# What is the sum of 2 1/3, 3 5/6, and 6 2/3?

Jan 30, 2018

$2 \frac{1}{3} + 3 \frac{5}{6} + 6 \frac{2}{3}$

$\frac{7}{3} + \frac{23}{6} + \frac{20}{3}$

$\frac{14}{6} + \frac{23}{6} + \frac{40}{6}$ (taking common denominator)

$\frac{14 + 23 + 40}{6}$

$\frac{77}{6}$

$12 \frac{5}{6}$

Jan 30, 2018

See a solution process below:

#### Explanation:

First, the sum means to add. So, we can write the expression as:

$2 \frac{1}{3} + 3 \frac{5}{6} + 6 \frac{2}{3}$

We can rewrite this as:

$2 + \frac{1}{3} + 3 + \frac{5}{6} + 6 + \frac{2}{3} \implies$

$2 + 3 + 6 + \frac{1}{3} + \frac{5}{6} + \frac{2}{3} \implies$

$11 + \frac{1}{3} + \frac{5}{6} + \frac{2}{3}$

We need each of the fractions over a common denominator:

$11 + \left(\frac{2}{2} \times \frac{1}{3}\right) + \frac{5}{6} + \left(\frac{2}{2} \times \frac{2}{3}\right) \implies$

$11 + \frac{2}{6} + \frac{5}{6} + \frac{4}{6} \implies$

$11 + \frac{2 + 5 + 4}{6} \implies$

$11 + \frac{11}{6} \implies$

$11 + \frac{6 + 5}{6} \implies$

$11 + \frac{6}{6} + \frac{5}{6} \implies$

$11 + 1 + \frac{5}{6} \implies$

$12 + \frac{5}{6} \implies$

$12 \frac{5}{6}$