# How to multiply and divide the fractions ?

Multiplication of Fractions:

To multiply two fractions $\frac{a}{b}$ and $\frac{c}{d}$, we multiply the numerators of both the numbers and denominators of both the numbers.

$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} = \frac{ac}{bd}$.

For example,

$\frac{1}{3} \times \frac{7}{10} = \frac{1 \times 7}{3 \times 10}$

$= \frac{7}{30}$.

Division of Fractions:

Dividing a fraction by another fraction is the same as multiplying the fraction by the reciprocal (inverse) of the other. We get the reciprocal of a fraction by interchanging its numerator and denominator.

For example, the reciprocal of $\frac{2}{7}$ is $\frac{7}{2}$.

$\frac{1}{2} \div \frac{1}{3}$

Step 1: Find the reciprocal of the second fraction (divisor). Reciprocal of $\frac{1}{3}$ is $\frac{3}{1}$.

Step 2: Multiply the first fraction (dividend) by the reciprocal of the second fraction (divisor). $\frac{1}{2}\times\frac{3}{1}$.

Step 3: Multiply the numerators and denominators of the fractions.

$\frac{1}{2}\times\frac{3}{1}=\frac{1\times3}{2\times1}=\frac{3}{2}$.

Updated on: 10-Oct-2022

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