# Mixed number multiplication

In this lesson, we are dealing with multiplication of a mixed number with another fraction.

Rules for mixed number multiplication

• First, the mixed number is converted into an improper fraction and then multiplied with the given fraction.

• The numerators of the two fractions are multiplied at the top and the denominators are multiplied at the bottom to get the resulting fraction.

• Simplification is done, if required, the fraction is converted into a mixed fraction in simplest form.

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

### Solution

Step 1:

First, we write the mixed number $2\frac{2}{5}$ as an improper fraction

$2\frac{2}{5} = \frac{\left ( 2 \times 5 + 2 \right )}{5} = \frac{12}{5}$

Step 2:

$2\frac{2}{5} \times \frac{3}{4} = \frac{12}{5} \times \frac{3}{4}$

Step 3:

Cross cancelling 12 and 4 we get

$\frac{12}{5} \times \frac{3}{4} = \frac{3}{5} \times \frac{3}{1} = \frac{(3 \times 3)}{(5 \times 1)} = \frac{9}{5}$

Step 4:

$\frac{9}{5}$ can be written as a mixed number as follows

$\frac{9}{5} = 1\frac{4}{5}$

Step 5:

So, $2\frac{2}{5} \times \frac{3}{4} = 1\frac{4}{5}$

$1\frac{4}{5} \times \frac{2}{3}$

### Solution

Step 1:

First, we write the mixed number $1\frac{4}{5}$ as an improper fraction $1\frac{4}{5} = \frac{\left ( 1 \times 5 + 4 \right )}{5} = \frac{9}{5}$

Step 2:

$1\frac{4}{5} \times \frac{2}{3} = \frac{9}{5} \times \frac{2}{3}$

Step 3:

Cross cancelling 9 and 3 we get

$\frac{9}{5} \times \frac{2}{3} = \frac{3}{5} \times \frac{2}{1} = \frac{(3 \times 2)}{(5 \times 1)} = \frac{6}{5}$

Step 4:

$\frac{6}{5}$ can be written as a mixed number as follows

$\frac{6}{5} = 1\frac{1}{5}$

Step 5:

So, $1\frac{4}{5} \times \frac{2}{3} = 1\frac{1}{5}$

$3\frac{2}{5} \times \frac{1}{4}$

### Solution

Step 1:

First, we write the mixed number $3\frac{2}{5}$ as an improper fraction $3\frac{2}{5} = \frac{\left ( 3 \times 5 + 2 \right )}{5} = \frac{17}{5}$

Step 2:

$3\frac{2}{5} \times \frac{1}{4} = \frac{17}{5} \times \frac{1}{4}$

Step 3:

Simplifying

$\frac{17}{5} \times \frac{1}{4} = \frac{(17 \times 1)}{(5 \times 4)} = \frac{17}{20}$

Step 4:

So, $3\frac{2}{5} \times \frac{1}{4} = \frac{17}{20}$