Gonzalez Chang
03/03/2024 · Middle School
What is the product of \( 1 \frac{2}{3} \) and \( -3 \frac{1}{2} ? \)
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Tutor-Verified Answer
Step-by-step Solution
To find the product of \( 1 \frac{2}{3} \) and \( -3 \frac{1}{2} \), we first convert the mixed numbers into improper fractions.
Starting with \( 1 \frac{2}{3} \):
\[
1 \frac{2}{3} = 1 + \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3}
\]
Next, we convert \( -3 \frac{1}{2} \):
\[
-3 \frac{1}{2} = -\left(3 + \frac{1}{2}\right) = -\left(\frac{6}{2} + \frac{1}{2}\right) = -\frac{7}{2}
\]
Now we can multiply the two improper fractions:
\[
\frac{5}{3} \times -\frac{7}{2} = \frac{5 \times -7}{3 \times 2} = \frac{-35}{6}
\]
Thus, the product of \( 1 \frac{2}{3} \) and \( -3 \frac{1}{2} \) is:
\[
\boxed{-\frac{35}{6}}
\]
Quick Answer
The product is \( -\frac{35}{6} \).
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