# 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.

Multiply. Write your answer as a mixed number 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, $2\frac{2}{5} \times \frac{3}{4} = 1\frac{4}{5}$

Multiply. Write your answer as a mixed number in simplest form.

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

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

Multiply. Write your answer as a mixed number in simplest form.

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

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