NCERT Solutions for Class 5 Maths (Math Magic) Chapter 13 Ways to Multiply and Divide

NCERT
SOLUTIONS
CLASS - 5th

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Class : 5th
Subject : Maths
Chapter : 13
Chapter Name : Ways To Multiply And Divide

Q1 Use Bela's method to multiply these numbers.
(a) 32 × 46 (b) 67 × 18

Answer.
(a) 32 × 46

×46

192

+1280

1472

(b) 67 × 18

× 18

536

+670

1206

Page : 171 , Block Name : Practice Time

Q2 Do these in your notebook using Bela's method.
(a) 47 × 19 (b) 188 × 91 (c) 63 × 57

(d) 225 × 22 (e) 360 × 12 (f) 163 × 42

Answer.
(a)

×19

423

+470

893

(b)

188

× 91

188

+16920

17108

(c)

63

× 57

441

+3150

3591

(d)

225

× 22

450

+4500

4950

(e)

360

× 12

720

+3600

4320

(f )

163

× 42

326

+6520

6846

Page : 171 , Block Name : Practice Time

Q1 Shantaram is a special cook who comes only on party days. Last year he was called for only 28
days. For each day he has to be paid ? 165. Find out how much money he will get in all.

Answer.
Wages for one day = = Rs 165.
The Number of days = 28

165

× 28

1320

+3300

4620

Shantaram will get Rs 4,620.

Page : 172 , Block Name : Shantaram A Special Cook

Q2 If he called for all days of the year, how much salary will he get?

Answer. No. of Days in year = 365
165

×365

825

9900

+49500

60225

He will get total Rs 60,225

Page : 172 , Block Name : Shantaram A Special Cook

Q3 Now nd the salaries of the minister and horse rider for 1 year.

Answer. Minister’s salary for one day = Rs 195.
Number of days in one year = 365
195

×365

975

11700

+58500

71175

Minister’s salary = 71,175

Horse rider’s salary for one day = Rs 76.
76

×365

380

+4560

+22800

27720

Horse rider’s salary = 27,720

Page : 172 , Block Name : Shantaram A Special Cook

Q1 Sohan drinks 8 glasses of water everyday.
(a) How many glasses will he drink in one month?
(b) How many glasses will he drink in one year?
(c) If 25 people living in a colony drink 8 glasses of water in a day, how much water – will they
drink in a year?
(d) Can you guess how many glasses of drinking water are used in a day in your colony?

Answer.
(a) 8 × 30 = 240

(b) 8 × 365 = 2920

(c) 8 × 125 = 1000 , they drink 1000 glasses of water in a day. Hence, in 365 days they

will drink 365 × 1000 = 365, 000 glass of water.

(d) Number of people in my colony = 450

Hence, 8 × 450 = 3600.

Page : 172 , Block Name : Years And Years

Q2 If Soha’s heart beats 72 times in one minute, how many times does it beat in one hour?Now
nd out how many times it beats in one day.Count your own heart beats to nd out how many
times your heart beats in one week.

Answer. Heartbeats in 1 minute = 72 times.
Now, heartbeats in 1 hour or 60 minutes = 60 x 72 = 4320.
Heartbeats in 1 day or 24 hours = 4320 x 24 = 103680.
4320

×24

17280

+86400

103680

My heart beats in 1 minute = 60 times.
Hence, my heart beat in 1 hour = 60 x 60 = 3600.
My heart beats in 1 day = 3600 x 24 = 86,400.
My heart beats in 1 week = 86,400 x 7 = 604,800.

Page : 172 , Block Name : Years And Years

Q3 A baby elephant drinks around 12 L of milk every day. How much milk will it drink in two
years?

Answer.

Milk drink in 1 day = 12L

The Number of days in 2 years = 365 × 2 = 730 .

Hence, milk drink in 730 days = 730 × 12

730

×12

1460

+7300

8760

Hence, the baby elephant consumes 8,760 L of milk in two years.

Page : 172 , Block Name : Years And Years

Q4 A baby blue whale drinks around 200 L of milk in one day. Just imagine how much milk that is!
Find out how many days your family would use 200 L milk. How much milk would the baby blue
whale drink in eight months?

Answer. Milk consumed by the baby blue whale in 1 day = 200 L.
Milk consumed by the baby blue whale in 1 month or 30 days = 200 × 30 = 6000L
Milk consumed in 8 months = 6000 × 8 = 48000L
My family consumed 4 L milk in 1 day.
Hence, the number of consuming 200 L milk = 200÷4=50 days.

Page : 172 , Block Name : Years And Years

Q1

Find the area of all the three elds.
Field(A)..........square meter.
Field(B)..........square meter.
Field(C)..........square meter.

Answer. Area of eld A :
Area of rectangle = Length × Breath
= 28 × 27

28

196

+560

756

= 756 square meters.

Area of eld B :
Area of rectangle = Length × Breath

= 36 × 12

36

72

+360

732

= 432 square meter

Area of eld C :
Area of rectangle = Length × Breath
= 27 × 19

27

27

×19

243

+270

513

= 513 square meter

Page : 173 , Block Name : Karunya — The Landlord

Q2 He bought eld (A) at the rate of Rs 95 for a square metre, eld (B) at Rs110 for a square metre
and eld (C) at Rs 120 for a square metre. Find the cost of all three elds.

Answer. Cost of eld A :
The rate of eld A = Rs 95
Hence, cost = Area × Rate
=756x95 = Rs 71820
Cost of eld B:
The rate of eld B= Rs 110
Hence, cost = Area × Rate
=432x110= Rs 47520
Cost of eld C:
The rate of eld C= Rs 120
Hence, cost = Area × Rate
=513x120= Rs 61560
Now, the total cost is = 71820 +47520+61560 = Rs 180900.

Page : 174 , Block Name : Karunya — The Landlord

Q3 Thulasi and her husband work on Karunya’s farm. The Government has said that farmworkers
should be paid at least Rs 71 for one day’s work. But he pays Rs 55 to Thulasi and Rs58 to her
husband.If Thulasi works for 49 days, how much money does she get? If her husband works for 42
days, how much money does he get? Find the money they earn together.

Answer. Thulasi's one days’ wages = Rs 55.
So, 49 day’s wages = 49 x35 = 2695

49

×55

245

+2450

2695

Her husband’s one day’s wages = Rs 58
Hence, 42 day’s wages = 58 x42 = 2436
58

×42

116

+2320

2436

So, the total earning is = 2695+2496 = Rs 5131

Page : 174 , Block Name : Karunya — The Landlord

Q4 “1 saw this in the newspaper. Governments of different states have said that farm workers
should not be paid less than this salary for a day's work.

The table shows the amounts xed by four states”.
For farm work which state has xed the highest amount? Which state has xed the lowest?

Answer. Haryana has xed the highest amount and Rajasthan has the lowest amount.

Page : 175 , Block Name : Karunya — The Landlord

Q5 Bhiron Singh isa worker in Rajan Cy. for 8 weeks on the farm, how much will he earn?

Answer. Wagws in Rajasthan for 1 day = Rs 73.
Wages for 1 week = 73 x 7 = Rs 511.
Wages for 8 week = 511 x 8 = Rs 4088.

Page : 175 , Block Name : Karunya — The Landlord

Q6 Neelam is worker in Haryana, If she works for 2 & half months on the farm, how much will she
earn ?

Answer. Wages in Haryana for 1 day = Rs 135
Number of days in 2 and 1 / 2 months

1
= 2 × 30 + × 30
2

= 60 + 15 = 75days

Wages for 75 days = 135 × 75

= Rs 10125

Page : 175 , Block Name : Karunya — The Landlord

Q7 How much more will a farm worker in Madhya Pradesh get than a worker in Orissa after
working for 9 weeks?

Answer. Wages in Madhya Pradesh in 1 day = Rs 97
Wages for a day in Orissa = Rs 75
Difference in daily wages = 97-75 = Rs 22
Number of the day in 9 weels = 9x7 = 63
The difference in wages for 9 weeks = 63x22 = Rs 1386

Page : 175 , Block Name : Karunya — The Landlord

Q1 Satta's story
Satish is a 13 years old boy. His father had taken a loan for farming. But the crops failed Now
Satish’s mother has to pay Rs 5000 every month for the loan.
Satish started working — be looked after 17 goats of the village. He earns Rupee 1 every day for
one goat

How much will be earn in one month?

Answer.
17 × 30 = Rs 510

Page : 176 , Block Name : Farmers In Vidarbha (Maharashtra)

Q2 Does he earn enough to help pay the loan every month?

Answer. No, he doesn't get enough money to pay the loan per month.

Page : 176 , Block Name : Farmers In Vidarbha (Maharashtra)

Q3 How much will he earn in one year?

Answer. Satish’s earn in 1 year = 510 × 12 = Rs 6120

Page : 176 , Block Name : Farmers In Vidarbha (Maharashtra)

Q1 Kamla Bat's story:
To help farmers the State Government gave cows. Kamla Bai Gudhe also got a cow. The cost of the
cow was Rs 17,500. She had to pay Rs 5,500 and the government spent the rest of the money. How
much did the government spend on the cow?

Answer. Cost of cow = Rs 17,500
Money paid by Kamla Bai = Rs 5500
Hence, money spent by the government = 17500 - 5500 = Rs 12000

Page : 176 , Block Name : Farmers In Vidarbha (Maharashtra)

Q2 If 9 people from her village got cows, how much did the government spend in all?

Answer. Government spent for 1 cow = 12000
For 9 cows = 12000 × 9 = Rs108000

Page : 176 , Block Name : Farmers In Vidarbha (Maharashtra)

Q3 If Kamla Bai spends Rs 85 a day, nd out how much she will spend in one month.

Answer. Money Spent i n1 day = Rs 85
Hence, money spent in 1 month = 85 × 30 = Rs 2550

Page : 176 , Block Name : Farmers In Vidarbha (Maharashtra)

Q4 The cow gives 8 liters of milk every day. How much will it give in one month?

Answer. Milk in 1 month = 8 × 30 = 240L

Page : 176 , Block Name : Farmers In Vidarbha (Maharashtra)

Q5 If the milk is sold at Rs 9 per liter, how much money will Kamla Bai make in one month?

Answer.
240 L milk = 9 × 240 = Rs 2160

Page : 177 , Block Name : Farmers In Vidarbha (Maharashtra)

Q6 So the money spent on keeping the cow was?

Answer. Rs. 2550.

Page : 177 , Block Name : Farmers In Vidarbha (Maharashtra)

Q7 Money earned by selling the milk?

Answer. Rs 2160.

Page : 177 , Block Name : Farmers In Vidarbha (Maharashtra)

Q8 Which is more money spent on the cow or money earned from it ? how much?

Answer. Money spent on a cow is more than the money earned from it.

Page : 177 , Block Name : Farmers In Vidarbha (Maharashtra)

Q9 Explain why she wanted to sell the cow?

Answer. She is running losses. So, she wants to sell the cow.

Page : 177 , Block Name : Farmers In Vidarbha (Maharashtra)

Q1 Sukhi works on a farm. He is paid Rs 98 for one day. If he works for 52 days, how much will he
earn?

Answer. Wages for 1 day = Rs 98
Hence, wages for 52 days = = 98 × 52 = Rs 5006

Page : 177 , Block Name : Practice Time

Q2 Hariya took a loan to build his house. He has to pay back Rs. 2,750 every month for two years.
How much will he pay back in 2 years?

Answer. Amount of loan per month = Rs 2750
Loan to be paid in 1 year = 2750 × 12 = Rs 33000
Loan to be paid in 2 years = 3300 × 2 = Rs 66000

Page : 177 , Block Name : Practice Time

Q3 Ratiram is a milk seller in the city. He sells 13 liters of milk every day at Rs 23 per liter. How
much does he earn?

Answer. Price of 1 L milk = Rs 23
Price of 13 L milk = 23 × 13 = 299

Page : 177 , Block Name : Practice Time

Q4 A farmer sells 1 L of milk for Rs 11. In one month he sells 210 Liters of milk. how much does

he earn in a month?

Answer. 210 × 11 = Rs 2310

Page : 177 , Block Name : Practice Time

Q5 A company sells 1 L of packed water for 12,A shopkeeper buys 240 liters pf packed water. How
much does he pay?

Answer.
12 × 240 = Rs 2880.

He will pay a total of 2880.

Page : 177 , Block Name : Practice Time

Q1 Look for the pattern and take this forward
(0 × 9) + 1 = 1

(1 × 9) + 2 = 11

(12 × 9) + 3 = 111

(123 × 9) + 4 = 1111

(1234 × 9) + 5 = 11111

(12345 × 9) + 6 = 111111

Answer. The number of 1’s increases at every step in this pattern

Page : 178 , Block Name : Fun with multiplication

Q2 Each letter a,b,c here stands for a number.

Take a = 1, then nd what the numbers b and c will be.

Answer. Put a = 1, then we have

Hence, b = 2, & c = 3.

Page : 178 , Block Name : Fun With Multiplication

Q3 Tricks with your age
Write your age:
Multiply it by 7:
Again, multiply the answer by 13:
Multiply again that answer by 11:
Now look at your last answer. Can you nd your age in that answer?

Answer. My age = 9 years
Multiply by 7:
9 x 7 = 63
Multiply by 13:
63 x 13 = 819
Multiply by 11:
819 x 11 = 9009
The age is 9.

Page : 178 , Block Name : Fun With Multiplication

Q4 Going round and round!
142857 x 1 = ?
142857 x 2 = ?
142857 x 3 = ?
142857 x 4 = ?
142857 x 5 = ?

Answer.
142857 × 1 = 142857

142857 × 2 = 285714

142857 × 3 = 428571

142857 × 4 = 571428

142857 × 5 = 714285

Page : 178 , Block Name : Fun With Multiplication

Q1 Dolma took a loan from a friend to buy a moped for Rs 9.588. She has to pay it back in equal
amounts every month for six months. How much will she have to pay every month? She asked her
children to calculate.Her daughter did it this way

Her son starts this way.
1000+

9588

−6000

⟶

Now you complete it.

Answer.

Daughter’s solution = 500+500+500+90+8 = 1598
Son’s Solution = 1000+500+90+8 = 1598
Since both of them got the same solution, so she will have to pay Rs 1598 every month for 6
months.

Page : 179 , Block Name : Division

Q1 Try to solve these using as few steps as you can
a) 4228 ÷ 4 b) 770 ÷ 22 c) 9872 ÷ 8

d) 672 ÷ 21 e) 772 ÷ 7 f) 639 ÷ 13

Answer. a) 4228 ÷ 4
1000+50+7

4228

−4000

228

−200

28

−28

X

Hence, 4228 ÷ 4 = 1000 + 50 + 7 = 1057

b)
770 ÷ 22

22)770(35

−66

110

−110

0

c) Missing

d)
672 ÷ 21

21) 672 (32

−63

42

−42

0

Hence, 672 ÷ 21 = 30 + 2 = 32

e)
772 ÷ 7
100+10

7)772

−700

72

−70

2

Hence, 772 ÷ 7 = 100 + 10 = 110

f)
639 ÷ 13

40+9

639

−520

119

−117

2

639 ÷ 13 = 40 + 9 = 49

Page : 180 , Block Name : Practice Time

Q2 976 children are going on a picnic. They will be taken in mini buses. If 25 children can go in
one bus, how many buses do they need?Two children have solved it. Check if they have made a
mistake, correct it. Discuss
a)
5+10+10+10+4

25)976

−125

851

−250

601

−250

351

−250

101

−100

X

b)
20+10+4+1

25)976

−500

476

−250

226

−125

101

−100

1

Answer.
a)
In the rst answer, the mistake is in the remainder. The remainder should be 1 instead of zero.

b) the error is in the third and fourth steps of division, the quotients in those steps should be 5
and 4 as shown below.
20+10+4+1

25)976

−500

476

−250

226

−125

101

−100

1

So, 1 child is left. The child can have accommodated in one of the buses then we need 39 buses.
Otherwise, we need 40 buses. Since taking 1 bus for 1 child is not possible so 39 buses will do.

Page : 180 , Block Name : Practice Time

Q1 Isha has Rs 1000 with her. She wants to buy petrol. One litre of petrol costs Rs 47. How many
litres can she buy?

Answer.
20+1

1000

−940

60

−47

13

Isha can buy 21L of petrol.

Page : 181 , Block Name : How Much Petrol ?

Q2 If lisha comes to your city, how much petrol can she buy with the same money?

10+4

1000

Answer.
−680

320

−272

48

She can buy 14 Liters of petrol.

Page : 181 , Block Name : How Much Petrol?

Q1 Complete Inu's and Sreeni's way of division?

Answer.
100+100+40+2

4)969

−400

569

−400

169

−160

169

−8

1

quotient = 242
Remainder = 1
Sreeni’s division

200+40+2

4)969

−800

169

−160

9

−8

1

quotient = 242
Remainder = 1

Page : 181 , Block Name : Children’s Day

44, 576 books are to be packed in boxes. If one box has 24 books, how many boxes
Q1
are needed?

Answer.
20+4

24)576

−480

96

−96

X

Hence, 24 boxes are needed.

Page : 183 , Block Name : Practice Time

Q2 836 people are watching a movie in a hall. If the hall has 44 rows. How many people can sit in
1 row ?

Answer. Total number of people = 836
Number of rows = 44
Hence, number of people in 1 row = 836 ÷ 44 = 19

Page : 183 , Block Name : Practice Time

A gurdener bought 458 apple trees. He wants to plant 15 trues in each row:
Q3
How many rows can he plant

Answer. The Total number of trees in a row = 15
Number of row = 458 ÷ 15
30
15)
458

−450

8

quotient = 30
Remainder = 8
So, 450 trees will be planted in 30 rows and 8 trees will be left.

Page : 183 , Block Name : Practice Time

Q1 Shyamli bought a battery. She read on it ‘Life 2000 hours’, She uses it throughout the day the
might. How many days will the battery run?

Answer. Total life of battery = 2000 hours
Number of the hour in a day and night = 24
Number of days the battery lasts = 2000 ÷ 24
80+3

24)2000

−1920

80

72

8

quotient = 83
Remainder = 8 <
Since, 8/24 = ⅓
So, the battery will last 83 days and ⅓ days

Page : 183 , Block Name : Brain Teaser

Q1 A tank is full of 300 L of water. How much water will be lled in 25 tanks? If 15 buckets can be
lled with one tank of water, how many buckets in all can be lled with the water in 25 tanks?

Answer. Water in 1 tank = 300 L
Water in 25 Tank = 300 × 25 = 7500 L
Now, water in 25 tanks = 25 × 15 = 375 buckets

Page : 183 , Block Name : More With Multiplication And Division

Q2 There are 28 laddoos in 1kg . How many ladoos will be there in 12 kg ? If 16 Laddoos can be
packed in 1 box, how many boxes are needed to pack all these laddoos?

Answer. Number of laddoos in 1 kg = 28
Hence, number of laddoos in 12 kg = 28 × 12 = 336 laddoos
Number of laddoos in 1 box = 16
Total number of laddoos = 336
Hence, number of boxes needed for 336 laddoos = 336 ÷ 16 = 21

Page : 183 , Block Name : More With Multiplication And Division

Q3 There are 26 rooms in a school. Each room has 4 plants. If each plant needs 2 cups of water,
how much water do we need for all the plants?

Answer.

4 plants need 4 × 2 = 8

Water needed for 26 rooms = 26 × 8 = 208 cup of water.

Page : 183 , Block Name : More With Multiplication And Division

Q1 A shopkeeper has 50 boxes. There are 48 fruits in one box.
Tick the one question which matches with the given problem.
(a) How much will the shopkeeper pay in all?
(b) How many fruits are there in all?
(c) How many more boxes will he need?

Answer. (b).

Page : 184 , Block Name : Make The Best Story Problem

Q2 children from a school went on a camping trip. Each tent had a group of 4 children.
(a) How many children did each tent have?
(b) How many tents do they need?
(c) How many children in all are in the school?

Answer. (b).

Page : 184 , Block Name : Make the Best Story Problem

Q3 A shopkeeper has 204 eggs. He puts them in egg trays. Each tray has 12 eggs.
(а) How many more eggs will he needed?
(b) How many fresh eggs does he sell?
(c) How many egg trays does he need?

Answer. (c).

Page : 184 , Block Name : Make The Best Story Problem

Q4 The cost of one book is Rs47. Sonu buys 23 books.
(а) How much money books?
(b) How much money does she pay for the books?
(c) What is the cost of 47 books?

Answer. (b).

Page : 185 , Block Name : Make The Best Story Problem

Q1 Do these divisions, Check your results by multiplication.
a) 438 ÷ 9 b) 3480 ÷ 12 c) 450 ÷ 7

d)900 ÷ 10 e) 678 ÷ 6 f) 2475 ÷ 11

Answer.
(a) 438 + 9

Quotient = 48 and remainder = 6

48 × 9 + 6 = 432 + 6 = 438 hence, verified

(b) 3480 ÷ 12
200 + 90

12)3480

−2400

1080

−1080

X

quotient = 290

12 × 290 = 3480 hence, veri ed.
(c) 450 ÷ 7
60+4

7)450

−420

30

−28

2

Quotient = 64 and remainder = 2

64 × 7 + 2 = 448 + 2 = 450 hence, verified.

(d) 900 ÷ 10
10)900(90

−900

X

Quotient = 90

90 × 10 = 100 hence, verified

(e) 678 ÷ 6
100+10+3

6)678

−600

78

−60

18

−18

X

Quotient = 113

113 × 6 = 678 hence verificd

(f) 2475 ÷ 11
200+20+5

11)2475

−2200

275

−220

55

−55

X

Quotient = 225

225 × 11 = 2475

Page : 186 , Block Name : Practice Time

Q2 Solve the given sums and colour the answers in the grid given below. See what you nd.
Multiply :
a) 21 × 16

b) 15 × 7

c) 93 × 2

d) 17 × 5

e) 10 × 10

f) 10 × 26

g) 77 × 10

h) 50 × 10

i) 11 × 11

j) 59 × 7

k) 3 × 9

l) 85 × 30

m) 64 × 42

n) 19 × 3

Divide :
a) 3200 ÷ 40

b) 248 ÷ 8

c) 432 ÷ 18

d) 729 ÷ 9

e) 825 + 5

f) 221 + 13

g) 576 ÷ 12

h) 288 ÷ 4

i) 869 ÷ 11

j) 847 ÷ 7

k) 981 + 3

l) 475 ÷ 19

Answer. Multiply :
a) 21 × 16 = 336

b) 15 × 7 = 105

c) 93 × 2 = 186

d) 17 × 5 = 85

e) 10 × 10 = 100

f) 26 × 26 = 676

g) 77 × 10 = 770

h) 50 × 10 = 500

i) 11 × 11 = 121

j) 59 × 7 = 413

k) 31 × 19 = 589

l) 85 × 30 = 2550

m) 64 × 42 = 2688

n) 19 × 3 = 57

Divide :

a) 3200 ÷ 40 = 80

b) 248 ÷ 8 = 31

c) 432 ÷ 18 = 24

d) 729 ÷ 9 = 81

e) 825 + 5 = 165

f) 221 ÷ 13 = 17

g) 576 ÷ 12 = 48

h) 288 ÷ 4 = 72

i) 869 ÷ 11 = 79

j) 847 + 7 = 121

k) 981 + 3 = 327

l) 475 + 19 = 25

Page : 186 , Block Name : Practice Time