Bowers Powers
03/27/2024 · High School
Which three of the following pairs of fractions have an LCD of 10 ? (Select all that apply.) \( \square \frac{2}{5} \) and \( \frac{1}{10} \) \( \square \frac{3}{2} \) and \( \frac{3}{5} \) \( \square \frac{3}{20} \) and \( \frac{5}{5} \) \( \square \frac{11}{10} \) and \( \frac{1}{2} \)
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Step-by-step Solution
To determine which pairs of fractions have a least common denominator (LCD) of 10, we need to find the denominators of each pair and see if their least common multiple (LCM) is 10.
1. **Pair: \( \frac{2}{5} \) and \( \frac{1}{10} \)**
- Denominators: 5 and 10
- LCM(5, 10) = 10
- **This pair has an LCD of 10.**
2. **Pair: \( \frac{3}{2} \) and \( \frac{3}{5} \)**
- Denominators: 2 and 5
- LCM(2, 5) = 10
- **This pair has an LCD of 10.**
3. **Pair: \( \frac{3}{20} \) and \( \frac{5}{5} \)**
- Denominators: 20 and 5
- LCM(20, 5) = 20
- **This pair does not have an LCD of 10.**
4. **Pair: \( \frac{11}{10} \) and \( \frac{1}{2} \)**
- Denominators: 10 and 2
- LCM(10, 2) = 10
- **This pair has an LCD of 10.**
Thus, the pairs of fractions that have an LCD of 10 are:
- \( \frac{2}{5} \) and \( \frac{1}{10} \)
- \( \frac{3}{2} \) and \( \frac{3}{5} \)
- \( \frac{11}{10} \) and \( \frac{1}{2} \)
The correct selections are:
- \( \frac{2}{5} \) and \( \frac{1}{10} \)
- \( \frac{3}{2} \) and \( \frac{3}{5} \)
- \( \frac{11}{10} \) and \( \frac{1}{2} \)
Quick Answer
The pairs with an LCD of 10 are \( \frac{2}{5} \) and \( \frac{1}{10} \), \( \frac{3}{2} \) and \( \frac{3}{5} \), and \( \frac{11}{10} \) and \( \frac{1}{2} \).
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