To verify if Clarice can check her answer correctly using multiplication, we need to analyze her division and the subsequent multiplication step.
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First, we convert the mixed numbers into 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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Now let's perform the division: \[ \frac{15}{2} \div \frac{3}{2} = \frac{15}{2} \times \frac{2}{3} = \frac{15 \times 2}{2 \times 3} = \frac{30}{6} = 5 \]
So, \(7 \frac{1}{2} \div 1 \frac{1}{2} = 5\) is correct.
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Now, to verify her answer, Clarice checks by multiplying her result \(5\) by \(1 \frac{1}{2}\): \[ 5 \times 1 \frac{1}{2} = 5 \times \frac{3}{2} = \frac{15}{2} \]
We know \(7 \frac{1}{2} = \frac{15}{2}\), so: \[ 5 \times 1 \frac{1}{2} = \frac{15}{2} \]
Thus, the multiplication confirms the original dividend.
- However, in her check, she wrote: \[ 5 \times 1 \frac{1}{2} = 5 \frac{1}{2} \]
This statement is incorrect because \(5 \frac{1}{2}\) is actually \(\frac{11}{2}\) (which is not equal to \(\frac{15}{2}\)).
In conclusion, while Clarice found the correct result for the division, her verification step had a mistake. Instead of getting \(5 \frac{1}{2}\), she should have confirmed that \(5 \times 1 \frac{1}{2}\) equals \(7 \frac{1}{2}\). Therefore, she did not verify her answer correctly.