Question

How do you evaluate \[\dfrac{1}{2} + \dfrac{5}{8}\]?

Answer 1

Hint: The above question is an addition between the two fractions where this type of fraction can be solved by making sure that both the terms denominator should be made equal and then further by adding the numerators and keeping denominator common, we get the final solution.

Complete step by step answer:
When you add fractions and if they are not mixed numbers and if they have the same denominator, so if you add the two fractions having the same denominator the sum is going to have the same denominator, and your numerator is just going to be the sum of the numerators.
So, in the above given question,
where the equation is \[\dfrac{1}{2} + \dfrac{5}{8}\].
It is not possible to directly add, subtract, or divide unless the denominator of what you’re dealing with is the same. The fractions having different denominators are also called, unlike fractions.
Here, the denominators for both terms are not equal, so we need to multiply 4 in the first term so that denominators are equal.
Therefore,
   \[
   \Rightarrow \left( {\dfrac{1}{2} \times \dfrac{4}{4}} \right) + \dfrac{5}{8} \\
   \Rightarrow \dfrac{4}{8} + \dfrac{5}{8} = \dfrac{9}{8} \\
 \]
If the numerator is greater than the denominator, the fraction is called the improper fraction. Thus, an improper fraction represents a quantity greater than one. So, the final answer is \[\dfrac{9}{8}\] which is an improper fraction.

Note:
An important thing to know is that for getting an equal denominator we can calculate the LCM i.e., the Least common multiple of both the denominators by another method where we choose the smallest positive integer that divides the numbers 8 and 2 without any remainder.