Pregunta
\( \frac{5}{6}, \frac{1}{3} \quad \begin{array}{l}\text { common } \\ \text { denominator }\end{array} \)
Ask by Owen Lewis. in the United States
Feb 27,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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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.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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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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