Year 8 Maths: Estimating

Estimating is an important mathematical skill that involves finding an approximate answer to a problem when an exact answer is not necessary or practical. Estimation helps to quickly assess whether an answer is reasonable or close to the correct value, which is especially useful in real-world situations.

Estimation is used in everyday tasks such as shopping, cooking, and planning. It helps you to make informed decisions quickly, without needing to carry out long or complex calculations.

Key Techniques in Estimation

1. Rounding

Rounding numbers to the nearest 10, 100, or 1000 helps simplify calculations and provides an estimated answer. For example:

• 46 rounded to the nearest 10 is 50.
• 875 rounded to the nearest 100 is 900.

2. Front-End Estimation

This involves focusing on the leading digits (the digits in the highest place value) to make quick estimates. For example:

• To estimate the sum of 483 + 215, focus on the hundreds digits:
• 400 + 200 = 600.

3. Compatible Numbers

These are numbers that are easy to work with mentally, often used in estimation to make calculations simpler. For example:

• To estimate the division $$63 \div 9$$, you might use $$60 \div 10$$ to get an estimate of 6.

4. Estimating Sums, Differences, Products, and Quotients

When estimating operations like addition, subtraction, multiplication, and division, rounding the numbers first can make calculations easier and faster.

For example:

• To estimate $$47 \times 6$$, round 47 to 50, then calculate $$50 \times 6 = 300$$.

Practice Questions on Estimating

Easy Level

1. Estimate $$49 + 52$$ by rounding to the nearest 10.
2. Estimate $$348 + 172$$ by rounding to the nearest 100.
3. Estimate $$723 – 289$$ by rounding to the nearest 10.
4. Estimate $$86 \times 5$$ by rounding to the nearest 10.
5. Estimate $$145 \div 7$$ by rounding to the nearest 10.
6. Round 67 to the nearest 10.
7. Round 482 to the nearest 100.
8. Estimate $$29 \times 3$$ by rounding to the nearest 10.
9. Estimate $$632 – 198$$ by rounding to the nearest 100.
10. Estimate $$58 + 61$$ by rounding to the nearest 10.
11. Round 759 to the nearest 100.
12. Estimate $$94 \times 7$$ by rounding to the nearest 10.
13. Estimate $$326 \div 8$$ by rounding to the nearest 10.
14. Round 847 to the nearest 100.
15. Estimate $$18 \times 9$$ by rounding to the nearest 10.
16. Estimate $$92 + 47$$ by rounding to the nearest 10.
17. Estimate $$236 + 519$$ by rounding to the nearest 100.
18. Round 75 to the nearest 10.
19. Estimate $$673 – 122$$ by rounding to the nearest 100.
20. Round 1345 to the nearest 1000.

Medium Level

1. Estimate $$658 + 439 + 217$$ by rounding to the nearest 100.
2. Estimate $$759 – 324$$ by rounding to the nearest 10.
3. Estimate $$824 \div 12$$ by rounding to the nearest 10.
4. Estimate $$236 \times 9$$ by rounding to the nearest 10.
5. Estimate $$1425 + 3678$$ by rounding to the nearest 1000.
6. Estimate $$437 + 583 – 297$$ by rounding to the nearest 100.
7. Estimate $$567 \times 4$$ by rounding to the nearest 100.
8. Estimate $$152 \div 7$$ by rounding to the nearest 10.
9. Round 2349 to the nearest 1000.
10. Estimate $$723 \times 6$$ by rounding to the nearest 10.
11. Estimate $$643 – 218$$ by rounding to the nearest 10.
12. Estimate $$512 \div 8$$ by rounding to the nearest 10.
13. Estimate $$782 + 459$$ by rounding to the nearest 100.
14. Estimate $$93 \times 4$$ by rounding to the nearest 10.
15. Estimate $$567 – 299$$ by rounding to the nearest 100.
16. Estimate $$1248 + 765$$ by rounding to the nearest 1000.
17. Estimate $$371 – 98$$ by rounding to the nearest 10.
18. Estimate $$924 \div 13$$ by rounding to the nearest 10.
19. Estimate $$485 \times 9$$ by rounding to the nearest 100.
20. Round 389 to the nearest 10.

Hard Level

1. Estimate $$658 \times 23$$ by rounding to the nearest 10.
2. Estimate $$849 \div 7$$ by rounding to the nearest 100.
3. Estimate $$932 \times 54$$ by rounding to the nearest 100.
4. Estimate $$1432 + 9678 – 2134$$ by rounding to the nearest 1000.
5. Estimate $$5487 \div 29$$ by rounding to the nearest 10.
6. Estimate $$6328 + 4987 – 1135$$ by rounding to the nearest 1000.
7. Estimate $$1765 \times 6$$ by rounding to the nearest 100.
8. Estimate $$3648 \div 18$$ by rounding to the nearest 100.
9. Estimate $$9843 \times 7$$ by rounding to the nearest 1000.
10. Estimate $$4258 + 1976 – 698$$ by rounding to the nearest 1000.
11. Estimate $$547 \times 76$$ by rounding to the nearest 100.
12. Estimate $$628 \div 22$$ by rounding to the nearest 10.
13. Estimate $$2945 + 6382 – 1567$$ by rounding to the nearest 1000.
14. Estimate $$472 \times 36$$ by rounding to the nearest 10.
15. Estimate $$9631 – 3847$$ by rounding to the nearest 1000.
16. Estimate $$7843 + 5612$$ by rounding to the nearest 1000.
17. Estimate $$453 \div 19$$ by rounding to the nearest 10.
18. Estimate $$764 \times 29$$ by rounding to the nearest 100.
19. Estimate $$5128 \div 18$$ by rounding to the nearest 100.
20. Estimate $$8765 + 3429 – 1976$$ by rounding to the nearest 1000.

Answers and Explanations

Easy Level

1. $$ 49 + 52 \approx 50 + 50 = 100 $$
2. $$ 348 + 172 \approx 300 + 200 = 500 $$
3. $$ 723 – 289 \approx 720 – 290 = 430 $$
4. $$ 86 \times 5 \approx 90 \times 5 = 450 $$
5. $$ 145 \div 7 \approx 150 \div 10 = 15 $$
6. $$ 67 \approx 70 $$
7. $$ 482 \approx 500 $$
8. $$ 29 \times 3 \approx 30 \times 3 = 90 $$
9. $$ 632 – 198 \approx 600 – 200 = 400 $$
10. $$ 58 + 61 \approx 60 + 60 = 120 $$
11. $$ 759 \approx 800 $$
12. $$ 94 \times 7 \approx 90 \times 7 = 630 $$
13. $$ 326 \div 8 \approx 320 \div 10 = 32 $$
14. $$ 847 \approx 800 $$
15. $$ 18 \times 9 \approx 20 \times 10 = 200 $$
16. $$ 92 + 47 \approx 90 + 50 = 140 $$
17. $$ 236 + 519 \approx 200 + 500 = 700 $$
18. $$ 75 \approx 80 $$
19. $$ 673 – 122 \approx 700 – 100 = 600 $$
20. $$ 1345 \approx 1000 $$

Medium Level

1. $$ 658 + 439 + 217 \approx 700 + 400 + 200 = 1300 $$
2. $$ 759 – 324 \approx 760 – 320 = 440 $$
3. $$ 824 \div 12 \approx 820 \div 10 = 82 $$
4. $$ 236 \times 9 \approx 240 \times 10 = 2400 $$
5. $$ 1425 + 3678 \approx 1000 + 4000 = 5000 $$
6. $$ 437 + 583 – 297 \approx 400 + 600 – 300 = 700 $$
7. $$ 567 \times 4 \approx 600 \times 4 = 2400 $$
8. $$ 152 \div 7 \approx 150 \div 10 = 15 $$
9. $$ 2349 \approx 2000 $$
10. $$ 723 \times 6 \approx 720 \times 6 = 432

0 $$

11. $$ 643 – 218 \approx 640 – 220 = 420 $$
12. $$ 512 \div 8 \approx 510 \div 10 = 51 $$
13. $$ 782 + 459 \approx 800 + 500 = 1300 $$
14. $$ 93 \times 4 \approx 90 \times 4 = 360 $$
15. $$ 567 – 299 \approx 570 – 300 = 270 $$
16. $$ 1248 + 765 \approx 1000 + 1000 = 2000 $$
17. $$ 371 – 98 \approx 370 – 100 = 270 $$
18. $$ 924 \div 13 \approx 920 \div 10 = 92 $$
19. $$ 485 \times 9 \approx 500 \times 10 = 5000 $$
20. $$ 389 \approx 390 $$

Hard Level

1. $$ 658 \times 23 \approx 660 \times 20 = 13200 $$
2. $$ 849 \div 7 \approx 800 \div 10 = 80 $$
3. $$ 932 \times 54 \approx 900 \times 50 = 45000 $$
4. $$ 1432 + 9678 – 2134 \approx 1000 + 10000 – 2000 = 9000 $$
5. $$ 5487 \div 29 \approx 5500 \div 30 = 183 $$
6. $$ 6328 + 4987 – 1135 \approx 6000 + 5000 – 1000 = 10000 $$
7. $$ 1765 \times 6 \approx 1800 \times 6 = 10800 $$
8. $$ 3648 \div 18 \approx 3600 \div 20 = 180 $$
9. $$ 9843 \times 7 \approx 10000 \times 7 = 70000 $$
10. $$ 4258 + 1976 – 698 \approx 4000 + 2000 – 700 = 5300 $$
11. $$ 547 \times 76 \approx 500 \times 80 = 40000 $$
12. $$ 628 \div 22 \approx 600 \div 20 = 30 $$
13. $$ 2945 + 6382 – 1567 \approx 3000 + 6000 – 2000 = 7000 $$
14. $$ 472 \times 36 \approx 470 \times 40 = 18800 $$
15. $$ 9631 – 3847 \approx 10000 – 4000 = 6000 $$
16. $$ 7843 + 5612 \approx 8000 + 6000 = 14000 $$
17. $$ 453 \div 19 \approx 450 \div 20 = 22.5 $$
18. $$ 764 \times 29 \approx 800 \times 30 = 24000 $$
19. $$ 5128 \div 18 \approx 5100 \div 20 = 255 $$
20. $$ 8765 + 3429 – 1976 \approx 9000 + 3000 – 2000 = 10000 $$

These estimation questions help students develop a practical approach to problem-solving by focusing on approximations rather than exact calculations. The skills acquired from estimating are highly applicable in real-world situations where quick, reasonable calculations are often needed.