Multiplication of Fraction - Multiplication of a Fraction by a Whole Number

Multiplication of a Fraction by a Whole Number:

Observe the following pictures, 

Each shaded part is `1/4` part of a square.

They will represent `1/4 + 1/4 + 1/4 = 1/4 xx 3`

Combining the three shaded parts, we get `3/4` part of a square.

Similarly,

Each shaded part is `2/9` part of a square.

They will represent `2/9 + 2/9 + 2/9 = 2/9 xx 3`

Combining the three shaded parts, we get `6/9 = 2/3` part of a square.

1. Multiplication of a whole number with a proper or an improper fraction:

To multiply a whole number with a proper or an improper fraction, we multiply the whole number with the numerator of the fraction, keeping the denominator the same.

`5 xx 2/3 = (2 xx 5)/3 = 10/3`.

`3 xx 1/2 = (3 xx 1)/2 = 3/2`.

`3 xx 2/7 = (3 xx 2)/7 = 6/7`.

`4 xx 3/5 = (4 xx 3)/5 = 12/5`.

The fractions that we considered till now, i.e., `1/2, 2/3, 2/7, and 3/5` were proper fractions.

`2 xx 5/3 = (2 xx 5)/3 = 10/3`.

`3 xx 7/2 = (3 xx 7)/2 = 21/2`.

`5 xx 5/5 = (5 xx 5)/5 = 5/1`.

2. Multiplication Of A Whole Number With A Mixed Fraction:

To multiply a mixed fraction to a whole number, first convert the mixed fraction to an improper fraction and then multiply.

1) `3 xx 3 7/2 = 3 xx (2 xx 3 + 7)/2 = 3 xx 13/2 = 39/2 = 19 1/2`.

2) `7 xx 2 3/5 = 7 xx (5 xx 2 +3)/5 = 7 xx 13/5 = 91/5 = 18 1/5`.