Math Problem Statement

By estimating the answer to each calculation, work out which two of his answers are obviously wrong.

Solution

Let's estimate each calculation to identify the wrong answers:

A) 31.45×48.2=1515.8931.45 \times 48.2 = 1515.89
We can round the numbers for a rough estimate:
31.453031.45 \approx 30 and 48.25048.2 \approx 50.
30×50=150030 \times 50 = 1500, which is quite close to 1515.891515.89.
So, A seems reasonable.

B) (32.36×5.9)+25.1=2160.24(32.36 \times 5.9) + 25.1 = 2160.24
Estimate:
32.363032.36 \approx 30 and 5.965.9 \approx 6.
30×6=18030 \times 6 = 180, and adding 25.125.1, we get approximately 205205, which is much smaller than 2160.242160.24.
So, B seems wrong.

C) 204.7×0.813=16.641204.7 \times 0.813 = 16.641
Estimate:
204.7200204.7 \approx 200 and 0.8130.80.813 \approx 0.8.
200×0.8=160200 \times 0.8 = 160, but the given result is 16.64116.641, which is far too small.
So, C is wrong.

D) (298+97)×7.4=2923(298 + 97) \times 7.4 = 2923
Estimate:
298+97=395298 + 97 = 395.
395×7.4400×7=2800395 \times 7.4 \approx 400 \times 7 = 2800, which is close to 29232923.
So, D seems reasonable.

Conclusion:

The two incorrect answers are B and C.

Would you like more details or have any further questions? Here are some related questions for deeper understanding:

  1. What are the benefits of using estimation in math?
  2. How can rounding help simplify multiplication?
  3. How do you identify when an answer is far off without exact calculations?
  4. Why does small rounding not significantly affect larger estimates?
  5. How would using more precise rounding affect the results?

Tip: Estimation is useful for quickly verifying results without the need for detailed calculation.

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Math Problem Analysis

Mathematical Concepts

Estimation
Multiplication
Addition
Rounding

Formulas

Multiplication formula: a × b
Basic addition: a + b

Theorems

Basic Arithmetic Theorems
Rounding Theorem

Suitable Grade Level

Grades 5-7