Question

Write five equivalent fractions of $ \dfrac{3}{5} $

Answer 1

Hint: We know that a fraction is represented by two numbers separated by a horizontal line. The number above the horizontal line is the numerator and the number below the horizontal line is the denominator of the fraction.

Complete step-by-step answer:
Therefore the above fraction has the numerator 3 and the denominator 5. Concept of equivalent fraction can be understood by, the fractions having the same value are called equivalent fractions.
We must note that the value of a fraction does not change by multiplying or dividing the fraction by the same number, therefore an equivalent fraction can be obtained by either multiplying or dividing the numerator and the denominator by the same number. Hence five equivalent fraction of $ \dfrac{3}{5} $ will be;
Let us multiply both the numerator and the denominator by 2. We have,
 $ \Rightarrow \dfrac{3}{5} \times \dfrac{2}{2} = \dfrac{6}{{10}} $
Multiplying both the numerator and denominator by 3, we have
 $ \Rightarrow \dfrac{3}{5} \times \dfrac{3}{3} = \dfrac{9}{{15}} $
Multiplying both the numerator and denominator by 4, we have
 $ \Rightarrow \dfrac{3}{5} \times \dfrac{4}{4} = \dfrac{{12}}{{20}} $
Multiplying both the numerator and denominator by 5, we have
 $ \Rightarrow \dfrac{3}{5} \times \dfrac{5}{5} = \dfrac{{15}}{{25}} $
Multiplying both the numerator and denominator by 6, we have
 $ \Rightarrow \dfrac{3}{5} \times \dfrac{6}{6} = \dfrac{{18}}{{30}} $
Therefore multiplying the numerator and denominator by the same non zero number we have the five equivalent fractions as:
 $ \Rightarrow \dfrac{6}{{10}},\dfrac{9}{{15}},\dfrac{{12}}{{20}},\dfrac{{15}}{{25}},\dfrac{{18}}{{30}} $
So, the correct answer is “$\dfrac{6}{{10}},\dfrac{9}{{15}},\dfrac{{12}}{{20}},\dfrac{{15}}{{25}},\dfrac{{18}}{{30}} $ ”.

Note: In order to check whether the given fractions are equivalent or not, we do cross-multiplication. If the product of the numerator of first fraction and the denominator of the second fraction is equal to the product of the denominator of the first fraction and the numerator of the second fraction. Then the given fractions are said to be equivalent.