Question
Estimate the sum by rounding the mixed numbers to the nearest whole numbers. \( 13 \frac{2}{3}+22 \frac{1}{5}+9 \frac{11}{15} \) (A) 44 (B) 45 (C) 46 (D) 47
Ask by Vaughn Santiago. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The estimated sum is 46.
Solution
We need to round each mixed number to the nearest whole number before summing.
1. For 13 2/3: Since 2/3 (approximately 0.67) is more than 0.5, round up to 14.
2. For 22 1/5: Since 1/5 (which is 0.2) is less than 0.5, round down to 22.
3. For 9 11/15: Since 11/15 (approximately 0.73) is more than 0.5, round up to 10.
Now, sum the rounded numbers:
14 + 22 + 10 = 46
Thus, the estimated sum is 46, which corresponds to choice (C).
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Simplify this solution The Deep Dive
To round the mixed numbers to the nearest whole numbers: - \( 13 \frac{2}{3} \) rounds to 14 (since \( \frac{2}{3} \) is closer to 1). - \( 22 \frac{1}{5} \) rounds to 22 (since \( \frac{1}{5} \) is closer to 0). - \( 9 \frac{11}{15} \) rounds to 10 (since \( \frac{11}{15} \) is closer to 1). Now, add the rounded numbers: \( 14 + 22 + 10 = 46 \). The estimated sum is 46, making the answer (C) 46!
