Question

Finding common denominators 2/5 and 1/3

Answer 1

To find a common denominator for the fractions \( \frac{2}{5} \) and \( \frac{1}{3} \), follow these steps:

1. **Identify the denominators:** The denominators are 5 and 3.

2. **Find the least common multiple (LCM):** The LCM of the denominators will be the common denominator.

- The multiples of 5 are: 5, 10, 15, 20, 25, ...
- The multiples of 3 are: 3, 6, 9, 12, 15, 18, ...

The smallest common multiple is 15.

3. **Convert each fraction to have the common denominator of 15:**
- For \( \frac{2}{5} \):
\[
\frac{2}{5} \times \frac{3}{3} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}
\]
- For \( \frac{1}{3} \):
\[
\frac{1}{3} \times \frac{5}{5} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
\]

Now both fractions have a common denominator of 15:
- \( \frac{2}{5} = \frac{6}{15} \)
- \( \frac{1}{3} = \frac{5}{15} \)

Thus, the common denominator for \( \frac{2}{5} \) and \( \frac{1}{3} \) is 15.