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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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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