# Give the rational numbers equivalent to:$(i)$. $\frac{-2}{7}$$(ii). \frac{5}{-3}$$(iii)$. $\frac{4}{9}$

Given: Rational numbers:

$(i)$. $\frac{-2}{7}$

$(ii)$. $\frac{5}{-3}$

$(iii)$. $\frac{4}{9}$

To do: To write the rational numbers equivalent to the above given rational numbers.

Solution:

$(i).\ -\frac{2}{7}$

Multiplying the given rational number by the same numerator and denominator, the product obtained will be equal to the given rational number.

Now we will multiply the given rational number by $\frac{2}{2},\ \frac{3}{3},\ \frac{4}{4}$ and $\frac{5}{5}$ to write other rational numbers equivalent to the given rational number.

$\frac{(-2\times 2)}{(7\times 2)}=-\frac{4}{14}$,

$\frac{(-2\times 3)}{(7\times 3)}=-\frac{6}{21}$,

$\frac{(-2\times 4)}{(7\times 4)}=-\frac{8}{28}$,

$\frac{(-2\times 5)}{(7\times 5)}=-\frac{10}{35}$

Therefore, the equivalent fractions to the number $-\frac{2}{7}$ are, $-\frac{4}{14},\ -\frac{6}{21},\ -\frac{8}{28},\ -\frac{10}{35}$

$(ii).\ \frac{5}{(-3)}$

Multiplying the given rational number by the same numerator and denominator, the product obtained will be equal to the given rational number.

Now we will multiply the given rational number by $\frac{2}{2},\ \frac{3}{3},\ \frac{4}{4}$ and $\frac{5}{5}$ to write other rational numbers equivalent to the given rational number.

$\frac{(5\times 2)}{(-3\times 2)}=\frac{10}{(-6)}$,

$\frac{(5\times 3)}{(-3\times 3)}=\frac{15}{(-9)}$,

$\frac{(5\times 4)}{(-3\times 4)}=\frac{20}{(-12)}$,

$\frac{(5\times 5)}{(-3\times 5)}=\frac{25}{(-15)}$

Therefore, the equivalent fractions to the number $\frac{5}{(-3)}$ are $\frac{10}{(-6)},\ \frac{15}{(-9)},\ \frac{20}{(-12)},\ \frac{25}{(-15)}$

$(iii)$. $\frac{4}{9}$

Multiplying the given rational number by the same numerator and denominator, the product obtained will be equal to the given rational number.

Now we will multiply the given rational number by $\frac{2}{2},\ \frac{3}{3},\ \frac{4}{4}$ and $\frac{5}{5}$ to write other rational numbers equivalent to the given rational number.

$\frac{(4\times 2)}{(9\times 2)}=\frac{8}{18}$,

$\frac{(4\times 3)}{(9\times 3)}=\frac{12}{27}$,

$\frac{(4\times 4)}{(9\times 4)}=\frac{16}{36}$,

$\frac{(4\times 5)}{(9\times 5)}=\frac{20}{45}$

Therefore, the equivalent fractions to the number $\frac{4}{9}$ are $\frac{8}{18},\ \frac{12}{27},\ \frac{16}{36}$ and $\frac{20}{45}$.
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