Question

Find the sum $ \left( {\dfrac{8}{9}} \right) + \left( {\dfrac{7}{{12}}} \right) $

Answer 1

Hint: Here we are given two fractions. Fraction is the term expressed in the form of the numerator upon the denominator. First of all we will find the LCM (least common multiple) and by getting its equivalent fraction, having both the denominators same, then combine the denominators.

Complete step-by-step answer:
Take the given expression: $ \left( {\dfrac{8}{9}} \right) + \left( {\dfrac{7}{{12}}} \right) $
Here first find the LCM (least common multiple) for both the denominators of the above fractions.
 $
 12 = 2 \times 2 \times 3 \\
  9 = 3 \times 3 \;
 $
The LCM of the above two terms is equal to $ 36 $
 $ = \left( {\dfrac{8}{9} \times \dfrac{4}{4}} \right) + \left( {\dfrac{7}{{12}} \times \dfrac{3}{3}} \right) $
Find the product of the terms in the above expression –
 $ = \left( {\dfrac{{32}}{{36}}} \right) + \left( {\dfrac{{21}}{{36}}} \right) $
When denominators are equal, combine the numerator.
 $ = \left( {\dfrac{{32 + 21}}{{36}}} \right) $
Simplify the above expression by adding the terms in the numerator-
 $ = \left( {\dfrac{{53}}{{36}}} \right) $
Convert the above expression in the form of the mixed fraction –
 $ = 1\dfrac{{17}}{{36}} $
Hence, the required solution is $ \left( {\dfrac{8}{9}} \right) + \left( {\dfrac{7}{{12}}} \right) = 1\dfrac{{17}}{{36}} $
So, the correct answer is “ $ 1\dfrac{{17}}{{36}} $ ”.

Note: Remember by taking LCM (least common multiple) we get the equivalent fraction of the given term. Do not get confused between the LCM and HCF (highest common factor) and apply the concepts accordingly. LCM can be calculated by using the prime factorization method, long division and the factor tree method. Prime factorization can be defined as the process of finding which prime numbers can be multiplied together to make the original number.