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\( \frac{5}{6}, \frac{1}{3} \quad \begin{array}{l}\text { common } \\ \text { denominator }\end{array} \)

Ask by Owen Lewis. in the United States
Feb 27,2025

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The common denominator for 5/6 and 1/3 is 6.

Solución

To find a common denominator for 5/6 and 1/3, we look for the least common multiple (LCM) of the denominators 6 and 3. 1. The prime factorization of 6 is 2 × 3. 2. The prime factorization of 3 is 3. The LCM is found by taking the highest power of each prime that appears: • For 2: the highest power is 2¹ (from 6). • For 3: the highest power is 3¹ (from both 6 and 3). Thus, LCM = 2 × 3 = 6. Therefore, the common denominator is 6. Rewriting the fractions: • 5/6 already has the denominator 6. • 1/3 can be rewritten as 1 × 2 / (3 × 2) = 2/6. So, the fractions with the common denominator are 5/6 and 2/6.

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Extra Insights

To find a common denominator for \( \frac{5}{6} \) and \( \frac{1}{3} \), you'll want to look for the least common multiple (LCM) of the denominators, which are 6 and 3. The LCM of 6 and 3 is 6. This means you can keep the fraction \( \frac{5}{6} \) as is, while converting \( \frac{1}{3} \) into sixths by multiplying the numerator and the denominator by 2, resulting in \( \frac{2}{6} \). Now you can easily compare or perform operations with both fractions, as they now share the same denominator of 6!

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