Std 5 Mathematics · Chapter 4

4. Multiplication and Division

Solutions to Problem Sets 14 to 16 — multiplication by three-digit numbers, long division and mixed word problems, with full working. Maharashtra State Board (Balbharati), Grade Five Mathematics, Part One.

Key Ideas

Multiplying by a three-digit number: multiply by the units digit, then by the tens (put one 0 first), then by the hundreds (put two 0s first). Add the three partial products.

Long division: Divide → Multiply → Subtract → Bring down the next digit. Repeat until all digits are used.

Guessing a quotient digit: compare the first digits of the number being divided and the divisor, try the guess, and reduce it by 1 if the product is too big.

Checking a division: Divisor × Quotient + Remainder = Dividend. The remainder must always be smaller than the divisor.

Problem Set 14

1Multiply.

(1) 327× 92 654+ 29,430 30,084

(2) 807× 126 4,842+ 16,140+ 80,700 1,01,682

(3) 567× 890 0+ 51,030+ 4,53,600 5,04,630

(4) 4,317× 824 17,268+ 86,340+ 34,53,600 35,57,208

(5) 6,092× 203 18,276+ 0+ 12,18,400 12,36,676

(6) 1,177× 99 10,593+ 1,05,930 1,16,523

(7) 456× 187 3,192+ 36,480+ 45,600 85,272

(8) 6,543× 79 58,887+ 4,58,010 5,16,897

(9) 2,306× 832 4,612+ 69,180+ 18,44,800 19,18,592

(10) 6,429× 509 57,861+ 0+ 32,14,500 32,72,361

(11) 4,321× 678 34,568+ 3,02,470+ 25,92,600 29,29,638

(12) 20,304× 87 1,42,128+ 16,24,320 17,66,448

327 × 92 = 30,084
807 × 126 = 1,01,682
567 × 890 = 5,04,630
4,317 × 824 = 35,57,208
6,092 × 203 = 12,36,676
1,177 × 99 = 1,16,523
456 × 187 = 85,272
6,543 × 79 = 5,16,897
2,306 × 832 = 19,18,592
6,429 × 509 = 32,72,361
4,321 × 678 = 29,29,638
20,304 × 87 = 17,66,448

In (3), 890 has 0 in the units place, so the first partial product is 0. In (5), (10) the multiplier has 0 in the tens place, so that partial product is 0. You can skip writing a zero row once you are confident.

2As part of the ‘Avoid Plastic’ campaign, each of 745 students made 25 paper bags. What was the total number of paper bags made?

745× 25 3,725+ 14,900 18,625

Total paper bags = number of students × bags made by each = 18,625 paper bags.

3In a plantation, saplings of 215 medicinal trees have been planted in each of the 132 rows of trees. How many saplings are there in the plantation altogether?

215× 132 430+ 6,450+ 21,500 28,380

Total saplings = saplings in one row × number of rows = 28,380 saplings.

4One computer costs 27,540 rupees. How much will 18 such computers cost?

27,540× 18 2,20,320+ 2,75,400 4,95,720

18 computers will cost ₹ 4,95,720.

5Under the ‘Inspire Awards’ scheme, 5000 rupees per student were granted for the purchase of science project materials. If 154 students in a certain taluka were covered under the scheme, find the total amount granted to that taluka.

5,000× 154 20,000+ 2,50,000+ 5,00,000 7,70,000

The total amount granted to the taluka is ₹ 7,70,000.

6If a certain two-wheeler costs 53,670 rupees, how much will 35 such two-wheelers cost?

53,670× 35 2,68,350+ 16,10,100 18,78,450

35 two-wheelers will cost ₹ 18,78,450.

7One hour has 3,600 seconds. How many seconds do 365 hours have?

3,600× 365 18,000+ 2,16,000+ 10,80,000 13,14,000

365 hours have 13,14,000 seconds.

8Frame a multiplication word problem with the numbers 5473 and 627 and solve it.

Problem: A cloth shop sells one saree for 627 rupees. If 5473 sarees were sold during the Diwali season, how much money did the shop receive?

5,473× 627 38,311+ 1,09,460+ 32,83,800 34,31,571

The shop received ₹ 34,31,571.

Students may frame their own problem. Whatever the story, the product of 5473 and 627 is always 34,31,571.

9Find the product of the biggest three-digit number and the biggest four-digit number.

The biggest three-digit number is 999 and the biggest four-digit number is 9999.

9,999× 999 89,991+ 8,99,910+ 89,99,100 99,89,001

The product is 99,89,001.

10One traveller incurs a cost of 7,650 rupees for a certain journey. What will be the cost for 26 such travellers?

7,650× 26 45,900+ 1,53,000 1,98,900

The cost for 26 travellers will be ₹ 1,98,900.

Pairing Off Objects from Two Groups

ASuresh has three balls marked A, B and C and three bats marked P, Q and R. In how many ways can he pair off a ball and a bat?

The pairs are AP, AQ, AR, BP, BQ, BR, CP, CQ and CR. Each of the 3 balls can go with each of the 3 bats, so there are 3 × 3 = 9 different pairs.

BSanju, John and Ali each had a photo taken wearing each of five types of hats. How many photographs were taken in all?

Each of the 3 boys was photographed with each of the 5 hats, so 3 × 5 = 15 photographs were taken.

CTake two collections with the given number of objects and complete the table.

Objects in one collection	Objects in the other collection	How many ways to form pairs?
3	2	3 × 2 = 6
5	2	5 × 2 = 10
2	4	2 × 4 = 8
3	4	3 × 4 = 12

What does this table tell us? The number of different pairs formed by taking one object from each of two groups is equal to the product of the numbers of objects in the two groups.

Problem Set 15

1Solve the following and write the quotient and remainder.

(1) 4032 ) 1284 − 128 4 − 0 4

(2) 6487 ) 5586 − 522 366 − 348 18

(3) 4427 ) 1207 − 108 127 − 108 19

(4) 20841 ) 8543 − 82 34 − 0 343 − 328 15

(5) 5343 ) 2304 − 215 154 − 129 25

(6) 218226 ) 56741 − 52 47 − 26 214 − 208 61 − 52 9

1,284 ÷ 32: Quotient 40, Remainder 4 (check: 32 × 40 + 4 = 1,284)
5,586 ÷ 87: Quotient 64, Remainder 18 (check: 87 × 64 + 18 = 5,586)
1,207 ÷ 27: Quotient 44, Remainder 19 (check: 27 × 44 + 19 = 1,207)
8,543 ÷ 41: Quotient 208, Remainder 15 (check: 41 × 208 + 15 = 8,543)
2,304 ÷ 43: Quotient 53, Remainder 25 (check: 43 × 53 + 25 = 2,304)
56,741 ÷ 26: Quotient 2,182, Remainder 9 (check: 26 × 2,182 + 9 = 56,741)

2How many hours will it take to travel 336 km at a speed of 48 km per hour?

748 ) 336 − 336 0

Time = distance ÷ distance covered in one hour = 336 ÷ 48. It will take 7 hours.

3Girija needed 35 cartons to pack 1400 books. There are an equal number of books in every carton. How many books did she pack into each carton?

4035 ) 1400 − 140 0 − 0 0

Books in each carton = 1400 ÷ 35 = 40 books.

4The contribution for a picnic was 65 rupees each. Altogether, 2925 rupees were collected. How many had paid for the picnic?

4565 ) 2925 − 260 325 − 325 0

Number of people = total collected ÷ contribution of one person = 2925 ÷ 65 = 45. So 45 people paid for the picnic.

5Which number, on being multiplied by 56, gives a product of 9688?

17356 ) 9688 − 56 408 − 392 168 − 168 0

Number × 56 = 9688, so the number = 9688 ÷ 56 = 173. Check: 173 × 56 = 9688.

6If 48 sheets are required for making one notebook, how many notebooks at the most will 5880 sheets make and how many sheets will be left over?

12248 ) 5880 − 48 108 − 96 120 − 96 24

5880 ÷ 48 gives quotient 122 and remainder 24. So at the most 122 notebooks can be made and 24 sheets will be left over.

7What will the quotient be when the smallest five-digit number is divided by the smallest four-digit number?

The smallest five-digit number is 10,000 and the smallest four-digit number is 1,000.

10,000 ÷ 1,000 = 10, because 1,000 × 10 = 10,000. The quotient is 10 and the remainder is 0.

Problem Set 16

1From a total of 10,000 rupees, Anna donated 7,000 rupees to a school. The remaining amount was to be divided equally among six students as the ‘all-round student’ prize. What was the amount of each prize?

Amount remaining: 10,000 − 7,000 = 3,000 rupees

Each prize: 3,000 ÷ 6 = 500 rupees

Each prize was ₹ 500.

2An amount of 260 rupees each was collected from 50 students for a picnic. If 11,450 rupees were spent for the picnic, what is the amount left over?

Amount collected: 260 × 50 = 13,000 rupees

Amount left over: 13,000 − 11,450 = 1,550 rupees

The amount left over is ₹ 1,550.

3A shopkeeper bought a sack of 50 kg of sugar for 1750 rupees. As the price of sugar fell, he had to sell it at the rate of 32 rupees per kilo. How much less money did he get than he had spent?

Selling amount: 50 × 32 = 1,600 rupees

Difference: 1,750 − 1,600 = 150 rupees

He got ₹ 150 less than he had spent.

4A shopkeeper bought 7 pressure cookers at the rate of 1870 rupees per cooker. He sold them all for a total of 14,230 rupees. Did he get less or more money than he had spent?

1,870× 7 13,090

Amount spent: 1,870 × 7 = 13,090 rupees

Amount received: 14,230 rupees

Compare: 14,230 > 13,090, and 14,230 − 13,090 = 1,140 rupees

He got more money than he had spent, by ₹ 1,140.

5Fourteen families in a Society together bought 8 sacks of wheat, each weighing 98 kilos. If they shared all the wheat equally, what was the share of each family?

Total wheat: 8 × 98 = 784 kg

Share of each family: 784 ÷ 14 = 56 kg

5614 ) 784 − 70 84 − 84 0

Each family’s share was 56 kg of wheat.

6The capacity of an overhead water tank is 3000 litres. There are 16 families living in this building. If each family uses 225 litres every day, will the tank filled to capacity be enough for all the families? If not, what will the daily shortfall be?

Water needed every day: 225 × 16 = 3,600 litres

Compare: 3,600 > 3,000, so the tank is not enough

Shortfall: 3,600 − 3,000 = 600 litres

No, a full tank is not enough. The daily shortfall is 600 litres.

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