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