Question

Give four rational numbers equivalent to:
i) $\frac{-2}{7}$ ii) $\frac{5}{-3}$

Answer 1

$i)$ Given rational number is $\frac{-2}{7}$

We know that, multiplying a number by $1$ gives the same number.

Hence, when we multiply a rational number by $\frac{a}{a}\left(1\right)$, it gives an equivalent rational number, without changing the simplest form of the rational number.

$\therefore$ four rational numbers equivalent to $\frac{-2}{7}$ will be:

$1.\frac{-2}{7}\times \frac{2}{2}=\frac{-4}{14}$

$2.\frac{-2}{7}\times \frac{3}{3}=\frac{-6}{21}$

$3.\frac{-2}{7}\times \frac{4}{4}=\frac{-8}{28}$

$4.\frac{-2}{7}\times \frac{5}{5}=\frac{-10}{35}$

Hence, four rational numbers equivalent to $\frac{-2}{7}$ are $\frac{-4}{14},\frac{-6}{21},\frac{-8}{28},\frac{-10}{35}$

$ii)$

Similarly, equivalent rational numbers of $\frac{5}{-3}$ will be:

$1.\frac{5}{-3}\times \frac{2}{2}=\frac{10}{-6}$

$2.\frac{5}{-3}\times \frac{3}{3}=\frac{15}{-9}$

$3.\frac{5}{-3}\times \frac{5}{5}=\frac{20}{-12}$

$4.\frac{5}{-3}\times \frac{5}{5}=\frac{25}{-15}$

Hence, four rational numbers equivalent to $\frac{5}{-3}$ are $\frac{10}{-6},\frac{15}{-9},\frac{20}{-12},\frac{25}{-15}$