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.

Example: ⅓ and ¼
List multiples of 3 and 4 until you find a common multiple.
3: 3, 6, 9, 12
4: 4, 8, 12
-12 is our common denominator
⅓ = (1x4 = 4 and 3 x 4 = 12) 4/12
¼ = (1 x 3 = 3 and 4 x 3 = 12) 3/12

1/6 and 1/9
6:
9:
-Common denominator is:
1/6 =
1/9 =


1/2 and 2/7
2:
7:
-Common denominator is:
1/2 =
2/7 =


3/8 and 3/4
8:
4:
-Common denominator is:
3/8 =
3/4 =

Answer 1

Let's find a common denominator for each set of fractions and convert them into equivalent fractions using the multiples strategy.

### 1. Fractions: \( \frac{1}{6} \) and \( \frac{1}{9} \)

**List multiples:**
- **6**: 6, 12, 18, 24, 30, 36, ...
- **9**: 9, 18, 27, 36, ...

- **Common denominator**: 18

**Convert fractions:**
- \( \frac{1}{6} = \frac{1 \times 3}{6 \times 3} = \frac{3}{18} \)
- \( \frac{1}{9} = \frac{1 \times 2}{9 \times 2} = \frac{2}{18} \)

### Summary:
- Common denominator is: **18**
- \( \frac{1}{6} = \frac{3}{18} \)
- \( \frac{1}{9} = \frac{2}{18} \)


### 2. Fractions: \( \frac{1}{2} \) and \( \frac{2}{7} \)

**List multiples:**
- **2**: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, ...
- **7**: 7, 14, 21, 28, ...

- **Common denominator**: 14

**Convert fractions:**
- \( \frac{1}{2} = \frac{1 \times 7}{2 \times 7} = \frac{7}{14} \)
- \( \frac{2}{7} = \frac{2 \times 2}{7 \times 2} = \frac{4}{14} \)

### Summary:
- Common denominator is: **14**
- \( \frac{1}{2} = \frac{7}{14} \)
- \( \frac{2}{7} = \frac{4}{14} \)


### 3. Fractions: \( \frac{3}{8} \) and \( \frac{3}{4} \)

**List multiples:**
- **8**: 8, 16, 24, 32, 40, ...
- **4**: 4, 8, 12, 16, 20, 24, 28, ...

- **Common denominator**: 8

**Convert fractions:**
- \( \frac{3}{8} = \frac{3}{8} \) (already has a denominator of 8)
- \( \frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8} \)

### Summary:
- Common denominator is: **8**
- \( \frac{3}{8} = \frac{3}{8} \)
- \( \frac{3}{4} = \frac{6}{8} \)

### Final Results:
1. \( \frac{1}{6} \) and \( \frac{1}{9} \)
- Common denominator: **18**
- \( \frac{1}{6} = \frac{3}{18} \)
- \( \frac{1}{9} = \frac{2}{18} \)

2. \( \frac{1}{2} \) and \( \frac{2}{7} \)
- Common denominator: **14**
- \( \frac{1}{2} = \frac{7}{14} \)
- \( \frac{2}{7} = \frac{4}{14} \)

3. \( \frac{3}{8} \) and \( \frac{3}{4} \)
- Common denominator: **8**
- \( \frac{3}{8} = \frac{3}{8} \)
- \( \frac{3}{4} = \frac{6}{8} \)