Properties of Multiplication of Fractional Numbers

The properties of multiplication of fractional numbers are discussed here.

Property 1: If two fractional numbers are multiplied in either order, the product remains the same.

For Example:

(i) $\frac{2}{3}$ × $\frac{7}{5}$

= $\frac{2 × 7}{3 × 5}$

= $\frac{14}{15}$

And now if you interchange the place of the fractional numbers the product does not change.

$\frac{7}{5}$ × $\frac{2}{3}$

= $\frac{7 × 2}{5 × 3}$

= $\frac{14}{15}$

We observe that the product in both the cases are same.

So, $\frac{2}{3}$ × $\frac{7}{5}$ = $\frac{7}{5}$ × $\frac{2}{3}$.

Note: From the above example we understand that, changing the order of fractional numbers does not change the product.

(ii) (4$\frac{2}{3}$ × 5$\frac{1}{3}$) × $\frac{1}{5}$ = 4$\frac{2}{3}$ (5$\frac{1}{3}$ × $\frac{1}{5}$)

$Properties of Multiplication of Fractional Numbers$

Property 2: If a fractional number is multiplied by one, the product is the fractional number itself.

For Example:

(i) $\frac{7}{9}$ × 1

= $\frac{7}{9}$ × $\frac{1}{1}$

= $\frac{7 × 1}{9 × 1}$

= $\frac{7}{9}$

So, we observe that a fraction multiplied by 1 is the fraction itself.

(ii) $\frac{5}{8}$ × 1

= $\frac{5}{8}$ × $\frac{1}{1}$

= $\frac{5 × 1}{(8 × 1}$

= $\frac{5}{8}$

(iii) $\frac{15}{19}$ × 1

= $\frac{15}{19}$ × $\frac{1}{1}$

= $\frac{15 × 1}{(19 × 1}$

= $\frac{15}{19}$