Ray Ward
12/08/2023 · Senior High School
1) \( \frac{7}{2}=\left(\frac{2}{3} \cdot \frac{1}{2}\right) \div \frac{5}{3} \)
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Tutor-Verified Answer
Step-by-step Solution
To verify the equation \( \frac{7}{2}=\left(\frac{2}{3} \cdot \frac{1}{2}\right) \div \frac{5}{3} \), we will simplify the right-hand side step by step.
1. **Calculate \( \frac{2}{3} \cdot \frac{1}{2} \)**:
\[
\frac{2}{3} \cdot \frac{1}{2} = \frac{2 \cdot 1}{3 \cdot 2} = \frac{2}{6} = \frac{1}{3}
\]
2. **Now divide \( \frac{1}{3} \) by \( \frac{5}{3} \)**:
\[
\frac{1}{3} \div \frac{5}{3} = \frac{1}{3} \cdot \frac{3}{5} = \frac{1 \cdot 3}{3 \cdot 5} = \frac{3}{15} = \frac{1}{5}
\]
Now we have simplified the right-hand side to \( \frac{1}{5} \).
3. **Compare with the left-hand side**:
The left-hand side is \( \frac{7}{2} \).
Since \( \frac{7}{2} \) is not equal to \( \frac{1}{5} \), the equation is not true.
Thus, the statement \( \frac{7}{2}=\left(\frac{2}{3} \cdot \frac{1}{2}\right) \div \frac{5}{3} \) is **false**.
Quick Answer
The equation \( \frac{7}{2}=\left(\frac{2}{3} \cdot \frac{1}{2}\right) \div \frac{5}{3} \) is false.
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