# How do you simplify 2 1/2+7(6/7-1/7)?

Dec 13, 2016

$\frac{15}{2}$ or $7 \frac{1}{2}$

#### Explanation:

Step 1) Combine the terms within parenthesis:

$2 \frac{1}{2} + 7 \cdot \frac{5}{7}$

$2 \frac{1}{2} + \cancel{7} \cdot \frac{5}{\cancel{7}}$

$2 \frac{1}{2} + 5$

Next we need to convert the mixed fraction to an improper fractions by multiplying the integer by the appropriate for of $1$ and adding it to the fraction:

$\left(\left(\frac{2}{2} \cdot 2\right) + \frac{1}{2}\right) + 5$

(4/2 + 1/2) + 5)

$\frac{5}{2} + 5$

Finally, we need to get the integer over a common denominator so we can add the terms by multiplying the integer by the appropriate form of $1$:

$\frac{5}{2} + \left(\frac{2}{2} \cdot 5\right)$

$\frac{5}{2} + \frac{10}{2}$

$\frac{5 + 10}{2}$

$\frac{15}{2}$

or converting to a mixed fraction:

$\frac{14 + 1}{2}$

$\frac{14}{2} + \frac{1}{2}$

$7 + \frac{1}{2}$

$7 \frac{1}{2}$