# Division with a mixed number and a whole number

In this lesson, we are dealing with division of a mixed number and a whole number.

Rules for division with a mixed number and a whole number

• The mixed number is converted into an improper fraction and the whole number is written as a fraction with denominator 1.

• Division of the fractions is converted into a multiplication operation by multiplying the improper fraction with the reciprocal of the whole number.

• The resulting fraction, if required, is written as a mixed number in simplest form.

$2\frac{1}{3} \div 7$

### Solution

Step 1:

First, we write the mixed number $2\frac{1}{3}$ as an improper fraction

$2\frac{1}{3} = \frac{\left ( 2 \times 3 + 1 \right )}{3} = \frac{7}{3}$; $7 = \frac{7}{1}$

Step 2:

The division is converted into multiplication as follows

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

Step 3:

Multiplying numerators and denominators

$\frac{7}{3} \times \frac{1}{7} = \frac{(7 \times 1)}{(3 \times 7)} = \frac{7}{21}$

Step 4:

$\frac{7}{21}$ can be simplified and written as follows

$\frac{7}{21} = \frac{1}{3}$

Step 5:

So, $2\frac{1}{3} \div 7 = \frac{1}{3}$

$5 \div 1\frac{3}{4}$

### Solution

Step 1:

First, we write the mixed number $1\frac{3}{4}$ as an improper fraction

$1\frac{3}{4} = \frac{\left ( 1 \times 4 + 3 \right )}{4} = \frac{7}{4}$; $5 = \frac{5}{1}$

Step 2:

$5 \div 1\frac{3}{4} = \frac{5}{1} \div \frac{7}{4}= \frac{5}{1} \times \frac{4}{7}$

Step 3:

Multiplying numerators and denominators

$\frac{5}{1} \times \frac{4}{7} = \frac{(5 \times 4)}{(1 \times 7)} = \frac{20}{7}$

Step 4:

$\frac{20}{7}$ can be written as a mixed number as follows

$\frac{20}{7} = 2\frac{6}{7}$

Step 5:

So, $5 \div 1\frac{3}{4} = 2\frac{6}{7}$