Question
1.Which is greater? How do you know? \[ 3 \frac{1}{2} \times \frac{1}{3} \text { or } \frac{2}{3} \times \frac{3}{2} \]
Ask by Gibbs Blake. in the United States
Mar 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(3 \frac{1}{2} \times \frac{1}{3}\) is greater than \(\frac{2}{3} \times \frac{3}{2}\).
Solution
1. Convert \(3 \frac{1}{2}\) to an improper fraction:
\[
3 \frac{1}{2} = \frac{7}{2}
\]
2. Calculate the first product:
\[
\frac{7}{2} \times \frac{1}{3} = \frac{7}{6}
\]
3. Calculate the second product:
\[
\frac{2}{3} \times \frac{3}{2} = \frac{6}{6} = 1
\]
4. Compare the two results:
\[
\frac{7}{6} > 1
\]
Thus,
\[
3 \frac{1}{2} \times \frac{1}{3} \text{ is greater than } \frac{2}{3} \times \frac{3}{2}.
\]
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Simplify this solution The Deep Dive
Let's break this down step-by-step! First, we convert \(3 \frac{1}{2}\) to an improper fraction, which is \(\frac{7}{2}\). Now, we can calculate the first expression: \[ 3 \frac{1}{2} \times \frac{1}{3} = \frac{7}{2} \times \frac{1}{3} = \frac{7}{6}. \] For the second expression, we simplify it: \[ \frac{2}{3} \times \frac{3}{2} = 1. \] Now we compare \(\frac{7}{6}\) (which is approximately 1.16667) to 1. Clearly, \(\frac{7}{6}\) is greater than 1. Thus, \(3 \frac{1}{2} \times \frac{1}{3}\) is greater than \(\frac{2}{3} \times \frac{3}{2}\). So, the answer is: \[ 3 \frac{1}{2} \times \frac{1}{3} \text{ is greater.} \]
