Product of a Fraction and a Whole Number: Problem Type 2

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Introduction

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 $\frac{3}{8}$ 5

Solution

Step 1:

First, we write the whole number 5 as a fraction $\frac{5}{1}$

Step 2:

$\frac{3}{8}$ 5 = $\frac{3}{8}$ $\frac{5}{1}$

Step 3:

Multiply the numerators and denominators of both fractions as follows.

$\frac{3}{8}$ $\frac{5}{1}$ = $\frac{(3 5)}{(8 1)}$ = $\frac{15}{8}$

Step 4:

So $\frac{3}{8}$ 5 = $\frac{15}{8}$

Problem 1

Multiply $\frac{2}{15}$ 5

Solution

Step 1:

First, we write the whole number 5 as a fraction $\frac{5}{1}$

$\frac{2}{15}$ 5 = $\frac{2}{15}$ $\frac{5}{1}$

Step 2:

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

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

Step 3:

Multiply the numerators and denominators of both fractions as follows.

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

Step 4:

So $\frac{2}{15}$ 5 = $\frac{2}{3}$

Problem 2

Multiply $\frac{3}{7}$ 2

Solution

Step 1:

First, we write the whole number 2 as a fraction $\frac{2}{1}$

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

Step 2:

Multiply the numerators and denominators of both fractions as follows.

$\frac{3}{7}$ $\frac{2}{1}$ = $\frac{(3 2)}{(7 1)}$ = $\frac{6}{7}$

Step 3:

So $\frac{3}{7}$ 2 = $\frac{6}{7}$