Dividing Fractions

For example, to divide the fractions $\dfrac{1}{2}\div\dfrac{1}{3},$ we follow these steps:

1. We invert the numerator and denominator of the fraction on the right. 
   
   $$\frac{1}{2}\div\frac{3}{1}$$
    
2. We change the division sign to a multiplication sign.
   
   $$\frac{1}{2}{\color{red}\times} \frac{3}{1}$$
    
3. We multiply the fractions.
   
   $$\frac{1}{2}\times \frac{3}{1} =\frac{3}{2}$$

$$\frac{2}{3}\div\frac{1}{9}=\frac{2}{3}\times\frac{9}{1}=\frac{2\times9}{3\times1}=\frac{18}{3}=6$$

$$\frac{4}{5}\div\frac{2}{3}=\frac{4}{5}\times\frac{3}{2}=\frac{4\times3}{5\times2}=\frac{12}{10}=\frac{6}{5}$$

• When dividing 2 numbers with the same sign, the quotient will be positive.
   
• When dividing 2 numbers with opposite signs, the quotient will be negative.

$$4\frac{1}{3}\div\frac{2}{5}=\frac{13}{3}\div\frac{2}{5}=\frac{13}{3}\times\frac{5}{2}=\frac{65}{6}=10\frac{5}{6}$$

$$8\frac{1}{2}\div4\frac{1}{3} =\frac{17}{2}\div\frac{13}{3}=\frac{17}{2}\times\frac{3}{13} =\frac{51}{26}$$