Question
b. Choose the best approximation for \( 5 \frac{7}{10} \cdot 8 \frac{17}{120} \). 50 40 54 48 . 54
Ask by Dunn Rodriguez. in the United States
Jan 25,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The best approximation is 48.
Solution
Let's calculate the approximation for \( 5 \frac{7}{10} \times 8 \frac{17}{120} \).
1. **Convert Mixed Numbers to Improper Fractions:**
- \( 5 \frac{7}{10} = \frac{57}{10} \)
- \( 8 \frac{17}{120} = \frac{977}{120} \)
2. **Multiply the Fractions:**
\[
\frac{57}{10} \times \frac{977}{120} = \frac{57 \times 977}{10 \times 120} = \frac{55,689}{1,200} \approx 46.4075
\]
3. **Choose the Best Approximation:**
- The calculated value is approximately **46.4**.
- Among the options provided (50, 40, 54, 48), the closest approximation is **48**.
**Answer:** 48
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To simplify \(5 \frac{7}{10} \cdot 8 \frac{17}{120}\), we can first convert the mixed numbers into improper fractions. So, \(5 \frac{7}{10} = \frac{57}{10}\) and \(8 \frac{17}{120} = \frac{977}{120}\). Multiplying these gives us \(\frac{57 \cdot 977}{10 \cdot 120}\). However, approximating the fractions can simplify the math. For quick estimation, round \(5 \frac{7}{10}\) to 6 and \(8 \frac{17}{120}\) to 8. Thus, \(6 \cdot 8 = 48\). Therefore, the best approximation from the options given is 48.
