Question
3.3.6. B Practice Problems
*Find a common denominator for each fraction. Rewrite the problems using equivalent fractions with a common denominator. Then add the two fractions to get the answer.
½ + 1/4
Answer:
5/12 + 1/4
Answer:
⅓ + ¼
Answer:
2/6 + 3/4
Answer:
*Find a common denominator for each fraction. Rewrite the problems using equivalent fractions with a common denominator. Then add the two fractions to get the answer.
½ + 1/4
Answer:
5/12 + 1/4
Answer:
⅓ + ¼
Answer:
2/6 + 3/4
Answer:
Answers
GPT-4o mini
To find a common denominator for each pair of fractions, we will follow the steps outlined in your practice problems.
1. **For \( \frac{1}{2} + \frac{1}{4} \)**:
- The denominators are 2 and 4.
- The least common denominator (LCD) is 4.
- Rewrite \( \frac{1}{2} \) as \( \frac{2}{4} \) (since \( 1 \times 2 = 2 \) and \( 2 \times 2 = 4 \)).
- Now add \( \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \).
**Answer:** \( \frac{3}{4} \)
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2. **For \( \frac{5}{12} + \frac{1}{4} \)**:
- The denominators are 12 and 4.
- The least common denominator (LCD) is 12.
- Rewrite \( \frac{1}{4} \) as \( \frac{3}{12} \) (since \( 1 \times 3 = 3 \) and \( 4 \times 3 = 12 \)).
- Now add \( \frac{5}{12} + \frac{3}{12} = \frac{8}{12} \).
- Simplifying \( \frac{8}{12} \) gives \( \frac{2}{3} \).
**Answer:** \( \frac{2}{3} \)
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3. **For \( \frac{1}{3} + \frac{1}{4} \)**:
- The denominators are 3 and 4.
- The least common denominator (LCD) is 12.
- Rewrite \( \frac{1}{3} \) as \( \frac{4}{12} \) (since \( 1 \times 4 = 4 \) and \( 3 \times 4 = 12 \)).
- Rewrite \( \frac{1}{4} \) as \( \frac{3}{12} \) (since \( 1 \times 3 = 3 \) and \( 4 \times 3 = 12 \)).
- Now add \( \frac{4}{12} + \frac{3}{12} = \frac{7}{12} \).
**Answer:** \( \frac{7}{12} \)
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4. **For \( \frac{2}{6} + \frac{3}{4} \)**:
- The denominators are 6 and 4.
- The least common denominator (LCD) is 12.
- Rewrite \( \frac{2}{6} \) as \( \frac{4}{12} \) (since \( 2 \times 2 = 4 \) and \( 6 \times 2 = 12 \)).
- Rewrite \( \frac{3}{4} \) as \( \frac{9}{12} \) (since \( 3 \times 3 = 9 \) and \( 4 \times 3 = 12 \)).
- Now add \( \frac{4}{12} + \frac{9}{12} = \frac{13}{12} \).
- This can also be expressed as \( 1 \frac{1}{12} \) in mixed number form.
**Answer:** \( \frac{13}{12} \) or \( 1 \frac{1}{12} \)
1. **For \( \frac{1}{2} + \frac{1}{4} \)**:
- The denominators are 2 and 4.
- The least common denominator (LCD) is 4.
- Rewrite \( \frac{1}{2} \) as \( \frac{2}{4} \) (since \( 1 \times 2 = 2 \) and \( 2 \times 2 = 4 \)).
- Now add \( \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \).
**Answer:** \( \frac{3}{4} \)
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2. **For \( \frac{5}{12} + \frac{1}{4} \)**:
- The denominators are 12 and 4.
- The least common denominator (LCD) is 12.
- Rewrite \( \frac{1}{4} \) as \( \frac{3}{12} \) (since \( 1 \times 3 = 3 \) and \( 4 \times 3 = 12 \)).
- Now add \( \frac{5}{12} + \frac{3}{12} = \frac{8}{12} \).
- Simplifying \( \frac{8}{12} \) gives \( \frac{2}{3} \).
**Answer:** \( \frac{2}{3} \)
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3. **For \( \frac{1}{3} + \frac{1}{4} \)**:
- The denominators are 3 and 4.
- The least common denominator (LCD) is 12.
- Rewrite \( \frac{1}{3} \) as \( \frac{4}{12} \) (since \( 1 \times 4 = 4 \) and \( 3 \times 4 = 12 \)).
- Rewrite \( \frac{1}{4} \) as \( \frac{3}{12} \) (since \( 1 \times 3 = 3 \) and \( 4 \times 3 = 12 \)).
- Now add \( \frac{4}{12} + \frac{3}{12} = \frac{7}{12} \).
**Answer:** \( \frac{7}{12} \)
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4. **For \( \frac{2}{6} + \frac{3}{4} \)**:
- The denominators are 6 and 4.
- The least common denominator (LCD) is 12.
- Rewrite \( \frac{2}{6} \) as \( \frac{4}{12} \) (since \( 2 \times 2 = 4 \) and \( 6 \times 2 = 12 \)).
- Rewrite \( \frac{3}{4} \) as \( \frac{9}{12} \) (since \( 3 \times 3 = 9 \) and \( 4 \times 3 = 12 \)).
- Now add \( \frac{4}{12} + \frac{9}{12} = \frac{13}{12} \).
- This can also be expressed as \( 1 \frac{1}{12} \) in mixed number form.
**Answer:** \( \frac{13}{12} \) or \( 1 \frac{1}{12} \)