Question

Convert the $ \dfrac{2}{3},\dfrac{5}{7} $ pair of fractions into like fractions?

Answer 1

Hint: Concept on like and unlike fraction
Like fractions: The group of two or more fractions that have exactly the same denominator are called like fractions
Ex. $ \dfrac{1}{7},\dfrac{2}{7},\dfrac{8}{7},\dfrac{{13}}{7} $
Unlike fractions: fractions with different denominator are called unlike fraction
Ex. $ \dfrac{2}{3},\dfrac{4}{9},\dfrac{6}{{13}},\dfrac{7}{8} $

Complete step-by-step answer:
Conversion of unlike to like fractions
Steps of conversion:
(i) Find the LCM of denominators of unlike fractions
(ii) Calculate their equivalent fractions with the same denominator that is the LCM.
In our question,
Given pair of unlike fraction is $ \left( {\dfrac{2}{3},\dfrac{5}{7}} \right) $ Step-1 Equivalent fraction with denominator as $ 21 $ ,is
 $ \dfrac{2}{3} \times \dfrac{7}{7} = \dfrac{{14}}{{21}} $
 $ \dfrac{5}{7} \times \dfrac{3}{3} = \dfrac{{15}}{{21}} $
So, like fraction $ = \left( {\dfrac{{14}}{{21}},\dfrac{{15}}{{21}}} \right) $

Note: In simple language , for changing unlike to like fractions, just we have to make the denominator the same by taking LCM of unlike fractions. When making comparison of fractions , it is very difficult to compare unlike fractions therefore the conversion of unlike to like fractions is done as the same denominator which just compares the numerator.