Love Hodges
05/08/2024 · Senior High School
c) \( \left(\frac{3}{2}-1\right) * 1 \frac{1}{2}+\frac{3}{4} * \frac{-4}{3}= \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To solve the expression \( \left(\frac{3}{2}-1\right) * 1 \frac{1}{2}+\frac{3}{4} * \frac{-4}{3} \), we will break it down step by step.
1. **Calculate \( \frac{3}{2} - 1 \)**:
\[
\frac{3}{2} - 1 = \frac{3}{2} - \frac{2}{2} = \frac{3 - 2}{2} = \frac{1}{2}
\]
2. **Convert \( 1 \frac{1}{2} \) to an improper fraction**:
\[
1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}
\]
3. **Multiply \( \left(\frac{1}{2}\right) * \left(\frac{3}{2}\right) \)**:
\[
\frac{1}{2} * \frac{3}{2} = \frac{1 \cdot 3}{2 \cdot 2} = \frac{3}{4}
\]
4. **Calculate \( \frac{3}{4} * \frac{-4}{3} \)**:
\[
\frac{3}{4} * \frac{-4}{3} = \frac{3 \cdot -4}{4 \cdot 3} = \frac{-12}{12} = -1
\]
5. **Combine the results**:
\[
\frac{3}{4} + (-1) = \frac{3}{4} - 1 = \frac{3}{4} - \frac{4}{4} = \frac{3 - 4}{4} = \frac{-1}{4}
\]
Thus, the final result is:
\[
\boxed{-\frac{1}{4}}
\]
Quick Answer
The final result is \( -\frac{1}{4} \).
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