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Sagot :
Sure, let's go through each set of problems and estimate the answers.
### Multiplication Estimates
a) [tex]\( 62 \times 19 \)[/tex]
- Estimate: [tex]\( 60 \times 20 = 1200 \)[/tex]
b) [tex]\( 270 \times 12 \)[/tex]
- Estimate: [tex]\( 270 \approx 300 \)[/tex]
- [tex]\( 300 \times 12 = 3600 \)[/tex]
c) [tex]\( 55 \times 60 \)[/tex]
- Estimate: [tex]\( 55 \approx 60 \)[/tex]
- [tex]\( 60 \times 60 = 3600 \)[/tex]
d) [tex]\( 4950 \times 28 \)[/tex]
- Estimate: [tex]\( 4950 \approx 5000 \)[/tex]
- [tex]\( 5000 \times 30 = 150,000 \)[/tex]
e) [tex]\( 0.8 \times 0.95 \)[/tex]
- Estimate: [tex]\( 0.8 \approx 1 \)[/tex]
- [tex]\( 1 \times 1 = 1 \)[/tex]
f) [tex]\( 0.184 \times 475 \)[/tex]
- Estimate: [tex]\( 0.184 \approx 0.2 \)[/tex]
- [tex]\( 0.2 \times 475 \)[/tex]
- [tex]\( 475 \times 0.2 = 95 \)[/tex]
### Division Estimates
a) [tex]\( 3946 \div 18 \)[/tex]
- Estimate: [tex]\( 3946 \approx 4000 \)[/tex]
- [tex]\( 4000 \div 20 = 200 \)[/tex]
b) [tex]\( 8287 \div 42 \)[/tex]
- Estimate: [tex]\( 8287 \approx 8400 \)[/tex]
- [tex]\( 8400 \div 40 = 210 \)[/tex]
c) [tex]\( 906 \div 27 \)[/tex]
- Estimate: [tex]\( 906 \approx 900 \)[/tex]
- [tex]\( 900 \div 30 = 30 \)[/tex]
d) [tex]\( 5520 \div 13 \)[/tex]
- Estimate: [tex]\( 5520 \approx 5600 \)[/tex]
- [tex]\( 5600 \div 14 = 400 \)[/tex]
e) [tex]\( 48 \div 0.12 \)[/tex]
- Estimate: [tex]\( 0.12 \approx 0.1 \)[/tex]
- [tex]\( 48 \div 0.1 = 480 \)[/tex]
f) [tex]\( 610 \div 0.22 \)[/tex]
- Estimate: [tex]\( 0.22 \approx 0.2 \)[/tex]
- [tex]\( 610 \div 0.2 = 3050 \)[/tex]
### Mixed Operations Estimates
a) [tex]\( 78.45 + 51.02 \)[/tex]
- Estimate: [tex]\( 78.45 \approx 78 \)[/tex]
- [tex]\( 51.02 \approx 51 \)[/tex]
- [tex]\( 78 + 51 = 129 \)[/tex]
b) [tex]\( 168.3 - 87.09 \)[/tex]
- Estimate: [tex]\( 168.3 \approx 168 \)[/tex]
- [tex]\( 87.09 \approx 87 \)[/tex]
- [tex]\( 168 - 87 = 81 \)[/tex]
c) [tex]\( 2.93 \times 3.14 \)[/tex]
- Estimate: [tex]\( 2.93 \approx 3 \)[/tex]
- [tex]\( 3.14 \approx 3 \)[/tex]
- [tex]\( 3 \times 3 = 9 \)[/tex]
d) [tex]\( 84.2 \div 19.5 \)[/tex]
- Estimate: [tex]\( 84.2 \approx 84 \)[/tex]
- [tex]\( 19.5 \approx 20 \)[/tex]
- [tex]\( 84 \div 20 = 4.2 \)[/tex]
e) [tex]\( \frac{4.3 \times 752}{15.6} \)[/tex]
- Estimate: [tex]\( 4.3 \approx 4 \)[/tex]
- [tex]\( 752 \approx 750 \)[/tex]
- [tex]\( 15.6 \approx 16 \)[/tex]
- [tex]\( 750 \div 16 = 46.875 \)[/tex]
- [tex]\( 4 \times 46.875 = \approx 188 \)[/tex]
f) [tex]\( \frac{(9.8)^3}{(2.2)^2} \)[/tex]
- Estimate: [tex]\( 9.8 \approx 10 \)[/tex]
- [tex]\( (9.8)^3 \approx 1000 \)[/tex]
- [tex]\( 2.2 \approx 2 \)[/tex]
- [tex]\( (2.2)^2 = 4.84 \approx 4 \)[/tex]
- [tex]\( 1000 \div 4 = 250 \)[/tex]
These estimates provide an approximate value to the given arithmetic problems without using a calculator.
### Multiplication Estimates
a) [tex]\( 62 \times 19 \)[/tex]
- Estimate: [tex]\( 60 \times 20 = 1200 \)[/tex]
b) [tex]\( 270 \times 12 \)[/tex]
- Estimate: [tex]\( 270 \approx 300 \)[/tex]
- [tex]\( 300 \times 12 = 3600 \)[/tex]
c) [tex]\( 55 \times 60 \)[/tex]
- Estimate: [tex]\( 55 \approx 60 \)[/tex]
- [tex]\( 60 \times 60 = 3600 \)[/tex]
d) [tex]\( 4950 \times 28 \)[/tex]
- Estimate: [tex]\( 4950 \approx 5000 \)[/tex]
- [tex]\( 5000 \times 30 = 150,000 \)[/tex]
e) [tex]\( 0.8 \times 0.95 \)[/tex]
- Estimate: [tex]\( 0.8 \approx 1 \)[/tex]
- [tex]\( 1 \times 1 = 1 \)[/tex]
f) [tex]\( 0.184 \times 475 \)[/tex]
- Estimate: [tex]\( 0.184 \approx 0.2 \)[/tex]
- [tex]\( 0.2 \times 475 \)[/tex]
- [tex]\( 475 \times 0.2 = 95 \)[/tex]
### Division Estimates
a) [tex]\( 3946 \div 18 \)[/tex]
- Estimate: [tex]\( 3946 \approx 4000 \)[/tex]
- [tex]\( 4000 \div 20 = 200 \)[/tex]
b) [tex]\( 8287 \div 42 \)[/tex]
- Estimate: [tex]\( 8287 \approx 8400 \)[/tex]
- [tex]\( 8400 \div 40 = 210 \)[/tex]
c) [tex]\( 906 \div 27 \)[/tex]
- Estimate: [tex]\( 906 \approx 900 \)[/tex]
- [tex]\( 900 \div 30 = 30 \)[/tex]
d) [tex]\( 5520 \div 13 \)[/tex]
- Estimate: [tex]\( 5520 \approx 5600 \)[/tex]
- [tex]\( 5600 \div 14 = 400 \)[/tex]
e) [tex]\( 48 \div 0.12 \)[/tex]
- Estimate: [tex]\( 0.12 \approx 0.1 \)[/tex]
- [tex]\( 48 \div 0.1 = 480 \)[/tex]
f) [tex]\( 610 \div 0.22 \)[/tex]
- Estimate: [tex]\( 0.22 \approx 0.2 \)[/tex]
- [tex]\( 610 \div 0.2 = 3050 \)[/tex]
### Mixed Operations Estimates
a) [tex]\( 78.45 + 51.02 \)[/tex]
- Estimate: [tex]\( 78.45 \approx 78 \)[/tex]
- [tex]\( 51.02 \approx 51 \)[/tex]
- [tex]\( 78 + 51 = 129 \)[/tex]
b) [tex]\( 168.3 - 87.09 \)[/tex]
- Estimate: [tex]\( 168.3 \approx 168 \)[/tex]
- [tex]\( 87.09 \approx 87 \)[/tex]
- [tex]\( 168 - 87 = 81 \)[/tex]
c) [tex]\( 2.93 \times 3.14 \)[/tex]
- Estimate: [tex]\( 2.93 \approx 3 \)[/tex]
- [tex]\( 3.14 \approx 3 \)[/tex]
- [tex]\( 3 \times 3 = 9 \)[/tex]
d) [tex]\( 84.2 \div 19.5 \)[/tex]
- Estimate: [tex]\( 84.2 \approx 84 \)[/tex]
- [tex]\( 19.5 \approx 20 \)[/tex]
- [tex]\( 84 \div 20 = 4.2 \)[/tex]
e) [tex]\( \frac{4.3 \times 752}{15.6} \)[/tex]
- Estimate: [tex]\( 4.3 \approx 4 \)[/tex]
- [tex]\( 752 \approx 750 \)[/tex]
- [tex]\( 15.6 \approx 16 \)[/tex]
- [tex]\( 750 \div 16 = 46.875 \)[/tex]
- [tex]\( 4 \times 46.875 = \approx 188 \)[/tex]
f) [tex]\( \frac{(9.8)^3}{(2.2)^2} \)[/tex]
- Estimate: [tex]\( 9.8 \approx 10 \)[/tex]
- [tex]\( (9.8)^3 \approx 1000 \)[/tex]
- [tex]\( 2.2 \approx 2 \)[/tex]
- [tex]\( (2.2)^2 = 4.84 \approx 4 \)[/tex]
- [tex]\( 1000 \div 4 = 250 \)[/tex]
These estimates provide an approximate value to the given arithmetic problems without using a calculator.
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