Question

What fraction is between $ \dfrac{1}{3} $ and $ \dfrac{1}{2} $ ?

Answer 1

Hint: Here the given fraction is the number which can be stated as the ratio of two numbers or which can be stated as the p/q form or as the quotient or the fraction with a non-zero denominator. Here for both the given fractions we will convert the denominators the same by taking the LCM (least common multiple) and then will find the fraction between the two.

Complete step-by-step answer:
Given numbers are: $ \dfrac{1}{3} $ and $ \dfrac{1}{2} $
Now, since the denominators of the above two given fractions are different, first make the denominators common.
So, to make the common denominators-
Multiply $ \dfrac{1}{3} $ by $ \dfrac{2}{2} $ gives $ \dfrac{2}{6} $ …. (A)
Similarly, Multiply $ \dfrac{1}{2} $ by $ \dfrac{3}{3} $ gives $ \dfrac{3}{6} $ ….. (B)
Since equations (A) and (B) have the same denominators but both the numerators do not have much difference with only one number.
So again, multiply both the equations by $ \dfrac{2}{2} $
Multiply $ \dfrac{2}{6} $ by $ \dfrac{2}{2} $ gives $ \dfrac{4}{{12}} $ …. (C)
Similarly, multiply $ \dfrac{3}{6} $ by $ \dfrac{2}{2} $ gives $ \dfrac{6}{{12}} $ ... (D)
Hence, the fraction $ \dfrac{5}{{12}} $ is between the given fractions $ \dfrac{4}{{12}} $ and $ \dfrac{6}{{12}} $ .
So, the correct answer is “ $ \dfrac{5}{{12}} $ ”.

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. The value of the equivalent fractions when removing the common factors from the numerator and the denominator are the same.