Question

4/5 and 1/15 common denominator

Answer 1

To find a common denominator for the fractions \( \frac{4}{5} \) and \( \frac{1}{15} \), we need to determine the least common multiple (LCM) of the denominators 5 and 15.

1. **Factors of 5**: \( 5 = 5^1 \)
2. **Factors of 15**: \( 15 = 3^1 \times 5^1 \)

The LCM takes the highest power of each prime factor:
- For \( 3 \), the highest power is \( 3^1 \).
- For \( 5 \), the highest power is \( 5^1 \).

Thus, the LCM is:
\[
3^1 \times 5^1 = 3 \times 5 = 15
\]

Now that we know the common denominator is 15, we can convert the fractions:

1. **Convert \( \frac{4}{5} \)** to a denominator of 15:
\[
\frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}
\]

2. **Convert \( \frac{1}{15} \)** (it is already in terms of 15):
\[
\frac{1}{15} = \frac{1}{15}
\]

Now, the two fractions with a common denominator of 15 are:
- \( \frac{12}{15} \)
- \( \frac{1}{15} \)

So, the common denominator between \( \frac{4}{5} \) and \( \frac{1}{15} \) is **15**.