Question

Are $ \dfrac{4}{6} $ and $ \dfrac{8}{{12}} $ equal?

Answer 1

Hint: Here we are given two fractions which are the term expressed as the numerator upon the denominator. Here we will convert the given fractions in the more simplified equivalent fractions by removing common factors from the numerator and the denominator.

Complete step-by-step answer:
Take the given fraction: $ \dfrac{4}{6} $
Find the factors for the above expression, factors are the terms which when multiplied gives the original number.
 $ \dfrac{4}{6} = \dfrac{{2 \times 2}}{{2 \times 3}} $
Common factors from the numerator and the denominator cancel each other and therefore remove from the numerator and the denominator of the above fraction.
 $ \dfrac{4}{6} = \dfrac{2}{3} $ ….. (A)
Similarly find the equivalent fraction for the second given fraction –
Take the given fraction: $ \dfrac{8}{{12}} $
Find the factors for the above expression,
 $ \dfrac{8}{{12}} = \dfrac{{2 \times 4}}{{3 \times 4}} $
Common factors from the numerator and the denominator cancel each other and therefore remove from the numerator and the denominator of the above fraction.
 $ \dfrac{8}{{12}} = \dfrac{2}{3} $ ….. (B)
From the equation (A) and (B) we can say that the given fractions are equal.

Note: Be good in multiples and division and remember the multiples at least till twenty. A single fraction can have a number of equivalent fractions when the same number is multiplied to the numerator and the denominator of the fraction. For equivalent fractions, the same number in the numerator and the denominator are multiplied. In simple language it is multiplying and dividing with the same number which keeps the original value as it is.