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3. Extend Your Thinking Mark said he can decompose the fraction \( \frac{5}{6} \) into three fractions with three different numerators. Is this possible? Explain.

Ask by Craig Marshall. in the United States
Feb 03,2025

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Yes, \( \frac{5}{6} \) can be decomposed into three fractions with different numerators, such as \( \frac{2}{5} + \frac{1}{4} + \frac{11}{60} \).

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Mind Expander

Absolutely, it's possible! Mark can decompose \( \frac{5}{6} \) into three distinct fractions by using clever thinking. For example, he can express it as \( \frac{1}{6} + \frac{2}{6} + \frac{2}{6} \). However, since he needs different numerators, he might try something like \( \frac{1}{6} + \frac{2}{6} + \frac{3}{6} \). In this case, the sum still equals \( \frac{5}{6} \). One common mistake is to assume that the fractions need to be significantly different or require the use of integers only. It's important to remember they can be scaled or simplified as needed, as long as the total remains \( \frac{5}{6} \). So, it can be fun to experiment!

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