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 spanided 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 simppfication or cross cancelpng 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 cancelpng 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 cancelpng 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 cancelpng 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