Question

Add the fractions $\frac{3}{8}and\frac{2}{3}$.

• A. $\frac{25}{24}$
• B. $\frac{20}{24}$
• C. $\frac{24}{25}$
• D. $\frac{18}{24}$

Answer 1

The correct option is A $\frac{25}{24}$

The given fractions $\frac{3}{8}$ and $\frac{2}{3}$ are not like fractions as they are not having the same denominator.

To convert the given fractions into like fractions, let's find the LCM of the denominators of $\frac{3}{8}$ and $\frac{2}{3}$ i.e. LCM of 8 and 3.

$\begin{array}{cc}2& 8,3\\ 2& 4,3\\ 2& 2,3\\ 3& 1,3\\ & 1,1\end{array}$

$\therefore$ LCM of 8 and 3 = 2 $\times$ 2 $\times$ 2 $\times$ 3 = 24

Now, we convert the given fractions into equivalent fractions with denominator 24.

So, $\frac{3}{8}=\frac{3\times 3}{8\times 3}=\frac{9}{24}$ and $\frac{2}{3}=\frac{2\times 8}{3\times 8}=\frac{16}{24}$

$\therefore \frac{3}{8}+\frac{2}{3}=\frac{9}{24}+\frac{16}{24}=\frac{25}{24}$