After division the rectangle would look like this:

After calculating the division we get:

Now the solution is \frac{1}{6} of the rectangle

Hence after dividing the fraction with whole number, we have made the fraction smaller

## How to divide Fraction by Whole Number

Suppose one fraction and whole number is given.
And you have to divide the whole number

You can do the division by following below steps

Step 01
Convert the whole number into fraction by putting denominator 1

Step 02
Convert the division into multiplication by inversing digits of the right fraction

Step 03
Multiply the numerators of both fractions

Step 04
Multiply the denominators of both fractions

Step 05

If possible reduce the numerator and denominator to its lowest terms

I hope the process is clear.
Let us practice the division concept with the help of examples.

Example 01
Divide the given fraction and whole number

Do the following steps

Step 01
Convert the whole number into fraction
Put 1 in the denominator of whole number

Step 02
Convert the division into multiplication by inverting the fraction of right side

Step 03
Multiply the numerator and denominator separately

Step 04
Reduce the fraction to lowest level

The resultant fraction now cannot be further divided.
Hence \frac{4}{21} is the solution

Example 02
Divide the below fraction and the whole number

Do the following steps

Step 01
Convert the whole number into fraction by putting denominator 1

Step 02
Convert the division into multiplication by inverting the right fraction

Step 03
Multiply the numerator and denominator separately

Step 04
Reduce the result into lowest numbers

Divide both numerator and denominator by 2

Hence \frac{3}{5} is the solution

Example 03
Divide the given fraction and whole number

Do the following steps

Step 01
Convert the whole number into fraction by putting denominator 1

Step 02
Convert the division into multiplication by inverting the fraction on right side

Step 03
Multiply the numerator and denominator separately

Step 04
Reduce the fraction to its lowest terms

Divide both numerator and denominator by 5

Hence \frac{3}{13} is the solution

## Dividing Fractions with Whole Numbers Worksheet

Given below are collection of questions related to the division of fractions with whole number.

All questions are to the standard of Grade 5 with detailed solution and explanation.

### Divide the below fraction and whole numbers

Here one fraction and one whole number is provided.

You have to divide the numbers and find the right solution

(a) \frac{1}{3} \ \div \ 3 \\\ \\ Read Solution

Step 01
Convert the whole number into fraction by putting denominator 1
\Longrightarrow \ \frac{1}{3} \ \div \ \frac{3}{1}

Step 02
Convert the division into multiplication by inverting the right fraction
\Longrightarrow \ \frac{1}{3} \ \times \ \frac{1}{3}

Step 03
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{1\times 1}{3\times 3} \ \Longrightarrow \ \frac{1}{9}

Step 04
Reduce numerator and denominator to lowest order

Here further simplification is not possible.

Hence \frac{1}{9} is the solution

(b) \frac{2}{6} \ \div \ 5 \\\ \\ Read Solution

Step 01
Convert the whole number into fraction by putting denominator 1
\Longrightarrow \ \frac{2}{6} \ \div \ \frac{5}{1}

Step 02
Convert the division into multiplication by inverting the right fraction
\Longrightarrow \ \frac{2}{6} \ \times \ \frac{1}{5}

Step 03
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{2\times 1}{6\times 5} \ \Longrightarrow \ \frac{2}{30}

Step 04
Reduce numerator and denominator to lowest order

Divide numerator and denominator by 2

Hence \frac{1}{15} is the solution

(c) \frac{3}{12} \ \div \ 6 \\\ \\

Step 01
Convert the whole number into fraction by putting denominator 1
\Longrightarrow \ \frac{3}{12} \ \div \ \frac{6}{1}

Step 02
Convert the division into multiplication by inverting the right fraction
\Longrightarrow \ \frac{3}{12} \ \times \ \frac{1}{6}

Step 03
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{3\times 1}{12\times 6} \ \Longrightarrow \ \frac{3}{72}

Step 04
Reduce numerator and denominator to lowest order

Divide numerator and denominator by 3

Hence \frac{1}{24} is the solution

(d) \frac{7}{4} \ \div \ 7 \\\ \\

Step 01
Convert the whole number into fraction by putting denominator 1
\Longrightarrow \ \frac{7}{4} \ \div \ \frac{7}{1}

Step 02
Convert the division into multiplication by inverting the right fraction
\Longrightarrow \ \frac{7}{4} \ \times \ \frac{1}{7}

Step 03
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{7\times 1}{4\times 7} \ \Longrightarrow \ \frac{7}{28}

Step 04
Reduce numerator and denominator to lowest order

Divide numerator and denominator by 7

Hence \frac{1}{4} is the solution

(e) \frac{8}{2} \ \div \ 6 \\\ \\

Step 01
Convert the whole number into fraction by putting denominator 1
\Longrightarrow \ \frac{8}{2} \ \div \ \frac{6}{1}

Step 02
Convert the division into multiplication by inverting the right fraction
\Longrightarrow \ \frac{8}{2} \ \times \ \frac{1}{6}

Step 03
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{8\times 1}{2\times 6} \ \Longrightarrow \ \frac{8}{12}

Step 04
Reduce numerator and denominator to lowest order

Divide numerator and denominator by 4

Hence \frac{2}{3} is the solution

(f) \frac{13}{5} \ \div \ 2 \\\ \\

Step 01
Convert the whole number into fraction by putting denominator 1
\Longrightarrow \ \frac{13}{5} \ \div \ \frac{2}{1}

Step 02
Convert the division into multiplication by inverting the right fraction
\Longrightarrow \ \frac{13}{5} \ \times \ \frac{1}{2}

Step 03
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{13\times 1}{5\times 2} \ \Longrightarrow \ \frac{13}{10}

Step 04
Reduce numerator and denominator to lowest order

Number cannot be simplified further

Hence \frac{13}{10} is the solution

(g) \frac{9}{4} \ \div \ 4 \\\ \\

Step 01
Convert the whole number into fraction by putting denominator 1
\Longrightarrow \ \frac{9}{4} \ \div \ \frac{4}{1}

Step 02
Convert the division into multiplication by inverting the right fraction
\Longrightarrow \ \frac{9}{4} \ \times \ \frac{1}{4}

Step 03
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{9\times 1}{4\times 4} \ \Longrightarrow \ \frac{9}{16}

Step 04
Reduce numerator and denominator to lowest order

Number cannot be simplified further

Hence \frac{9}{16} is the solution

(h) \frac{1}{6} \ \div \ 3 \\\ \\

Step 01
Convert the whole number into fraction by putting denominator 1
\Longrightarrow \ \frac{1}{6} \ \div \ \frac{3}{1}

Step 02
Convert the division into multiplication by inverting the right fraction
\Longrightarrow \ \frac{1}{6} \ \times \ \frac{1}{3}

Step 03
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{1\times 1}{6\times 3} \ \Longrightarrow \ \frac{1}{18}

Step 04
Reduce numerator and denominator to lowest order

Number cannot be simplified further

Hence \frac{1}{18} is the solution

(i) \frac{9}{15} \ \div \ 6 \\\ \\

Step 01
Convert the whole number into fraction by putting denominator 1
\Longrightarrow \ \frac{9}{15} \ \div \ \frac{6}{1}

Step 02
Convert the division into multiplication by inverting the right fraction
\Longrightarrow \ \frac{9}{15} \ \times \ \frac{1}{6}

Step 03
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{9\times 1}{15\times 6} \ \Longrightarrow \ \frac{9}{90}

Step 04
Reduce numerator and denominator to lowest order

Divide numerator and denominator by 9

Hence \frac{1}{10} is the solution

(j) \frac{7}{3} \ \div \ 7 \\\ \\

Step 01
Convert the whole number into fraction by putting denominator 1
\Longrightarrow \ \frac{7}{3} \ \div \ \frac{7}{1}

Step 02
Convert the division into multiplication by inverting the right fraction
\Longrightarrow \ \frac{7}{3} \ \times \ \frac{1}{7}

Step 03
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{7\times 1}{3\times 7} \ \Longrightarrow \ \frac{7}{21}

Step 04
Reduce numerator and denominator to lowest order

Divide numerator and denominator by 7

Hence \frac{1}{3} is the solution

(k) \frac{11}{13} \ \div \ 11 \\\ \\

Step 01
Convert the whole number into fraction by putting denominator 1
\Longrightarrow \ \frac{11}{13} \ \div \ \frac{11}{1}

Step 02
Convert the division into multiplication by inverting the right fraction
\Longrightarrow \ \frac{11}{13} \ \times \ \frac{1}{11}

Step 03
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{11\times 1}{13\times 11} \ \Longrightarrow \ \frac{11}{143}

Step 04
Reduce numerator and denominator to lowest order

Divide numerator and denominator by 11

Hence \frac{1}{13} is the solution

(l) \frac{9}{10} \ \div \ 3 \\\ \\

Step 01
Convert the whole number into fraction by putting denominator 1
\Longrightarrow \ \frac{9}{10} \ \div \ \frac{3}{1}

Step 02
Convert the division into multiplication by inverting the right fraction
\Longrightarrow \ \frac{9}{10} \ \times \ \frac{1}{3}

Step 03
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{9\times 1}{10\times 3} \ \Longrightarrow \ \frac{9}{30}

Step 04
Reduce numerator and denominator to lowest order

Divide numerator and denominator by 3

Hence \frac{3}{10} is the solution

(m) \frac{5}{8} \ \div \ 4 \\\ \\

Step 01
Convert the whole number into fraction by putting denominator 1
\Longrightarrow \ \frac{5}{8} \ \div \ \frac{4}{1}

Step 02
Convert the division into multiplication by inverting the right fraction
\Longrightarrow \ \frac{5}{8} \ \times \ \frac{1}{4}

Step 03
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{5\times 1}{8\times 4} \ \Longrightarrow \ \frac{5}{32}

Step 04
Reduce numerator and denominator to lowest order

Further simplification is not possible

Hence \frac{5}{32} is the solution

(n) \frac{18}{6} \ \div \ 3 \\\ \\

Step 01
Convert the whole number into fraction by putting denominator 1
\Longrightarrow \ \frac{18}{6} \ \div \ \frac{3}{1}

Step 02
Convert the division into multiplication by inverting the right fraction
\Longrightarrow \ \frac{18}{6} \ \times \ \frac{1}{3}

Step 03
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{18\times 1}{6\times 3} \ \Longrightarrow \ \frac{18}{18}

Step 04
Reduce numerator and denominator to lowest order

Divide both numerator and denominator by 18

Hence \frac{1}{1} is the solution

(o) \frac{0}{5} \ \div \ 5 \\\ \\

Step 01
Convert the whole number into fraction by putting denominator 1
\Longrightarrow \ \frac{0}{5} \ \div \ \frac{5}{1}

Step 02
Convert the division into multiplication by inverting the right fraction
\Longrightarrow \ \frac{0}{5} \ \times \ \frac{1}{5}

Step 03
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{0\times 1}{5\times 5} \ \Longrightarrow \ \frac{0}{25}

Step 04
Reduce numerator and denominator to lowest order

0 is the solution of this problem

### Divide Fraction and Whole number using Area Model

Here an image of box is provided in each question. Each image depict some fraction number.

You have to divide the given numbers and find the solution which is similar to the fraction shown by image.

(a) \frac{6}{5} \ \div \ 6 \\\ \\

Observing the given model we can see that:
Total number of boxes = 15
Total Colored Boxes = 3

Fraction of colored boxes = \frac{3}{15}

Solving the given division

\Longrightarrow \ \frac{6}{5} \ \div \ \frac{6}{1}\\\ \\ \Longrightarrow \ \frac{6}{5} \ \times \ \frac{1}{6}\\\ \\ \Longrightarrow \ \frac{6\times 1}{5\times 6}\\\ \\ \Longrightarrow \ \frac{6}{30} \\ \\

Dividing numerator and denominator by 2

Hence \frac{3}{15} is the solution

(02) Complete the division sentence to match the model

\frac{1}{3} \ \div \ 2 \\\ \\ Read Solution

Observing the given model we can see that:
Total number of boxes = 6
Total Colored Boxes = 1

Fraction of colored boxes = \frac{1}{6}

Solving the given division

\Longrightarrow \ \frac{1}{3} \ \div \ \frac{2}{1}\\\ \\ \Longrightarrow \ \frac{1}{3} \ \times \ \frac{1}{2}\\\ \\ \Longrightarrow \ \frac{1\times 1}{3\times 2}\\\ \\ \Longrightarrow \ \frac{1}{6} \\ \\

(03) Compute the division problem to match the below model
\frac{3}{12} \ \div \ 2 \\\ \\

Observing the given model we can see that:
Total number of boxes = 24
Total Colored Boxes = 3

Fraction of colored boxes = \frac{3}{24}

Solving the given division

\Longrightarrow \ \frac{3}{12} \ \div \ \frac{2}{1}\\\ \\ \Longrightarrow \ \frac{3}{12} \ \times \ \frac{1}{2}\\\ \\ \Longrightarrow \ \frac{3\times 1}{12\times 2}\\\ \\ \Longrightarrow \ \frac{3}{24} \\ \\

(04) Compute the division with whole number and match the below model
\frac{4}{2} \ \div \ 5 \\\ \\

In the above image we can see that:
Total number of boxes = 10
Number of colored box = 4

Fraction of colored boxes = \frac{4}{10}

Solving the given division

\Longrightarrow \ \frac{4}{2} \ \div \ \frac{5}{1}\\\ \\ \Longrightarrow \ \frac{4}{2} \ \times \ \frac{1}{5}\\\ \\ \Longrightarrow \ \frac{4\times 1}{2\times 5}\\\ \\ \Longrightarrow \ \frac{4}{10} \\ \\

(05) Compute the multiplication of fraction with the whole number
And find the solution as per the given image

\frac{6}{4} \ \div \ 4 \\\ \\ Read Solution

Total number of boxes = 16
Total colored boxes = 6

Fraction of colored boxes = \frac{6}{16}

Solving the given division

\Longrightarrow \ \frac{6}{4} \ \div \ \frac{4}{1}\\\ \\ \Longrightarrow \ \frac{6}{4} \ \times \ \frac{1}{4}\\\ \\ \Longrightarrow \ \frac{6\times 1}{4\times 4}\\\ \\ \Longrightarrow \ \frac{6}{16} \\ \\