If $\frac{a}{b}$ and $\frac{c}{d}$ are two rational numbers such that $\frac{c}{d}$ ? 0, we define ( $\frac{a}{b}$ ÷ $\frac{c}{d}$ )

= ( $\frac{a}{b}$ × $\frac{d}{c}$ ).When $\frac{a}{b}$ is divided by $\frac{c}{d}$ , then $\frac{a}{b}$ is called the dividend; $\frac{c}{d}$ is called the divisor and the result is known as quotient.

**Examples for Dividing Rational Numbers**

1. $\frac{9}{16}$ by $\frac{5}{8}$

= $\frac{9}{16}$ ÷ $\frac{5}{8}$

= $\frac{9}{16}$ × $\frac{8}{5}$ [here reverse the number $\frac{5}{8}$ as $\frac{8}{5}$ as well as division sign change to multiplication sign]

= $\frac{(9\times8)}{(16\times5)}$ [here take the numbers together and then multiply]

= $\frac{72}{80}$ [here $\frac{72}{80}$ = $\frac{9}{10}$ so, we observe that both numerator and the denominator of $\frac{72}{80}$ are divisible by 8]

= $\frac{9}{10}$

2. $\frac{(-6)}{25}$ by $\frac{3}{5}$

= $\frac{(-6)}{25}$ ÷ $\frac{3}{5}$

= $\frac{(-6)}{25}$ × $\frac{5}{3}$ [here reverse the number $\frac{3}{5}$ as $\frac{5}{3}$ as well change the division sign to multiplication sign]

= $\frac{((-6)\times5)}{(25\times3)}$ [here take the numbers together and then multiply them]

= $\frac{(-30)}{75}$ [here $\frac{(-30)}{75}$ = $\frac{(-2)}{5}$ so, we observe that both numerator and denominator of $\frac{(-30)}{75}$ are divisible by 15]

= $\frac{(-2)}{5}$

3. $\frac{11}{24}$ by $\frac{(-5)}{8}$

= $\frac{11}{24}$ ÷ $\frac{(-5)}{8}$

= $\frac{11}{24}$ × $\frac{8}{(-5)}$ [here reverse the number $\frac{(-5)}{8}$ as $\frac{8}{(-5)}$ as well as change the division sign to a multiplication sign]

= $\frac{(11\times8)}{(24\times(-5))}$ [here take the numbers together and then multiply them]

= $\frac{88}{-120}$ [here $\frac{88}{(-120)}$ = so, we observe that both numerator and denominator of are divisible by 8]

= $\frac{11}{(-15)}$ .

4. $\frac{(-9)}{40}$ by $\frac{(-3)}{8}$

= $\frac{(-9)}{40}$ ÷ $\frac{(-3)}{8}$

= $\frac{(-9)}{40}$ × $\frac{8}{(-3)}$ [here reverse the number $\frac{(-3)}{8}$ as $\frac{8}{(-3)}$ as well as change the division sign to a multiplication sign]

= $\frac{((-9)\times8)}{(40\times(-3))}$ [here take the numbers together and then multiply them]

= $\frac{-72}{-120}$ [here $\frac{-72}{-120}$ = $\frac{3}{5}$ so, we observe that both numerator and denominator of

$\frac{(-72)}{(-120)}$ are divisible by 24]

= $\frac{3}{5}$ .

5. $\frac{4}{9}$ by $\frac{8}{3}$ by $\frac{5}{8}$

= $\frac{4}{9}$ ÷ $\frac{8}{3}$ ÷ $\frac{5}{8}$

= $\frac{4}{9}$ × $\frac{3}{8}$ × $\frac{5}{8}$ [here reverse the number $\frac{8}{3}$ as $\frac{3}{8}$ again

$\frac{5}{8}$ as $\frac{8}{5}$ as well as division sign change to multiplication sign]

= $\frac{(4\times3\times8)}{(9\times8\times5)}$ [here take the numbers together and then multiply them]

= $\frac{96}{360}$ [here $\frac{96}{360}$ = $\frac{4}{15}$ so, we observe that both the numerator and the denominator are divisible by 24]

= $\frac{4}{15}$ .