Question

Evaluate the expression
1/3 + 1/5 divided by 4/5

Answer 1

To evaluate the expression \( \frac{1}{3} + \frac{1}{5} \div \frac{4}{5} \), we first handle the division and then the addition.

1. **Calculate \( \frac{1}{5} \div \frac{4}{5} \)**:
Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we have:
\[
\frac{1}{5} \div \frac{4}{5} = \frac{1}{5} \times \frac{5}{4} = \frac{1 \times 5}{5 \times 4} = \frac{5}{20} = \frac{1}{4}
\]

2. **Now, add \( \frac{1}{3} + \frac{1}{4} \)**:
To add these fractions, we need a common denominator. The least common multiple of 3 and 4 is 12. We rewrite each fraction:

\[
\frac{1}{3} = \frac{4}{12} \quad \text{and} \quad \frac{1}{4} = \frac{3}{12}
\]

Now we can add:
\[
\frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12}
\]

Thus, the final result of the expression \( \frac{1}{3} + \frac{1}{5} \div \frac{4}{5} \) is:
\[
\boxed{\frac{7}{12}}
\]