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.

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 = 4/12
¼ = 3/12

⅖ and 1/6
5:
6:
-Common denominator is:
⅖ =
¼ =


⅓ and 4/5
3:
5:
-Common denominator is:
⅓ =
⅘ =


7/9 and 2/3
9:
3:
-Common denominator is:
7/9 =
⅔ =

Answer 1

Let's find the common denominators for each set of fractions.

**1. \(\frac{2}{5}\) and \(\frac{1}{6}\)**
List multiples of 5 and 6:
5: 5, 10, 15, 20, 25, 30
6: 6, 12, 18, 24, 30

- Common denominator is: **30**
- To convert \(\frac{2}{5}\) to have a denominator of 30:
\(\frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30}\)

- To convert \(\frac{1}{6}\) to have a denominator of 30:
\(\frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30}\)

So,
\(\frac{2}{5} = \frac{12}{30}\)
\(\frac{1}{6} = \frac{5}{30}\)

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**2. \(\frac{1}{3}\) and \(\frac{4}{5}\)**
List multiples of 3 and 5:
3: 3, 6, 9, 12, 15
5: 5, 10, 15, 20, 25

- Common denominator is: **15**
- To convert \(\frac{1}{3}\) to have a denominator of 15:
\(\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}\)

- To convert \(\frac{4}{5}\) to have a denominator of 15:
\(\frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}\)

So,
\(\frac{1}{3} = \frac{5}{15}\)
\(\frac{4}{5} = \frac{12}{15}\)

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**3. \(\frac{7}{9}\) and \(\frac{2}{3}\)**
List multiples of 9 and 3:
9: 9, 18, 27
3: 3, 6, 9, 12, 15, 18, 21, 24, 27

- Common denominator is: **9** (the least common multiple of 9 and 3)
- \(\frac{7}{9}\) already has a denominator of 9:
So, \(\frac{7}{9} = \frac{7}{9}\)

- To convert \(\frac{2}{3}\) to have a denominator of 9:
\(\frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}\)

So,
\(\frac{7}{9} = \frac{7}{9}\)
\(\frac{2}{3} = \frac{6}{9}\)

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### Final Summary
1. **\(\frac{2}{5}\) and \(\frac{1}{6}\)**
- Common denominator is: **30**
- \(\frac{2}{5} = \frac{12}{30}\)
- \(\frac{1}{6} = \frac{5}{30}\)

2. **\(\frac{1}{3}\) and \(\frac{4}{5}\)**
- Common denominator is: **15**
- \(\frac{1}{3} = \frac{5}{15}\)
- \(\frac{4}{5} = \frac{12}{15}\)

3. **\(\frac{7}{9}\) and \(\frac{2}{3}\)**
- Common denominator is: **9**
- \(\frac{7}{9} = \frac{7}{9}\)
- \(\frac{2}{3} = \frac{6}{9}\)