Question

Find a common denominator for the fractions in the set. Then write the equivalent fractions using the common denominators. You can use the multiples strategy or the butterfly method. Remember whatever number you multiply the denominator by, you need to multiply the numerator by the same number.

1/6 and 1/9
6: 6, 12, 18, 24, 30, 36,
9: 9, 18, 27, 36,
-Common denominator is:18
1/6 =3/18
1/9 =2/18


1/2 and 2/7
2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30,
7:7, 14, 21, 28,
-Common denominator is:14
1/2 =7/14
2/7 = 4/14

3/8 and 3/4
8: 8, 16, 24, 32, 40
4:4, 8, 12, 16, 20, 24, 28
-Common denominator is:8
3/8 = 3/8
3/4 =6/8

Answer 1

Let's find a common denominator for the fractions in each pair and write the equivalent fractions using that common denominator.

### 1. \( \frac{1}{6} \) and \( \frac{1}{9} \)
- Denominators: 6 (multiples: 6, 12, 18, ...) and 9 (multiples: 9, 18, 27, ...)
- **Common denominator** is: **18**
- To convert:
- For \( \frac{1}{6} \): Multiply both numerator and denominator by 3.
\[
\frac{1 \times 3}{6 \times 3} = \frac{3}{18}
\]

- For \( \frac{1}{9} \): Multiply both numerator and denominator by 2.
\[
\frac{1 \times 2}{9 \times 2} = \frac{2}{18}
\]

### 2. \( \frac{1}{2} \) and \( \frac{2}{7} \)
- Denominators: 2 (multiples: 2, 4, 6, ...) and 7 (multiples: 7, 14, 21, ...)
- **Common denominator** is: **14**
- To convert:
- For \( \frac{1}{2} \): Multiply both numerator and denominator by 7.
\[
\frac{1 \times 7}{2 \times 7} = \frac{7}{14}
\]

- For \( \frac{2}{7} \): Multiply both numerator and denominator by 2.
\[
\frac{2 \times 2}{7 \times 2} = \frac{4}{14}
\]

### 3. \( \frac{3}{8} \) and \( \frac{3}{4} \)
- Denominators: 8 (multiples: 8, 16, 24, ...) and 4 (multiples: 4, 8, 12, ...)
- **Common denominator** is: **8**
- To convert:
- For \( \frac{3}{8} \): It stays the same because the denominator is already 8.
\[
\frac{3}{8} = \frac{3}{8}
\]

- For \( \frac{3}{4} \): Multiply both numerator and denominator by 2.
\[
\frac{3 \times 2}{4 \times 2} = \frac{6}{8}
\]

### Summary of Equivalent Fractions:
1. \( \frac{1}{6} = \frac{3}{18} \) and \( \frac{1}{9} = \frac{2}{18} \)
2. \( \frac{1}{2} = \frac{7}{14} \) and \( \frac{2}{7} = \frac{4}{14} \)
3. \( \frac{3}{8} = \frac{3}{8} \) and \( \frac{3}{4} = \frac{6}{8} \)