NCERT Solutions for Class 5 Maths Chapter 13 Ways To Multiply And Divide
NCERT Textbook Page 170
Maniratnam is the cashier of king Jayan. His job is to find out the salary of all the people who work for the king. This chart shows how much salary each person gets in a day.
Maniratnam wanted to calculate the salary of the cook for the month of January. He wrote:
Rupees 1800 + 150 + 60 + 5 = Rs2015
Maniratnam’s daughter Bela had learnt another method to multiply. She wrote like this and showed it to Bhanu, her brother.
Akka, how did you do this?
You can multiply 65 with 31 in two steps. You know that 31 is 30 + 1. So, in the
first step multiply 65 with 1 and in the second step multiply 65 with 30.
Now Bhanu tried to find the salary of a minister for the month of January. He
wanted to multiply 195 x 31
First step: Multiply 195 by 1
Second step: Multiply 195 by 30
NCERT Textbook Page 171
1.Use Bela’s method to multiply these numbers.
2.Do these in your notebook using Bela’s method.
(a) 47 x 19 (b) 188 x 91 (c) 63 x 57
(d) 225 x 22 (e) 360 x 12 (f) 163 x 42
NCERT Textbook Page 172
Shantaram—A Special Cook
1. 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.
Ans.Wages for a day = Rs 165
Number of days worked = 28
Shantaram got Rs 4620
2.If he is called for all days of the year, how much salary will he get?
3.Now find the salaries of the minister and horse rider for 1 year.
Ans. Minister’s salary for one day = Rs 195
Horse rider’s salary for one day = Rs76
Years and Years
(а) Sohan drinks 8 glasses of water everyday.
1.How many glasses will he drink in one month?
Ans.8 x 30 = 240
2.How many glasses will he drink in one year?
Ans.8 x 365 = 2920
3.If 25 people living in a colony drink 8 glasses of water in a day, how much water –
will they drink in a year?
Ans.8 x 125 = 1000
They will drink 1000 glassed of water in a day
Hence, in 365 days they will drink:
365 x 1000 = 365,000 glasses of water
4.Can you guess how many glasses of drinking water are used in a day in your colony?
Ans.Number of people in my colony = 500 Hence, 8 x 500 = 4000
NCERT Textbook Page 173
(b)If Soha’s heart beats 72 times in one minute, how many times does it beat in one hour?
•Now find out how many times it beats in one day.
•Count your own heart beats to find out how many times your heart beats in one week.
Ans.Number of heart beats in 1 minute = 72
Hence,number of heart beats in 1 hour or 60 minutes = 60 x 72 = 4320
Number of heart beats in 1 day or 24 hours = 4320 x 24 = 103680
My heart beats 70 times in a minute.
Hence, my heart beats in 1 hour = 70 x 60 = 4200
My heart beats in 1 day = 4200 x 24 = 100800
My heart beats in 1 week = 104800 x 7 = 705600
(c)A baby elephant drinks around 12 L of milk every day. How much milk will it drink in two years?
Ans.Number of days in 2 years = 365 x 2 = 730
Milk consumed in 1 day = 12 L
Hence, milk consumed in 730 days = 730 x 12 = 8760 L
Hence, the baby elephant consumes 8,760 L of milk in two years.
(d)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.
Ans. Milk consumed by baby whale in 1 day = 200 L
Milk consumed by baby whale in 30 days = 200 x 30 = 6000 L Milk consumed by baby whale in 8 months = 6000 x 8 = 48000 L My family consumes 5 L milk in a day
Hence, number of days for consuming 200 L milk = 200÷5=40 days
NCERT Textbook Page 173
Karunya bought three fields
1.Find the area of all the three fields.
Field (A)………………square metre
Field (B)………………square metre
Field (C)………………square metre
2.He bought field (A) at the rate of Rs95 for a square metre, field (B) at Rs110 for a square metre and field (C) at Rs 120 for a square metre. Find the cost of all three fields
Now, cost of all three fields
= 71820 + 47520 + 61560 = Rs 1,80,900
3.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.
Ans. Thulasi’s one day’s wages = Rs 55
Hence, 49 day’s wages = 49 x 55 = Rs 2695
Her husband’s one day’s wages = Rs 58
Hence, 42 day’s wages = 58 x 42 = Rs 2436
Their combined earnings 2695 + 2436 = Rs 5131
NCER.T Textbook Page 175
NCER.T Textbook Page 176
Satish is a 13 year old boy. His father had taken a loan for farming. But the crops failed. Now Satish’s mother has to pay ? 5000 every month for the loan. Satish started working-he looked after 17 goats of the village.
He earns Rupee 1 every day for one goat. .
How much will he earn in one month?
Does he earn enough to help pay the loan every month?
How much will he earn in one year?
Kamla Bai’s Story
To help farmers the State Government gave cows. Kamla Bai Gudhe also got a cow. The cost of the cow was Rs17500. She had to pay Rs 5500 and the government spent the rest of the money.
1.How much did the government spend on the cow?
Ans. Cost of the cow = Rs17500
Money paid by Kamla Bai = Rs5500 \-
Hence, money spent by the government = 17500 — 5500 =Rs 12000
2.If 9 people from her village got cows, how much did the government spend in all?
Ans.Government spends Rs12000 for one cow Hence, for 9 cows the government spends 12000 x 9 = Rs 108000.But Kamla Bai was not happy. She had to spend Rs 85 every day on the cow. She made some money by selling the milk. But still she wanted to sell the cow.
3.If Kamla Bai spends Rs85 a day, find out how much she will spend in one month.
Ans.Money spent in one day = Rs85 Hence, money spent in one month = 85 x 30 = Rs 2550
4.The cow gives 8 litres of milk every day. How much will it give in one month?
Ans.Milk in 1 day – 8 litre Milk in one month = 8 x 30 = 240 L
5.If the milk is sold at Rs 9 per litre, how much money will Kamla Bai make in one month?
Ans. Price of one litre milk = Rs 9
Hence, price of 240 L milk = 9 x 240 = Rs 2160
•So, the money spent on keeping the cow was ?
Ans. Rs 2550
•Money earned by selling the milk ?
Ans. Rs 2160
•Which is more money spent on the cow or money earned from it?
Ans. The money spent on cow is more than the money earned from it.
Difference = 2550 – 2160 = Rs390
6.Explain why she wanted to sell the cow.
Ans. She is running into losses. Hence, she wants to sell the cow.
NCERT Textbook Page 177
(a) Sukhi works on a farm. He is paid Rs 98 for one day. If he works for 52 days, how much will he earn?
(b) 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?
Ans. Amount of loan that is to be paid every month = Rs2750 Hence, loan to be paid in a year = 2750 x 12 = Rs 33000 Loan to be paid in 2 years = 33000×2 = Rs 66000
(c) Ratiram is a milk seller in the city. He sells 13 litres of milk everyday at Rs 23 per litre. How much does he earn?
NCERT Textbook Page 178
Fun with Multiplication
(A) Look for the pattern and take this forward
(0 x 9)+1 = 1
(1 x 9)+2 = 11
(12 x 9)+3 = 111
(123 x 9)+4 = 1111
(1234 x 9)+5 = 11111
(12345 x 9)+6 = 111111
Ans. Number of 1 increases at every step in this pattern
(B) Each letter a, b, c here stands for a number
Take a = 1, then find what the numbers b and c will be.
Ans.If a=1, then we have
Hence, b=2andc = 3
(C) Tricks with your age Write your age:
10 years Multiply it by 7:
7×10 = 70
Again multiply the answer by 13:
70×13 = 910
Multiply again that answer by 11:
910 x 11 = 10010
1.Now look at your last answer. Can you find your age in that answer?
Ans. Yes, my age ‘10’ occurs twice in the last answer.
2.Now try this trick with other people.
Ans.Let us take 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 ‘9’ occurs twice in the last answer.
(D)Going round and round!
142857 x 1 = 142857
142857 x 2 = 285714
142857 x 3 =428571
142857 x 4 = 571428
142857 x 5 = 714285
Do you find a pattern in all these answers? Discuss this with your friends.
Ans. Yes, we have some pattern each time take starting point 1 more than the previous, i.e. 1, 2, 4, 5, 7, etc.If we move clockwise we get the answer:
NCERT Textbook Page 179
Dolma took a loan from a friend to buy a moped for ? 9588. She has to pay it back in equal amounts every month for six months.
1.How much will she have to pay every month? She asked her children to calculate. Her daughter did it this way
NCERT Textbook Page 180
Try to solve these using as few steps as you can
(a) 4228 + 4
How Many Times?
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?
1.Two children have solved it. Check if they have made a mistake, correct it. Discuss
Ans. In the first solution, the mistake is in remainder. The remainder should be 1 instead of zero.
In the second solution; the error is in third and fourth steps of division. The quotients in those steps should be 5 and 4 as shown below:
If one extra child can be 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.
NCERT Textbook Page 181
How Much Petrol?
1.Isha has Rs1000 with her. She wants to buy petrol. One litre of petrol costs Rs47. How many litres can she buy
1.If Isha comes to your city, how much petrol can she buy with the same money? Ans. At present the cost of petrol is 168 per litre in my city.
NCERT Textbook Page 181
Children are happy today. They are celebrating Children’s Day. Each child will be given 4 coloured pencils from school. The school has got 969 pencils. To find out how many children can get pencils the teacher asks them to divide.
1.Complete Iru’s and Sreeni’s way of division.
NCERT Textbook Page 183
1.576 books are to be packed in boxes. If one box has 24 books, how many boxes’ are needed?
2.836 people are watching a movie in a hall. If the halt has 44 rows, how many people can sit in one row?
3.A gardener bought 458 apple trees. He wants to plant 15 trees in each row. How many rows can he plant?
How many trees would be left over?
4. Shyamli bought a battery. She read on it ‘Life: 2000 hours’. She uses it throughout the day and the night. How many days will the battery run?
More with Multiplication and Division
1.A tank is full of 300 L of water. How much water will be filled in 25 tanks? If 15 buckets can be filled with one tank of water, how many buckets in all can be filled with the water in 25 tanks?
Ans. Water in 1 tank = 300 L
So, water in 25 tanks = 300 x 25 = 7500 L
Now, Water in 1 tank = 15 buckets
So, water in 25 tanks = 25 x 15 = 375 buckets
2.There are 28 laddoos in 1 kg. How many laddoos 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?
Ans. Number of laddoos in 1 kg = 28
Hence, number of laddoos in 12 kg = 28 x 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 20 + 1 16) 336 -320 16 -16 X
3.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 plants?
Ans. Water needed for 4 plants = 4×2 = 8 cups
Water needed for 26 rooms = 26 x 8 = 208 cups
NCERT Textbook Page 184
Make the Best Story Problem
Each line gives a story. You have to choose the question which makes the best story problem. The first one is already marked.
1.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?
Ans. (6) is the best choice
Option (a) is not a good choice because price is not given in the story
Option (c) is not a good choice because total number of boxes is given in the story.
2.352 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?
Ans. (b) is the best choice
Option (a) is not a good choice because number of children for each tent is already given.
Option (c) is not a good choice because total number of children is already given.
3.A shopkeeper has 204 eggs. He puts them in egg trays. Each tray has 12 eggs.
(а) How many more eggs will he needed?
(б) How many fresh eggs does he sell?
(c) How many egg trays does he need?
Ans. (c) is the best choice.
Option (a) is not a good choice because total number of eggs is already given. Option (b) is not a good choice because there is no data on number of fresh or spoiled eggs. .
4.The cost of one book is Rs47. Sonu buys 23 books.
(а) How much moneybooks?
Ans. (b) is the best choice
NCER.T Textbook Page 186
1.Do these divisions. Check your results by multiplication.
Quotient = 48 and remainder = 6
48 x 9 + 6 = 432 + 6 = 438 Hence, verified
Quotient = 290 290 x 12 = 3480
(c) 450 + 7
Quotient = 64 and remainder = 2 64 x 7 + 2 = 448 + 2 = 450 verified
(d) 900 +10
Quotient = 90
90 x 10 = 900 verified
Quotient = 113 113 x 6 = 678 verified
(f) 2475 ÷11
Quotient = 225 225 x 11 = 2475
1.Solve the given sums and colour the answers in the grid given below. See what you find.
(a)21×16 = 336
(b)15x 7 = 105
(c)93x 2 = 186
(d)17x 5 = 85
(e)10×10 = 100
(f)26×26 = 676
(g)77×10 = 770
(h)50×10 = 500
(i)11×11 = 121
(j)59x 7 = 413
(k)31×19 = 58
(o)19×3 = 57
(p)248÷8 = 31
(r)729 ÷ 9 = 81
(s)825 ÷ 5 =165
(t)221 ÷13 = 17
(u)576 ÷12 = 48
(y)981÷3 = 327
(z)475÷19 = 25