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Answer
\[
\frac{8}{15} + \frac{2}{5} = \frac{14}{15}
\]
Solution
To add the fractions \( \frac{8}{15} \) and \( \frac{2}{5} \), follow these steps:
1. **Find a Common Denominator:**
The denominators are 15 and 5. The least common denominator (LCD) is 15.
2. **Convert Fractions to Have the LCD:**
- \( \frac{8}{15} \) already has the denominator 15.
- Convert \( \frac{2}{5} \) to a denominator of 15:
\[
\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}
\]
3. **Add the Fractions:**
\[
\frac{8}{15} + \frac{6}{15} = \frac{8 + 6}{15} = \frac{14}{15}
\]
**Final Answer:**
\[
\frac{8}{15} + \frac{2}{5} = \frac{14}{15}
\]
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Simplify this solution The Deep Dive
To add the fractions \( \frac{8}{15} + \frac{2}{5} \), we first need a common denominator. The least common multiple of 15 and 5 is 15. So we can rewrite \( \frac{2}{5} \) as \( \frac{6}{15} \) (since \( 2 \times 3 = 6 \) and \( 5 \times 3 = 15 \)). Now we can add the two fractions: \[ \frac{8}{15} + \frac{6}{15} = \frac{14}{15}. \] Thus, the result is \( \frac{14}{15} \).
