# Multiplication of Fractional Number by a Whole Number

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

$$\frac{1}{4}$$ is multiplied by 4 or 4 $$\frac{1}{4}$$ = 4 of $$\frac{1}{4}$$

 Suppose this is whole (1)
 This is the one fourth of 1 that is  $$\frac{1}{4}$$
 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.

(c) Always write the answer as a mixed fraction if it is not a proper fraction/whole number.

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

1. $$\frac{3}{4}$$ × 15

= $$\frac{3 ×15}{4}$$

= $$\frac{45}{4}$$

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

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

= $$\frac{4 × 2 + 1}{2}$$ of 3

= $$\frac{9}{2}$$ × 3

= $$\frac{9 × 3}{2}$$

= $$\frac{27}{2}$$

= 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

= $$\frac{29 × 7}{2}$$

= $$\frac{203}{2}$$

= 101$$\frac{1}{2}$$

5. 6$$\frac{2}{7}$$ of 4

= $$\frac{6 × 7 + 2}{7}$$ of 4

= $$\frac{44}{7}$$ × 4

= $$\frac{44 × 4}{7}$$

= $$\frac{176}{7}$$

= 25$$\frac{1}{7}$$

6. 18$$\frac{1}{4}$$ × 12

= $$\frac{18 × 4 + 1}{4}$$ × 12

= $$\frac{73}{4}$$ × 12

= $$\frac{73 × 12}{4}$$

= $$\frac{876}{4}$$

= 219

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