Question

Calculate the sum of the given two fractions, $\dfrac{5}{8}$ and $\dfrac{3}{{16}}$.

Answer 1

Check if the fractions are proper, or improper or mixed fractions. Use the LCM method for proper or improper fractions. Calculate the LCM of the denominators. Change the
numerators accordingly and add them to get the final answer.

Complete step by step solution:
From the question we can see that, the numerator is smaller than the denominator in both the
fractions and hence, both of them are proper fractions. To proceed with the question, we need to calculate the LCM of 8 and 16, which is 16.

Thus, we can write,
$\dfrac{5}{8} + \dfrac{3}{{16}} = \dfrac{{5 \times 2}}{{16}} + \dfrac{3}{{16}}$

It is evident that since the denominator of the second fraction doesn’t change, there is no change in
the numerator as well.
$= \dfrac{{10 + 3}}{{16}} = \dfrac{{13}}{{16}}$

The final answer for $\dfrac{5}{8} + \dfrac{3}{{16}}$= $\dfrac{{13}}{{16}}$.

Alternate Method: There is another way to solve the fractions. Convert the fractions to decimals and then add them.
$\dfrac{5}{8}$= 0.625
$\dfrac{3}{{16}}$= 0.1875

Adding the values, 0.625 + 0.1875 = 0.8125
0.8125 = $\dfrac{{8125}}{{10000}}$, which can be further simplified to $\dfrac{{13}}{{16}}$.

Note: There are various ways you can convert a fraction into a decimal. One of the most foolproof ways is long division. Another is changing the denominator of the fraction to the nearest multiple of 10 and accordingly change the numerator. In this question it wasn’t feasible to turn 8 or 16 into a multiple of 10, hence long division is suitable. For calculating the sum, the LCM method is fool proof and less lengthy.