Chapter 0.4, Problem 24E

To determine

To calculate: The simplified form of $\frac{3}{8}+\frac{1}{6}$ .

Answer to Problem 24E

The simplified form of $\frac{3}{8}+\frac{1}{6}$ is $\frac{13}{24}$ .

Explanation of Solution

Given information:

The statement “ $\frac{3}{8}+\frac{1}{6}$ .”

Formula used:

When two fractions with different denominators are added then the two unlike fractions are converted into like fractions by multiplying the denominators with a common factor of their lowest common multiple(LCM).

Consider the provided statement “ $\frac{3}{8}+\frac{1}{6}$ .”

Recall that when two fractions with different denominators are added then the two unlike fractions are converted into like fractions by multiplying the denominators with a common factor of their lowest common multiple(LCM).

LCM of $8$ and $6$ is $24$ .

So, multiply $\frac{3}{8}$ by 3 and $\frac{1}{6}$ by 4 in both numerator and denominator,

Thus, the given expression can be simplified as,

  $\begin{array}{c}\frac{3}{8}+\frac{1}{6}=\frac{3\times 3}{8\times 3}+\frac{1\times 4}{6\times 4}\\ \frac{3}{8}+\frac{1}{6}=\frac{9}{24}+\frac{4}{24}\\ \frac{3}{8}+\frac{1}{6}=\frac{9+4}{24}\\ \frac{3}{8}+\frac{1}{6}=\frac{13}{24}\end{array}$

Since, $\frac{\text{13}}{24}$ cannot be simplified further,

Hence, the simplified form of $\frac{3}{8}+\frac{1}{6}$ is $\frac{13}{24}$ .