To find out how many pieces Sarah can cut from \( \frac{5}{8} \) of a piece of fabric, with each piece being \( \frac{1}{4} \) of the original piece length, we first need to determine how many \( \frac{1}{4} \) pieces fit into \( \frac{5}{8} \).
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Finding a common denominator:
- The common denominator for \( \frac{5}{8} \) and \( \frac{1}{4} \) is 8.
- We can rewrite \( \frac{1}{4} \) as \( \frac{2}{8} \).
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Dividing:
- To find out how many \( \frac{2}{8} \) pieces fit into \( \frac{5}{8} \), we perform the division: \[ \frac{5}{8} \div \frac{2}{8} = \frac{5}{8} \times \frac{8}{2} = \frac{5 \times 8}{8 \times 2} = \frac{5}{2} \]
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Calculating the result:
- \( \frac{5}{2} = 2.5 \)
Thus, Sarah can cut the fabric into \( 2.5 \) pieces of \( \frac{1}{4} \) length from \( \frac{5}{8} \) of fabric. The options provided (A: \( \frac{2}{5} \), B: \( 2 \frac{1}{2} \), or C: \( \frac{5}{32} \)) give us:
- The answer is \( 2 \frac{1}{2} \) pieces, which corresponds to option B.
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