Question

Match the following.

• A. $\frac{23}{9}$
• B. $-4$
• C. $-\frac{25}{4}$
• D. $\frac{5}{7}$

Answer 1

$\text{Multiplication of two(or more) rational numbers}=\frac{\text{Product of their numerators}}{\text{Product of their denominators}}$
$⟹3\frac{5}{6}\times \frac{2}{3}=\frac{23}{6}\times \frac{2}{3}=\frac{23}{9}$ = $2\frac{5}{9}$
Similarly, $⟹\frac{10}{3}\times -\frac{6}{5}=-4$
Now, if $\frac{a}{b}$ and $\frac{c}{d}$ are rational numbers such that $\frac{c}{d}\ne 0$, then
$\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}\times \frac{d}{c}=\frac{ad}{bc}$
Thus, we have $-\frac{5}{2}÷\frac{2}{5}=-\frac{5}{2}\times \frac{5}{2}=-\frac{25}{4}$= $-6\frac{1}{4}$
And, $\frac{15}{28}÷\frac{3}{4}=\frac{15}{28}\times \frac{4}{3}=\frac{5}{7}$