Question

Match the equivalent fractions and write two more for each:

$\begin{array}{c}\left(i\right)\frac{250}{400}\left(a\right)\frac{2}{3}\\ \left(ii\right)\frac{180}{200}\left(b\right)\frac{2}{5}\\ \left(iii\right)\frac{660}{990}\left(c\right)\frac{1}{2}\\ \left(iv\right)\frac{180}{360}\left(d\right)\frac{5}{8}\\ \left(v\right)\frac{220}{550}\left(e\right)\frac{9}{10}\end{array}$

Answer 1

Equivalent fractions are fractions which represent the same part of the whole.
To find an equivalent fraction of a given fraction, we may multiply or divide both the numerator and the denominator of the given fraction by the same number.

For the fractions given below, we find the simplest form of the fractions and then multiply both the numerator and the denominator of the simplest form of the fraction by 2 and 3 respectively to get the equivalent fraction.

(A fraction is said to be in the simplest (or lowest) form if its numerator and denominator have no common factor except 1.)

$\begin{array}{cccc}\text{(i)}& \frac{250}{400}=\frac{5}{8},\frac{10}{16},\frac{15}{24}& \text{(d)}& \frac{5}{8}(\because \frac{250÷50}{400÷50}=\frac{5}{8})\\ \text{(ii)}& \frac{180}{200}=\frac{9}{10},\frac{18}{20},\frac{27}{30}& \text{(e)}& \frac{9}{10}(\because \frac{180÷20}{200÷20}=\frac{9}{10})\\ \text{(iii)}& \frac{660}{990}=\frac{2}{3},\frac{4}{6},\frac{6}{9}& \text{(a)}& \frac{2}{3}(\because \frac{660÷330}{990÷330}=\frac{2}{3})\\ \text{(iv)}& \frac{180}{360}=\frac{1}{2},\frac{2}{4},\frac{3}{6}& \text{(c)}& \frac{1}{2}(\because \frac{180÷180}{360÷180}=\frac{1}{2})\\ \text{(v)}& \frac{220}{550}=\frac{2}{5},\frac{4}{10},\frac{6}{15}& \text{(b)}& \frac{2}{5}(\because \frac{220÷110}{550÷110}=\frac{2}{5})\end{array}$