Question

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

Answer 1

Hint: In order to find the sum of the two fractions, we need to first of all evaluate the L.C.M of the denominators of the two fractions. After taking the L.C.M i.e. 8, the numerator \[1\] is multiplied by \[4\] and the numerator \[5\] is multiplied by \[1\].

Formula used:
The L.C.M for \[2\] and \[8\] can be taken by considering the least common multiples that are present in the factors of 2 and 8. After taking the L.C.M, the denominators for both the fractions become the same , in the first diffraction, in order to make the denominator equal to \[8\] , we have to multiply \[2\] by \[4\]. So the numerator is also multiplied by the same. However, the denominator for the second fraction is already \[8\] so no need to change the numerator for it.

Complete step by step solution:
In order to add the two fractions, Firstly we are going to take the L.C.M of both the denominators, \[2\] and \[8\]. This is because the denominators of these two fractions are not equal.
The factors of \[2\] are \[2\times 1\]
And the factors for 8 are \[2\times 2\times 2\times 1\]
So the least common multiple is \[2\times 2\times 2\times 1=8\]
Therefore, the L.C.M of \[2\] and \[8\] is \[8\]
Solving, we get
\[\begin{align}
  & \Rightarrow \dfrac{1}{2}+\dfrac{5}{8} \\
 & \Rightarrow \dfrac{\left( 1\times 4 \right)+\left( 5\times 1 \right)}{8} \\
 & \Rightarrow \dfrac{4+5}{8} \\
 & \Rightarrow \dfrac{9}{8} \\
\end{align}\]

Therefore, the answer is \[\dfrac{9}{8}\]

Note: It is to be noted that the dfractions cannot be added to each other until and unless the denominators are same so in order to make them equal, the L.C.M. is taken. After taking L.C.M , it is really important to balance the numerators accordingly otherwise the summation can lead to the wrong results.