Question

After completing a fraction division problem, Clarice used multiplication to check her answer.

Division: 7 and one-half divided by 1 and one-half = 5. Check: 5 times 1 and one-half = 5 and one-half.

Could Clarice verify her answer? Explain.

Answer 1

To verify if Clarice can check her answer correctly using multiplication, we need to analyze her division and the subsequent multiplication step.

1. 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 \(1 \times 2 + 1 = 3\))

2. 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.

3. 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.

4. 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.