# How do you solve 7\frac { 3} { 7}+ 5\frac { 2} { 3}?

##### 1 Answer
Mar 18, 2018

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$\left(7 + \frac{3}{7}\right) + \left(5 + \frac{2}{3}\right) \implies$

$7 + \frac{3}{7} + 5 + \frac{2}{3} \implies$

$7 + 5 + \frac{3}{7} + \frac{2}{3} \implies$

$12 + \frac{3}{7} + \frac{2}{3}$

To add the fractions we must put them over a common denominator by multiplying each fraction by the appropriate form of $1$:

$12 + \left(\frac{3}{3} \times \frac{3}{7}\right) + \left(\frac{7}{7} \times \frac{2}{3}\right) \implies$

$12 + \frac{3 \times 3}{3 \times 7} + \frac{7 \times 2}{7 \times 3} \implies$

$12 + \frac{9}{21} + \frac{14}{21} \implies$

$12 + \frac{9 + 14}{21} \implies$

$12 + \frac{23}{21}$

Now, we can convert the improper fraction to a mixed number:

$12 + \frac{21 + 2}{21} \implies$

$12 + \frac{21}{21} + \frac{2}{21} \implies$

$12 + 1 + \frac{2}{21} \implies$

$13 + \frac{2}{21} \implies$

$13 \frac{2}{21}$