Chapter 0.4, Problem 22E

To determine

To calculate: The simplified form of $\frac{3}{7}+\frac{5}{14}$ .

Answer to Problem 22E

The simplified form of $\frac{3}{7}+\frac{5}{14}$ is $\frac{11}{14}$ .

Explanation of Solution

Given information:

The statement “ $\frac{3}{7}+\frac{5}{14}$ .”

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 “ $\frac{3}{7}+\frac{5}{14}$ .”

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 7 and $14$ is $14$ .

So, multiply $\frac{3}{7}$ by 2 in both numerator and denominator,

Thus, the given expression can be simplified as,

  $\begin{array}{c}\frac{3}{7}+\frac{5}{14}=\frac{3\times 2}{7\times 2}+\frac{5}{14}\\ \frac{3}{7}+\frac{5}{14}=\frac{6}{14}+\frac{5}{14}\\ \frac{3}{7}+\frac{5}{14}=\frac{6+5}{14}\\ \frac{3}{7}+\frac{5}{14}=\frac{11}{14}\end{array}$

Since, $\frac{\text{11}}{\text{14}}$ cannot be simplified further,

Hence, the simplified form of $\frac{3}{7}+\frac{5}{14}$ is $\frac{11}{14}$ .