To determine if Clarice could verify her answer correctly, let's first analyze the division problem:
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Convert the mixed numbers to improper fractions:
- \(7 \frac{1}{2} = \frac{15}{2}\) (since \(7 \times 2 + 1 = 15\))
- \(1 \frac{1}{2} = \frac{3}{2}\) (since \(1 \times 2 + 1 = 3\))
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Perform the division:
- The division of fractions is the same as multiplying by the reciprocal: \[ \frac{15}{2} \div \frac{3}{2} = \frac{15}{2} \times \frac{2}{3} \]
- When multiplying, the \(2\)s in the numerator and denominator cancel out: \[ = \frac{15}{3} = 5 \]
So, the correct answer is indeed \(5\).
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Now let's check Clarice's multiplication:
- If her answer was \(5\), then to verify: \[ 5 \times 1 \frac{1}{2} = 5 \times \frac{3}{2} = \frac{15}{2} \]
- When we convert \(\frac{15}{2}\) back to a mixed number:
- \(15 \div 2 = 7\) remainder \(1\), which gives \(7 \frac{1}{2}\).
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Conclusion:
- Clarice's check shows that \(5 \times 1 \frac{1}{2}\) gives \(7 \frac{1}{2}\), which is equal to the original number \(7 \frac{1}{2}\) she divided by \(1 \frac{1}{2}\).
- However, the result of her check should have indicated that the final product of her multiplication should yield \(7 \frac{1}{2}\), but she mistook it as \(5 \frac{1}{2}\) in her statement.
Thus, Clarice cannot verify her answer correctly because she reported \(5 \frac{1}{2}\) instead of the actual \(7 \frac{1}{2}\), which shows that there was a misunderstanding in her checking process. The correct verification process would show that \(5 \times 1 \frac{1}{2}\) equals the original dividend \(7 \frac{1}{2}\).
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