Question

Find the equivalent fraction of \[\dfrac{3}{5}\] having
(i) denominator \[20\]
(ii) numerator \[9\]
(iii) denominator \[30\]
(iv) numerator \[27\]

Answer 1

Hint: An equivalent fraction can be defined as fractions with different Numerators and denominators that represent the same value or proportion of the whole
A fraction can be made equivalent by using the properties of the ratio i.e.
In ratio we can divide or multiply the numerator and the denominator by any number because the ratio remains same
Example of equivalent Fraction:
\[\dfrac{1}{2} = \dfrac{2}{4} = \dfrac{4}{8}\]
As fraction can be made equivalent by the rule-
Changing that denominator using multiply or divide and applying the same rule to numerator

Complete step-by-step solution:
Given,
Fraction \[ = \dfrac{3}{5}\]
(i) To find the equivalent fraction of \[\dfrac{3}{5}\] having denominators .
To make denominator \[5\] as \[20\], \[5\]must be multiplied by \[4\] hence to make the fraction equivalent \[3\] must be multiplied by \[4\] as well i.e. \[\dfrac{3}{5} \times \dfrac{4}{4} = \dfrac{{12}}{{20}}\].
Hence, \[\dfrac{{12}}{{20}}\] is an equivalent fraction of \[\dfrac{3}{5}\] with denominator \[20\].
(i) To find the equivalent fraction of \[\dfrac{3}{5}\] fraction with numerator \[9\].
To make numerator \[3\] as \[9\], \[3\]must be multiplied by \[9\]and to make the fraction equivalent, \[5\] must also be multiplied \[3\]with i.e. \[\dfrac{3}{5} \times \dfrac{3}{3} = \dfrac{9}{{15}}\]
Hence, \[\dfrac{9}{{15}}\] is an equivalent fraction of \[\dfrac{3}{5}\] with numerator \[9\].
(i) To find the equivalent fraction of \[\dfrac{3}{5}\] with denominator \[30\].
To make denominator \[5\] as \[30\] , must be multiplied by \[6\]and to make the fraction equivalent, \[3\] must also be multiplied with \[6\] i.e. \[\dfrac{3}{5} \times \dfrac{6}{6} = \dfrac{{18}}{{30}}\]
Hence, \[\dfrac{{18}}{{30}}\] is an equivalent fraction of \[\dfrac{3}{5}\] with denominator \[30\].
(i) To find the equivalent fraction \[\dfrac{3}{5}\] with numerator \[27\] .
To make the numerator \[3\] as \[27\], \[3\] must be multiplied by \[9\] and to make the fraction equivalent, \[5\] must also be multiplied by \[9\] i.e. \[\dfrac{3}{5} \times \dfrac{9}{9} = \dfrac{{27}}{{45}}\,\,\]
Hence, \[\dfrac{{27}}{{45}}\,\,\]is an equivalent fraction of \[\dfrac{3}{5}\] with numerator \[27\].

Note:If the numerator and denominator of a fraction are multiplied (or divided) by the same non-zero number, then the resulting fraction is equivalent to the original fraction.