Question

Fill in the blanks:
(i) $\frac{-9}{5}=\frac{---}{20}=\frac{27}{---}=\frac{-45}{---}$

(ii) $\frac{-6}{11}=\frac{-18}{---}=\frac{---}{44}$

Answer 1

If the simplest form two or more fractions is same then they are said to be equivalent fractions.

In general, by multiplying or dividing the numerators and denominators with same number we can convert into equivalent fractions.

(i)

$\frac{-9}{5}=\frac{---}{20}=\frac{27}{---}=\frac{-45}{---}$

$\frac{-9}{5}=\frac{-9\times 4}{5\times 4}=\frac{-36}{20}$---(1)

$\frac{-9}{5}=\frac{-9\times -3}{5\times -3}=\frac{27}{-15}$---(2)

$\frac{-9}{5}=\frac{-9\times 5}{5\times 5}=\frac{-45}{25}$----(3)

From (1), (2) and (3),

$\frac{-9}{5}=\frac{-36}{20}=\frac{27}{-15}=\frac{-45}{25}$

(ii)

$\frac{-6}{11}=\frac{-18}{---}=\frac{---}{44}$

$\frac{-6}{11}=\frac{-6\times 3}{11\times 3}=\frac{-18}{33}$ ---(4)

$\frac{-6}{11}=\frac{-6\times 4}{11\times 4}=\frac{-24}{44}$---(5)

From(4) and (5),

$\frac{-6}{11}=\frac{-18}{33}=\frac{-24}{44}$