Question

What is $\dfrac{1}{2}+\dfrac{3}{8}?$

Answer 1

Hint: We use the basic concepts of fraction addition here to solve this sum. We need to make the denominators equal in order to add the numerators of the two terms and this can be done by taking an LCM of the denominator 2 and 8. We then multiply both the numerator and denominator by this factor. After getting the same denominator, we get the result just by adding the numerators.

Complete step by step solution:
In order to solve this question, let us first calculate the LCM or least common multiple of the denominators of the given two fraction 8 and 2. Least common multiple of two numbers is the smallest number which is divisible by both the given numbers. Hence, the smallest number divisible by both 2 and 8 is 8. Hence, the LCM is 8.
To make the denominators of both the terms 8, we multiply the numerator and denominator of the first term by 4.
$\Rightarrow \dfrac{1\times 4}{2\times 4}+\dfrac{3}{8}$
Multiplying the terms in the numerator and denominator,
$\Rightarrow \dfrac{4}{8}+\dfrac{3}{8}$
Since we have the same denominator, we can take it common and add the numerators.
$\Rightarrow \dfrac{4+3}{8}$
Adding the terms in the numerator,
$\Rightarrow \dfrac{7}{8}$

Hence, $\dfrac{1}{2}+\dfrac{3}{8}$ is equal to $\dfrac{7}{8}.$

Note: We need to know the concept of fractional addition in order to solve such sums. LCM is an important concept too. We can also solve this question by considering the decimal equivalents of these numbers and taking their sum. The only difference is that the result will be in the decimal format and needs to be converted back to the fractional form if the answer is needed in the fractional form.