# Product of a Fraction and a Whole Number: Problem Type 1

In this lesson, we solve problems where we find the product of a fraction and a whole number.

Rules for finding the product of a fraction and a whole number

• We first write the whole number as a fraction, i.e., we write it divided by one; for example 5 is written as 5/1.

• We then multiply the numerators and then the denominators of both fractions to get the product fraction.

• If any simplification or cross cancelling is required, it is done and final answer is written.

Example

Multiply $\frac{5}{4}$ × 8

Solution

Step 1:

First, we write the whole number 8 as a fraction $\frac{8}{1}$

Step 2:

$\frac{5}{4}$ × 8 = $\frac{5}{4}$ × $\frac{8}{1}$

Step 3:

As 4 and 8 are multiples of 8, cross cancelling 4 and 8, we get

$\frac{5}{4}$ × $\frac{8}{1}$ = $\frac{5}{1}$ × $\frac{2}{1}$

Step 4:

Multiply the numerators and denominators of both fractions as follows.

$\frac{5}{1}$ × $\frac{2}{1}$ = $\frac{(5 × 2)}{(1 × 1)}$ = $\frac{10}{1}$ = 10

Step 5:

So $\frac{5}{4}$ × 8 = 10

Multiply $\frac{4}{5}$ × 15

### Solution

Step 1:

First, we write the whole number 15 as a fraction $\frac{15}{1}$

Step 2:

$\frac{4}{5}$ × 15 = $\frac{4}{5}$ × $\frac{15}{1}$

Step 3:

As 5 and 15 are multiples of 5, cross cancelling 5 and 15, we get

$\frac{4}{5}$ × $\frac{15}{1}$ = $\frac{4}{1}$ × $\frac{3}{1}$

Step 4:

We multiply the numerators and denominators of both fractions as follows.

$\frac{4}{1}$ × $\frac{3}{1}$ = $\frac{(4 × 3)}{(1 × 1)}$ = $\frac{12}{1}$ = 12

Step 5:

So $\frac{4}{5}$ × 15 = 12

Multiply $\frac{3}{7}$ × 14

### Solution

Step 1:

First, we write the whole number 14 as a fraction $\frac{14}{1}$

Step 2:

$\frac{3}{7}$ × 14 = $\frac{3}{7}$ × $\frac{14}{1}$

Step 3:

As 7 and 14 are multiples of 7, cross cancelling 7 and 14, we get

$\frac{3}{7}$ × $\frac{14}{1}$ = $\frac{3}{1}$ × $\frac{2}{1}$

Step 4:

Multiply the numerators and denominators of both fractions as follows.

$\frac{3}{1}$ × $\frac{2}{1}$ = $\frac{(3 × 2)}{(1 × 1)}$ = $\frac{6}{1}$ = 6

Step 5:

So $\frac{3}{7}$ × 14 = 6