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1. Estimate the following products using general rule:(a) 578 × 161(b) 5281 × 3491(c) 1291 × 592(d) 9250 × 29Make four more such examples.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 + 4317 (b) 108734 – 47599 (c) 8325 – 491 (d) 489348 – 48365Make four more such examples.3. Estimate each of the following using general rule:(a) 730 + 998 (b) 796 – 314 (c) 12904 + 2888 (d) 28292 – 21496Make ten more such examples of addition, subtraction and estimation of their outcome.4. A vessel has 4 litres and 500 ml of curd. In how many glasses, each of 25 ml capacity, can it be filled?5. The distance between the school and a student’s house is 1 km 875 m. Everyday she walks both ways. Find the total distance covered by her in six days. |
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Answer» 1 (a) 578 × 161 Rounding 568 to the nearest hundreds, we get 600 Rounding 161 to the nearest hundreds, we get 200 Therefore, 600 × 200 = 12000 (b) 5281 × 3491 Rounding off 5,291 to the nearest thousands, we get 5,000 And, rounding off 3,491 to the nearest hundreds, we get 3,500 Therefore, 5,000 × 3,500 = 1,75,00,000 (c) 1291 × 592 Rounding off 1291 to the nearest hundreds we get, 1300 And, rounding off 592 to the nearest hundreds, we get 600 Therefore, 1300 × 600 = 7,80,000 (d) 9250 × 29 Rounding off 9250 to the nearest thousands, we get, 9000 Rounding off 29 to the nearest tens, we get 30 Therefore, 9000 × 30 = 270000 Some examples are:- • 675 × 57 which can be rounded to 42,000 • 395 × 38 which can be rounded to, 16000 • 519 × 23 which can be rounded to, 10000 • 1234 × 19 which can be rounded to, 24000 2) (a) 439 + 334 + 4317 Rounding 439 to the nearest hundreds, we get, 400. Rounding 334 to the nearest hundreds, we get, 300 Rounding 4317 to the nearest hundreds, we get, 4300. Therefore, 400 + 300 + 4300 = 5000 ► The answer is 5,000 when we round off the given terms to the nearest hundreds Rounding 439 to the nearest tens, we get 440 Rounding 334 to the nearest tens, we get 330 Rounding 4317 to the nearest tens, we get 4320 Therefore, 440 + 330 + 4320 = 5090. ► The answer is, 5090 when we round the given terms to the nearest tens. (b) 108734 – 47599 Rounding off 1,08,734 to the nearest hundreds, we get 1,08,700 Rounding off 47,599 to the nearest hundreds, we get 47,600 Therefore, 1,08,700 - 47,600 = 61,100 ► The answer is 61,100 when we round off the given terms to the nearest hundreds. Rounding off 1,08,734 to the nearest tens, we get 1,08,730 Rounding off, 47599 to the nearest tens, we get 47,600 Therefore, 1,08,730 - 47,600 = 61,130 ► The answer is 61,130 when we round the given terms to the nearest tens. (c) 8325 – 491 Rounding off 8,325 to the nearest hundreds, we get 8,300 Rounding off 491 to the nearest hundreds, we get 500 Therefore, 8,300 - 500 = 7800 ► The answer is 7,800 when we round off the given terms to the nearest hundreds. Rounding off 8,325 to the nearest tens we get, 8330 Rounding off 491 to the nearest tens we get, 490 Therefore, 8330 - 490 = 7840 ► The answer is 7,840 when we round the given terms to the nearest tens. (d) 4,89,348 – 48,365 Rounding off 4,89,348 to the nearest hundreds we get 4,89,300 Rounding off 48,365 to the nearest hundreds, we get 48,400 Therefore, 4,89,300 - 48,400 = 4,40,900 ► The answer is 4,40,900 when we round off the given terms to the nearest hundreds. Rounding off 4,89,348 to the nearest tens, we get 4,89,350 Rounding off 48,365 to the nearest tens, we get 48,370 Therefore, 4,89,350 - 48,370 = 4,40,980 ► The answer is 4,40,980 when we round off the given terms to the nearest hundreds. Some examples are:- • 627 + 595 + 731 rounded to the nearest hundreds gives 1900 and rounded to the nearest tens gives 1960 • 183963 - 52567 rounded to the nearest hundreds gives 1,314,00 and rounded to the nearest tens gives 1,31,393. • 5256 - 934 rounded to the nearest hundreds gives, 4,400 and rounded to the nearest tens gives 4,330. • 197138 - 39465 rounded to the nearest hundreds gives, 1,57,600 and rounded to the nearest tens gives 1,57,670 3) (a) 730 + 998 Nearest rounding of 730 is 700 Nearest rounding of 998 is 1000 Therefore, 700 + 1000 = 1700 (b) 796 - 314 Nearest rounding of 796 is 800 Nearest rounding of 314 is 300 Therefore, 800 - 300 = 500 (c) 12904 + 2888 Nearest rounding of, 12904 is 13,000 Nearest rounding of 2888 is 3000, Therefore, 13000 + 3000 = 16,000 (d) 28292 – 21496 Nearest rounding of 28292 is 28000 Nearest rounding of, 21496 is, 21000 Therefore, 28000 - 21000 = 7,000 Ten such examples are:- • 435 + 282 which gives 700 • 3968 + 5870 which gives 10,000 • 7392 - 4789 which gives 2,000 • 5160 - 2792 which gives 2,000 • 2195 + 1306 which gives 3,000 • 1180 - 1382 which gives 0 • 920 + 565 which gives 1,500 • 6410 - 4860 which gives 1,000 • 3841 + 1450 which gives 5000 • 6375 - 4229 which gives 2,000 In all the examples, the general rule has been applied. 4) Capacity of Vessel = 4 litres and 5 ml = 4500 ml Capacity of one glass = 25 ml No of glasses that can be filled = 4500/25 = 180 5) Distance between school and student house = 1km 875m = 1875m Distance covered by the student in one day = 2 × 1875 = 3750m Total distance covered in 6 days = 6 × 3750 = 22500m Therefore, the total distance covered in 6 days is, 22km and 500m. 1. (a) 578 x 161 Rounding off 578 to the nearest hundreds, we get 600 And, rounding off 161 to the nearest hundreds, we get 200 Therefore, 600 x 200 = 1,20,000 It means that estimate of 578 x 161 is equal to 1,20,000 according to the general rule. (b) 5281 × 3491 Rounding off 5,291 to the nearest thousands, we get 5,000 And, rounding off 3,491 to the nearest hundreds, we get 3,500 Therefore, 5,000 x 3,500 = 1,75,00,000 It means that estimate of 5281 x 3491 is equal to 1,75,00,000 according to the general rule. (c) 1291 × 592 Rounding off 1291 to the nearest hundreds we get, 1300 And, rounding off 592 to the nearest hundreds, we get 600 Therefore, 1300 x 600 = 7,80,000 It means that estimate of 1291 x 592 is equal to 7,80,000 according to the general rule. (d) 9250 × 29 Rounding off 9250 to the nearest thousands, we get 9000 And, rounding off 29 to the nearest tens, we get 30 Therefore, 9000 x 30 = 2,70,000 It means that estimate of 9250 × 29 is equal to 2,70,000 using general rule. 2. (a) 439 + 334 + 4317 Rounding off to hundreds Rounding off 439 to the nearest hundreds= 400 Rounding off 334 to the nearest hundreds=300 Rounding off 4,317 to the nearest hundreds, we get 4,300 On adding we get, 400 + 300 + 4,300 = 5,000 Rounding off to tens Rounding off 439 to the nearest tens = 440 Rounding off 334 to the nearest tens= 330 And, rounding off 4,317 to the nearest tens =4,320 On adding we get 440 + 330 + 4,320 = 5,090
(b) 1,08,734 – 47,599 Rounding off to hundreds Rounding off 1,08,734 to the nearest hundreds= 1,08,700 And rounding off 47,599 to the nearest hundreds= 47,600 On subtracting we get 1,08,700-47,600=61,100 Rounding off to tens Rounding off 1,08,734 to the nearest tens =1,08,730 Rounding off 47,599 to the nearest tens =47,600 On subtracting we get 1,08,730-47,600=61,130
(c) 8325 – 491 Rounding off to hundreds Rounding off 8,325 to the nearest hundreds= 8,300 And, rounding off 491 to the nearest hundreds= 500 On subtracting, we get 8,300-500=7,800 Rounding off to tens Rounding off 8,325 to the nearest tens= 8,330 And, rounding off 491 to the nearest tens= 490 On subtracting we get, 8,330-490=7,840 The answer is 7800 when we round off the given terms to the nearest hundreds. (d) 4,89,348 – 48,365 Rounding off to hundreds Rounding off 4,89,348 to the nearest hundreds= 4,89,300 And, rounding off 48,365 to the nearest hundreds=48,400 On subtracting we get 4,89,300-48,400=4,40,900 Rounding off to tens Rounding off 4,89,348 to the nearest tens= 4,89,350 Rounding off 48,365 to the nearest tens= 48,370 On subtracting we get 4,89,350-48,370=4,40,980
3. (a) 730 + 998 Nearest round off of 730 = 700 (b) 796 - 314 Nearest round off of 796 = 800 (c) 12904 + 2888 Nearest round off of 12904 = 13000 (d) 28292 - 21496 Nearest round off of 28292 = 28000 Ten more such examples are (i) 435 + 282 = 400 + 300 = 700 4. Given that Capacity of curd in a vessel = 4 liters 500 ml = 4 × 1000 ml + 500 ml = 4500 ml Capacity of one glass = 25ml In how many glasses each of 25 ml capacity, can the given volume of curd be filled. Number of glasses can be filled = 4500/25= 180 Therefore, 180 glasses can be filled by curd. 5. Given that Distance between school and home = 1875m We have to find out the total distance covered by her in six days To determine the total distance covered by her in six days first we need to add the to and for distance covered by her in a day Total distance covered in one day = (1875m+1875m) = 3750m Distance covered in six days = 3750 x 6 = 22500m Therefore, 22 km 500 m distance was covered in six days. |
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