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Explain Multiplication and Division of Rational numbers.
Multiplication of Rational Numbers:
To multiply two rational numbers $\frac{a}{b}$ and $\frac{c}{d}$, we multiply numerators of both numbers and denominators of both numbers.
$\frac{a}{b} \times \frac{c}{d} = \frac{a\times c}{b \times d} = \frac{ac}{bd}$
Division of Rational Numbers:
Dividing a rational number by another rational number is the same as multiplying the rational number by the reciprocal (inverse) of the other. We get the reciprocal of a rational number by interchanging its numerator and denominator.
For example,
$\frac{1}{2} \div \frac{1}{3}$
Step 1: Find the reciprocal of the second rational number (divisor).
Reciprocal of $\frac{1}{3}$ is $\frac{3}{1}$
Step 2: Multiply the first rational number (dividend) by the reciprocal of the second rational number (divisor).
$\frac{1}{2}\times \frac{3}{1}$
Step 3: Multiply the numerators and denominators of the rational numbers.
$\frac{1}{2}\times \frac{3}{1}= \frac{1\times3}{2\times1}= \frac{3}{2}$.
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