Question

In the following exercises, simplify each expression.

$\left(\frac{8}{13}+\frac{5}{7}\right)+\frac{2}{7}$

Short answer

The simplified expression is$1\frac{8}{13}$.

Step-by-step solution

Step 1. Given Information.

The given expression is$\left(\frac{8}{13}+\frac{5}{7}\right)+\frac{2}{7}$.

Step 2. Notice that the last 2 terms have a common denominator, so change the grouping.

$\left(\frac{8}{13}+\frac{5}{7}\right)+\frac{2}{7}=\frac{8}{13}+\left(\frac{5}{7}+\frac{2}{7}\right)$

Step 3. Add the fraction.

Simplify the fractions.

$$\begin{gathered} \frac{8}{13}+\left(\frac{5}{7}+\frac{2}{7}\right) \\ =\frac{8}{13}+\left(\frac{5+2}{7}\right) \\ =\frac{8}{13}+\left(\frac{7}{7}\right) \\ =\frac{8}{13}+1 \\ =\frac{8+13}{13} \\ =\frac{21}{13} \\ =1\frac{8}{13} \end{gathered}$$

Step 4. Conclusion. 

The simplified form of the given expression is$1\frac{8}{13}$.