How do you evaluate 7 6/7 +4 5/7?

Mar 31, 2018

$12 \frac{4}{7}$

Explanation:

$\text{note that } 7 \frac{6}{7} = 7 + \frac{6}{7}$

$\text{and } 4 \frac{5}{7} = 4 + \frac{5}{7}$

$\Rightarrow 7 \frac{6}{7} + 4 \frac{5}{7}$

$= \textcolor{red}{7} + \frac{6}{7} \textcolor{red}{+ 4} + \frac{5}{7}$

$= \left(\textcolor{red}{7 + 4}\right) + \frac{6}{7} + \frac{5}{7}$

$\text{since fractions have a "color(blue)"common denominator}$
$\text{add the numerators leaving the denominator}$

$= 11 + \frac{6 + 5}{7}$

$= 11 + \frac{11}{7} = 11 + 1 \frac{4}{7} = 12 + \frac{4}{7}$