Question

How do you evaluate $\dfrac{5}{8} + \dfrac{5}{6}$?

Answer 1

Hint: We are given here two proper unlike fractions for additions. In order to do that, we have to make sure the denominators of the fractions are the same, that is, we have to make equivalents like fractions. This can be done by simultaneously multiplying or dividing the numerator and denominator of the fraction with a constant.

Complete step-by-step answer:
We are asked to evaluate $\dfrac{5}{8} + \dfrac{5}{6}$. But since the denominators of these fractions are not equal, let us first find the LCM of those, i.e., LCM of 8,6.
In order to do that, let us first prime factorise 6 and 8 as shown:
$8 = 2 \times 2 \times 2 \times 2$
$6 = 3 \times 2$
Now, we multiply each factor the maximum number of times it occurs in either number to find the LCM.
$ \Rightarrow LCM = 2 \times 2 \times 2 \times 2 \times 3$
 $ = 24$
Thus, we have found the LCM of 6,8 as 24.
Now let us form the equivalent fractions of these two fractions which have the denominator as 24.
Here we multiply the numerator and denominator of $\dfrac{5}{8}$ by 3.
$ \Rightarrow \dfrac{5}{8} = \dfrac{{5 \times 3}}{{8 \times 3}}$
$ = \dfrac{{15}}{{24}}$
Similarly, we multiply the numerator and denominator of $\dfrac{5}{6}$ by 4.
$ \Rightarrow \dfrac{5}{6} = \dfrac{{5 \times 4}}{{6 \times 4}}$
$ = \dfrac{{20}}{{24}}$
Thus, we have obtained two equivalents like fractions. For adding two like fractions, we just have to add the numerators while keeping the denominator constant.
That is,
$\dfrac{5}{8} + \dfrac{5}{6} = \dfrac{{15}}{{24}} + \dfrac{{20}}{{24}}$
$ = \dfrac{{35}}{{24}}$
Which is our final answer.

Note: If the denominators are co-prime numbers, then their LCM is their product itself.