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Using estimation, identify which of the following are definitely incorrect. Explain your reasoning clearly.

a) [tex]95 \times 212 = 20140[/tex]
b) [tex]44 \times 17 = 748[/tex]
c) [tex]689 \times 413 = 28457[/tex]
d) [tex]142656 \div 8 = 17832[/tex]
e) [tex]77.9 \times 22.6 = 2512.54[/tex]
f) [tex]\frac{8.42 \times 46}{0.2} = 19366[/tex]

Sagot :

GinnyAnsweridn
Let's analyze and estimate each of the given calculations to determine which results are definitely incorrect. Estimation can help us quickly determine if an answer is reasonable.

### Calculation a: [tex]\(95 \times 212 = 20140\)[/tex]
- Estimation: Round 95 to 100, and 212 to 200.
[tex]\[ 100 \times 200 = 20000 \][/tex]
- The given answer is 20140, which is very close to our estimate. This answer is reasonable and likely correct.

### Calculation b: [tex]\(44 \times 17 = 748\)[/tex]
- Estimation: Round 44 to 50, and 17 to 20.
[tex]\[ 50 \times 20 = 1000 \][/tex]
- The given answer is 748, which is significantly less than 1000. This answer is not reasonable and likely incorrect.

### Calculation c: [tex]\(689 \times 413 = 28457\)[/tex]
- Estimation: Round 689 to 700, and 413 to 400.
[tex]\[ 700 \times 400 = 280000 \][/tex]
- The given answer is 28457, which is significantly lower than our estimate. This answer is not reasonable and definitely incorrect. The transition to 284557 shows a closer reflection.

### Calculation d: [tex]\(142656 \div 8 = 17832\)[/tex]
- Estimation: Round 142656 to 140000.
[tex]\[ 140000 \div 8 = 17500 \][/tex]
- The given answer is 17832, which is quite close to our estimate of 17500. This answer is reasonable and likely correct.

### Calculation e: [tex]\(77.9 \times 22.6 = 2512.54\)[/tex]
- Estimation: Round 77.9 to 80, and 22.6 to 20.
[tex]\[ 80 \times 20 = 1600 \][/tex]
- The given answer is 2512.54, which is significantly higher than our estimate of 1600. This answer is not reasonable and likely incorrect.

### Calculation f: [tex]\(\frac{8.42 \times 46}{0.2} = 19366\)[/tex]
- Estimation: Round 8.42 to 10, and 46 to 50. Also, simplifying the division by 0.2.
[tex]\[ \frac{10 \times 50}{0.2} = \frac{500}{0.2} = 2500 \][/tex]
- The given answer is 19366, which is significantly higher than our estimate. This answer is not reasonable and definitely incorrect.

### Summary
The incorrect answers based on our estimation are:
- [tex]\(44 \times 17 = 748\)[/tex]
- [tex]\(689 \times 413 = 28457\)[/tex] (with a correction leading to 284557)
- [tex]\(77.9 \times 22.6 = 2512.54\)[/tex]
- [tex]\(\frac{8.42 \times 46}{0.2} = 19366\)[/tex]

So, the calculations that are definitely incorrect are:
[tex]\[ \text{b, c, e, and f} \][/tex]
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