# 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$$\frac{1}{3}$$ × $$\frac{1}{5}$$)

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

= $$\frac{15}{19}$$ × $$\frac{1}{1}$$

= $$\frac{15 × 1}{(19 × 1}$$

= $$\frac{15}{19}$$

Property 3: If a fractional number is multiplied by zero, the product is zero.

For Example:

(i) $$\frac{3}{11}$$ × 0

= $$\frac{3 × 0}{11}$$

= 0

(ii) $$\frac{7}{15}$$ × 0

= $$\frac{7 × 0}{15}$$

= 0