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: 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 \( \frac{3}{8} \) and \( \frac{2}{5} \).

### Step 1: List the multiples

**Multiples of 8**:
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112...

**Multiples of 5**:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100...

### Step 2: Find the least common multiple (LCM)

Looking at both lists, the first common multiple is **40**.

### Step 3: Convert to equivalent fractions

Now, we need to convert each fraction to have a denominator of 40.

1. For \( \frac{3}{8} \):

Multiply the numerator and denominator by 5:
\[
\frac{3}{8} = \frac{3 \times 5}{8 \times 5} = \frac{15}{40}
\]

2. For \( \frac{2}{5} \):

Multiply the numerator and denominator by 8:
\[
\frac{2}{5} = \frac{2 \times 8}{5 \times 8} = \frac{16}{40}
\]

### Final Result

The equivalent fractions with a common denominator of 40 are:
- \( \frac{3}{8} = \frac{15}{40} \)
- \( \frac{2}{5} = \frac{16}{40} \)