Question

Find the value of the following: $ \dfrac{3}{5} + \dfrac{7}{{10}} + \left( {\dfrac{{ - 8}}{{12}}} \right) + \dfrac{4}{3} $

Answer 1

Hint: Here in the above question we have to find the value by addition of all the fractions. Since we can see that these fractions are unlike fractions i.e. the fractions which have the different denominators are known as the unlike fractions. We know that of the denominators are not the same then we have to use the equivalent fractions which have a common denominator. To do this we need to find the L.C.M of the denominators to find the sum of the unlike fractions.

Complete step-by-step answer:
According to the given question we have: $ \dfrac{3}{5} + \dfrac{7}{{10}} + \left( {\dfrac{{ - 8}}{{12}}} \right) + \dfrac{4}{3} $ . We can take the negative sign out of the bracket, so the new form is \[\dfrac{3}{5} + \dfrac{7}{{10}} - \dfrac{8}{{12}} + \dfrac{4}{3}\].
So the denominators of the above are $ 5,10,12 $ and $ 3 $ . Now the L.C.M of the following are: $ 5 = 5 \times 1,10 = 5 \times 2,12 = 2 \times 2 \times 3 $ And $ 3 = 3 \times 1 $ .
 $ L.C.M = 5 \times 2 \times 2 \times 3 \times 2 = 120 $ .
So we can write the fractions as: \[\dfrac{3}{5} + \dfrac{7}{{10}} - \dfrac{8}{{12}} + \dfrac{4}{3} = \dfrac{{72 + 84 - 80 + 160}}{{120}}\]. On further solving we have, $ \dfrac{{236}}{{120}} $ . By simplifying it can be written as $ \dfrac{{59}}{{30}} $ .
Hence the required value is $ \dfrac{{59}}{{30}} $ .
So, the correct answer is “ $ \dfrac{{59}}{{30}} $ ”.

Note: We should be careful while adding or subtracting the unlike fractions, and we should also note that we have to find the L.C.M which means least common multiple of the numbers. So while calculating the L.C.M we have to take the numbers with the higher powers. We should avoid the calculation mistakes while adding or subtractions of the numbers.