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Multiplication of Fractional Number by a Whole Number

We will discuss here about the multiplication of fractional number by a whole number.

∙ $\frac{1}{4}$ $\frac{1}{4}$

$This is Whole Part$

Suppose this is whole (1)

$This is One Fourth Part$

This is the one fourth of 1 that is $\frac{1}{4}$

$This is 1 Part$

So, this figure shows 4 of $\frac{1}{4}$ or $\frac{1}{4}$ . (Since, 4 × $\frac{1}{4}$ = $\frac{1}{4}$ + $\frac{1}{4}$ + $\frac{1}{4}$ + $\frac{1}{4}$ )

Therefore, 4 × $\frac{1}{4}$ = $\frac{4}{1}$ × $\frac{1}{4}$ = $\frac{4 × 1}{1 × 4}$ = $\frac{4}{4}$ = 1

Hence we conclude that, to multiply a fraction by a whole number, the numerator of the fraction is multiplied by the whole number. This becomes the numerator of the product. The denominator does not change.

The following rules are given below for the multiplication of a fraction by a whole number:

(a) If the fraction is a mixed fraction, convert it to improper fraction.

$Multiplication of Fractional Number by a Whole Number$

Solved examples on multiplication of fractional number by a whole number:

1. $\frac{3}{4}$ × 15

$Multiplication of Fractional Number by a Whole Number$

= $\frac{3 ×15}{4}$

= $\frac{45}{4}$

$Multiplication of Fractional Number by a Whole Number$

= 11 $\frac{1}{4}$

2. 4 $\frac{1}{2}$ of 3

= $\frac{4 × 2 + 1}{2}$ of 3

= $\frac{9}{2}$ × 3

= $\frac{9 × 3}{2}$

= $\frac{27}{2}$

$Multiplication of Fractional Number by a Whole Number$

= 13 $\frac{1}{2}$

Note: ‘Of‘ stands for multiplication.

3. $\frac{9}{3}$ × 5

= $\frac{9 × 5}{3}$

= $\frac{45}{3}$

= 15

4. 14 $\frac{1}{2}$ of 7

= $\frac{14 × 2 + 1}{2}$ of 7

= $\frac{29}{2}$ × 7

= $\frac{29 × 7}{2}$