## MP Board Class 6th Maths Solutions Chapter 1 Knowing Our Numbers Ex 1.3

Question 1.

Estimate each of the following using general rule:

(a) 730 + 998

(b) 796 – 314

(c) 12,904 + 2,888

(d) 28,292 – 21,496

Make ten more such examples of addition, subtraction and estimation of their outcome.

Solution:

(a) 730 rounds off to 700

998 rounds off to 1,000

∴ Estimated sum = 700 + 1,000 = 1,700

(b) 796 rounds off to 800 314 rounds off to 300

∴ Estimated difference = 800 – 300 = 500

(c) 12,904 rounds off to 13,000 2,888 rounds off to 3,000

∴ Estimated sum = 13,000 + 3,000 = 16,000

(d) 28,292 rounds off to 28,000

21,496 rounds off to 21,000

∴ Estimated difference = 28,000 – 21,000 = 7,000

Ten more examples:

(i) 540 + 868

540 rounds off to 500

868 rounds off to 900

∴ Estimated sum = 500 + 900 = 1,400

(ii) 1,369 + 215

1, 369 rounds off to 1,000

215 rounds off to 200

∴ Estimated sum = 1,000 + 200 = 1,200

(iii) 46,352 – 11,867

46,352 rounds off to 46,000

11, 867 rounds off to 12,000

∴ Estimated difference = 46,000 – 12,000

= 34,000

(iv) 14,902 + 6,565

14,902 rounds off to 15,000

6,565 rounds off to 7,000

∴ Estimated sum = 15,000 + 7,000 = 22,000

(v) 514 – 386

514 rounds off to 500

386 rounds off to 400

∴ Estimated difference = 500 – 400 = 100

(vi) 27,904 + 69,592

27,904 rounds off to 28,000

69,592 rounds off to 70,000

∴ Estimated sum = 28,000 + 70,000 = 98,000

(vii) 530 – 98

530 rounds off to 500

98 rounds off to 100

∴ Estimated difference = 500 – 100 = 400

(viii) 18,230 – 3,666

18,230 rounds off to 18,000

3,666 rounds off to 4,000

∴ Estimated difference = 18,000 – 4,000 = 14,000

(ix) 56,306 + 17,693

56,306 rounds off to 56,000

17,693 rounds off to 18,000 Estimated sum = 56,000 + 18,000 = 74,000

(x) 4,275 – 125

4,275 rounds off to 4,000

125 rounds off to 100

∴ Estimated difference = 4,000 – 100 = 3,900

Question 2.

Give a rough estimate (by rounding off to nearest hundreds) and also a closer estimate (by rounding off to nearest tens):

(a) 439 + 334 + 4,317

(b) 1,08,734 – 47,599

(c) 8,325 – 491

(d) 4,89,348 – 48,365

Make four more such examples.

Solution:

(a) By rounding off to nearest hundreds, we get

439 rounds off to 400

334 rounds off to 300

4,317 rounds off to 4,300

∴ Estimated sum = 400 + 300 + 4,300 = 5,000

By rounding off to nearest tens, we get

439 rounds off to 440

334 rounds off to 330

4,317 rounds off to 4,320

∴ Estimated sum = 440 + 330 + 4,320 = 5,090

(b) By rounding off to nearest hundreds, we get

1,08,734 rounds off to 1,08,700

47,599 rounds off to 47,600

∴ Estimated difference = 1,08,700 – 47,600 = 61,100

By rounding off to nearest tens, we get 1,08,734 rounds off to 1,08,730

47,599 rounds off to 47,600

∴ Estimated difference = 1,08,730 – 47,600 = 61,130

(c) By rounding off to nearest hundreds, we get

8,325 rounds off to 8,300

491 rounds off to 500

∴ Estimated difference = 8,300 – 500 = 7,800

By rounding off to nearest tens, we get 8,325 rounds off to 8,330

491 rounds off to 490

∴ Estimated difference = 8,330 – 490 = 7,840

(d) By rounding off to nearest hundreds, we get

4,89,348 rounds off to 4,89,300

48,365 rounds off to 48,400

∴ Estimated difference = 4,89,300 – 48,400 = 4,40,900

By rounding off to nearest tens, we get 4,89,348 rounds off to 4,89,350

48,365 rounds off to 48,370

∴ Estimated difference = 4,89,350 – 48,370 = 4,40,980

Four more examples:

(i) 5,235 – 382

By rounding off to nearest hundreds, we get

5,235 rounds off to 5,200

382 rounds off to 400

∴ Estimated difference = 5,200 – 400 = 4,800

Now, by rounding off to nearest tens, we get

5,235 rounds off to 5,240

382 rounds off to 380

∴ Estimated difference = 5,240 – 380 = 4,860

(ii) 7,673+ 436+ 169

By rounding off to nearest hundreds, we get

7,673 rounds off to 7,700

436 rounds off to 400

169 rounds off to 200

∴ Estimated sum = 7,700 + 400 + 200 = 8,300

Now, by rounding off to nearest tens, we get

7,673 rounds off to 7,670

436 rounds off to 440

169 rounds off to 170

∴ Estimated sum = 7,670 + 440 + 170 = 8,280

(iii) 2,05,290 – 17,986

By rounding off to nearest hundreds, we get

2,05,290 rounds off to 2,05,300

17,986 rounds off to 18,000

∴ Estimated difference = 2,05,300 – 18,000 = 1,87,300

By rounding off to nearest tens, we get

2,05,290 rounds off to 2,05,290

17,986 rounds off to 17,990

∴ Estimated difference = 2,05,290 – 17,990 = 1,87,300

(iv) 6,830 + 35,764

By rounding off to nearest hundreds, we get

6,830 rounds off to 6,800

35,764 rounds off to 35,800

∴ Estimated sum = 6,800 + 35,800 = 42,600

Now, by rounding off to nearest tens, we get

6,830 rounds off to 6,830

35,764 rounds off to 35,760

∴ Estimated sum = 6,830 + 35,760 = 42,590

Question 3.

Estimate the following products using general rule:

(a) 578 × 161

(b) 5281 × 3491

(c) 1291 × 592

(d) 9250 × 29

Make four more such examples.

Solution:

(a) 578 × 161

578 rounds off to 600

161 rounds off to 200

∴ The estimated product

= 600 × 200 = 1,20,000

(b) 5281 × 3491

5281 rounds off to 5,000

3491 rounds off to 3,000

∴ The estimated product = 5,000 × 3,000 = 1,50,00,000

(c) 1291 × 592

1291 rounds-off to 1,000 592 rounds off to 600 The estimated product = 1,000 × 600 = 6,00,000

(d) 9250 × 29

9250 rounds off to 9,000 29 rounds off to 30 The estimated product = 9,000 × 30 = 2,70,000

Four more examples:

(i) 3260 × 86

3260 rounds off to 3,000 86 rounds off to 90

∴ Estimated product = 3,000 × 90 = 2,70,000

(ii) 7451 × 4,632

7451 rounds off to 7,000

4632 rounds off to 5,000

∴ Estimated product = 7,000 × 5,000 = 3,50,00,000

(iii) 356 × 204

356 rounds off to 400

204 rounds off to 200

∴ Estimated product = 400 × 200 = 80,000

(iv) 9860 × 692

9860 rounds off to 10,000

692 rounds off to 700

Estimated product = 10,000 × 700 = 70,00,000