Adding Fractions: Calculating 2/3 + 1/5 in Homework Completion

To solve this problem, we need to determine how much of her homework Sarah has completed by adding the fractions $\frac{2}{3}$ and $\frac{1}{5}$.

First, find the least common denominator (LCD) for the fractions. The denominators are 3 and 5. The LCD of 3 and 5 is 15.

Next, convert each fraction to an equivalent fraction with the denominator of 15:

• $\frac{2}{3}$ becomes $\frac{2 \times 5}{3 \times 5} = \frac{10}{15}$
• $\frac{1}{5}$ becomes $\frac{1 \times 3}{5 \times 3} = \frac{3}{15}$

Now, add the two fractions:

$\frac{10}{15} + \frac{3}{15} = \frac{10 + 3}{15} = \frac{13}{15}$

Thus, Sarah has completed $\frac{13}{15}$ of her total homework.

The correct answer is therefore $\frac{13}{15}$.