Question

Find the common denominator rename each fraction as a equivalent fraction with the common denominator 3/7 and 1/4

Answer 1

To find a common denominator for the fractions \( \frac{3}{7} \) and \( \frac{1}{4} \), we need to find the least common multiple (LCM) of the denominators 7 and 4.

The multiples of 7 are: 7, 14, 21, 28, 35, 42, ...
The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, ...

The least common multiple of 7 and 4 is 28.

Now, we will rename each fraction with the common denominator of 28.

1. **Converting \( \frac{3}{7} \):**
- To convert \( \frac{3}{7} \) to have a denominator of 28, we can use the following conversion:
\[
\frac{3}{7} \times \frac{4}{4} = \frac{3 \times 4}{7 \times 4} = \frac{12}{28}
\]

2. **Converting \( \frac{1}{4} \):**
- To convert \( \frac{1}{4} \) to have a denominator of 28:
\[
\frac{1}{4} \times \frac{7}{7} = \frac{1 \times 7}{4 \times 7} = \frac{7}{28}
\]

Now, we have both fractions with the common denominator of 28:
- \( \frac{3}{7} = \frac{12}{28} \)
- \( \frac{1}{4} = \frac{7}{28} \)

Thus, the equivalent fractions with the common denominator are:
- \( \frac{12}{28} \) and \( \frac{7}{28} \).