Ways to Multiply and Divide
Page No: 170
Manirathinam – The Cashier
1. 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.
|Person||Salary in a day|
|Horse rider||Rs 76|
Maniratnam wanted to calculate the salary of the cook for the month of January. He wrote —
Rupees 1800 + 150 + 60 + 5 = Rs ________
Rupees 1800 + 150 + 60 + 5 = Rs (1950 + 65) = Rs 2015
2. Maniratnams daughter Bela has learnt another method to multiply. She wrote like this and showed it to Bhanu, her brother.
3. Now Bhanu tried to find the salary of a minister for the month of January. He wanted to multiply 195 × 31.
1. Use Bela’s method to multiply these numbers.
a) 32 × 46 b) 67 × 18
a) 32 × 46 = 1472 b) 67 × 18 = 1206
2) 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
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 Rs 165. Find out how much money he will get in all.
Salary paid to Shantaram for 1 day = Rs 165
So, the salary paid to Shantaram for 28 days = Rs 165 × 28
Hence, the money Shantaram gets in all is Rs 4620.
2. If he is called for all days of the year, how much salary will he get?
Thus, the cook will get a salary of Rs 60,225
3. Now find the salaries of the minister and horse rider for 1 year.
The salary paid to the minister for 1 day = Rs 195
So, the salary paid to the minister for 365 days = Rs 195 × 365
Hence, the salary of the minister for 1 year is Rs 71,175
The salary paid to the horse rider for 1 day = Rs 95
So, the salary paid to the horse rider for 365 days = 365 × Rs 95
Hence, the salary of the minister for 1 year is Rs 34,675
Years and Years
(a) Sohan drinks 8 glasses of water every day.
• How many glasses will he drink in one month? __________
• How many glasses will he drink in one year?
• If 125 people living in a colony drink 8 glasses of water in a day, how much water will they drink in a year?
The number of glasses of water Sohan drinks everyday = 8
We know that, 1 months – 30 days
So, the number of glasses of water consumed by Sohan = 8 x 30
Hence, Sohan will drink 240 glasses of water in one month.
Now, we know 1 year = 365 days
So, the number of glasses of water consumed by Sohan in 365 days = 365 x 8
Hence, Sohan will drink 2,920 glasses of water in one year.
We have, the number of glasses of water consumed by 1 person for a year = 2,920
So, the number glasses of water consumed by 125 people of the colony for one year = 2920 x 125
Therefore, 125 people of the colony will drink 3, 65,000 glasses of water in one year.
(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.
The number of times Soha’s heart beats in one minute = 72
We know, 1 hour = 60 minutes
So, the number of times Soha’s heart beats in one hour = 72 x 60
Hence, Soha’s heart beats 4,320 times in one hour.
Now, we know one day has 24 hours.
So, the number of times Soha’s heart beats in a day = 4320 x 24
Hence, the number of times Soha’s heart beat in a day is 1, 03,680.
My heart beats 72 times in a minute. We know, 1 week has 7 days.
So, the number of times my heart beats in one week = 1, 03,680 x 7
Hence, the number times my heart beats in a week is 7, 25,760.
(c) A baby elephant drinks around 12 L of milk every day. How much milk will it drink in two years?
The number of litres of milk the baby elephant drinks in a day = 12 L
We know, number of days in a year = 365
And the number of days in two years = 365 x 2 = 730
So, the number of litres of milk the baby elephant drinks in two years = 12 x 730
Hence, the number of litres of milk the baby elephant will consume in two years is 8,760.
(d) A baby blue whale drinks around 200 L of milk in one day. Just imagine how much milk that is! Find out in how many days your family would use 200 L milk. How much milk would the baby blue whale drink in eight months?
Number of litres of milk a baby blue whale drinks in one day = 200
Number of litres of milk used in my family in one day = 2
So, the number of days for consuming 200 L of milk by my family = 200/2 = 100 days
We know 1 month = 30 days then, 8 months = 30 x 8 = 240 days
So, the number of litres of milk the baby blue whale will drink in eight months = 200 x 240
Hence, the baby blue whale will consume 48,000 L of milk in eight months.
Karunya – The landlord
Karunya bought three fields.
1. Find the area of all the three
Field (A) ____________ square metre.
Field (B) ____________ square metre.
Field (C) ____________ square metre.
Dimensions of field (A): Length = 27 m and breadth = 28 m
Area (A) = 27 x 28
Field (A) 756 square metre.
Dimensions of field (B): Length = 36 m and breadth = 12 m
Area (B) = 36 x 12
Field (B) 432 square metre.
Dimensions of field (C): Length = 27 m and breadth = 19 m
Area (C) = 27 x 19
Field (C) 513 square metre.
2. He bought field (A) at the rate of Rs 95 for a square metre, field
(B) at Rs 110 for a square metre and field (C) at Rs 120 for a square metre.
Find the cost of all three fields.
Cost of 1 square metre of field A = Rs 95
So, the cost of 756 square metre of field A = Rs (756 x 95)
Thus, the cost of field A is Rs 71,820
Cost of 1 square metre of field B = Rs 110
So, the cost of 432 square metre of field B = Rs (432 x 110)
Thus, the cost of field B is Rs 47,520
Cost of 1 square metre of field C = Rs 120
So, the cost of 513 square metre of field C = Rs (756 x 95)
Thus, the cost of field C is Rs 61,560
The total cost of all the fields = Rs 71,820 + Rs 47,520 + Rs 61,560 = Rs 1, 80,900
Thulasi and her husband work on Karunya’s farm. The Government has said that farm workers should be paid at least Rs 71 for one day’s work. But he pays Rs 55 to Thulasi and Rs 58 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 ___________
Thulasi is paid Rs 55 for one day’s work.
So, if she works for 49 days, she will get = Rs 55 x 49
Thus, Thulasi will get Rs 2,695 for working 49 days in the farm.
Thulasi’s husband is paid Rs 58 for a day’s work.
So, if he works for 42 days, he will get = Rs 58 x 42
Thus, Thulasi’s husband will get Rs 2,436 for working 42 days in the farm.
Total money earned by both of them = Rs 2,695 + Rs 2,436 = Rs 5,131
The table shows the amounts fixed by four states.
a) For farm work which state has fixed the highest amount? Which state has fixed the lowest?
b) Bhairon Singh is a worker in Rajasthan. If he works for 8 weeks on the farm, how much will he earn?
c) Neelam is a worker in Haryana. If she works for 2½ months on the farm, how much will she earn?
d) How much more will a farm worker in Madhya Pradesh get than a worker in Orissa after working for 9 weeks?
(a) For farm work, Haryana has fixed the highest amount of Rs 135 for one day. The lowest is for Rajasthan paying Rs 73 for one day.
(b) Bhairon Singh works in Rajasthan, so he will be paid Rs 73 for one day.
We know, 1 week = 7 days
Then, 8 weeks = 7 x 8 = 56 days
So, Bhairon Singh’s earnings for working in the farm for 56 days = Rs 73 x 56
Thus, Bhairon Singh will earn Rs 4,088 in 8 weeks.
(c) Neelam working in Haryana will be paid Rs 135 for one day.
We know, 1 month = 30 days and ½ month = 30/2 = 15 days
Then, 2 ½ months = (2 x 30) + 15 = 75 days
So, the earnings of Neelam for working in the farm for 2 ½ months = Rs 135 x 75
Hence, Neelam will earn Rs 10,125 in 2 ½ months.
(d) The salary of a farm workers for one day in Madhya Pradesh = Rs 97
We know, one week = 7 days
Then, 9 weeks = 9 x 7 = 63 days
So, the earning of a farm worker working for 63 days = Rs 97 x 63
Hence, a farm worker will get Rs 6,111 in 9 weeks working in Madhya Pradesh.
The salary of a farm workers for one day in Orissa = Rs 75
We know, one week = 7 days
Then, 9 weeks = 9 x 7 = 63 days
So, the earning of a farm worker working for 63 days = Rs 75 x 63
Hence, a farm worker will get Rs 4,725 in 9 weeks working in Madhya Pradesh.
Difference between the earning of the farm workers = Rs 6,111 – Rs 4,725 = Rs 1,386
Therefore, a farm worker in Madhya Pradesh will get Rs 1,386 more than a farm worker in Orissa after working for 9 weeks.
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 Rs 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?
Satish earns Rs 1 for one goat every day. He looked after 17 goats of his village.
So, Satish will earn = Rs 1 x 17 = Rs 17 for a day
For a month Satish will earn = Rs 17 x 30
Thus, Satish will earn Rs 510 in one month.
Satish’s mother has to pay Rs 5,000 every month for the loan. But, the earnings of Satish will not help pay the loan every month.
We know, 1 year = 12 months
Satish’s earning in one year = Rs 510 x 12
Therefore, Satish will earn Rs 6,120 in one year for looking after 17 goats.
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 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?
• If 9 people from her village got cows, how much did the government spend in all?
But Kamla Bai was not happy, She had to spend Rs 85 everyday on the cow. She made some money by selling the milk. But still she wanted to sell the cow.
• If Kamla Bai spends Rs 85 a day, find out how much she will spend in one month.
• The cow gives 8 litre of milk every day. How much will it give in one month?
• If the milk is sold at Rs 9 per litre, how much money will Kamla Bai make in one month? ___________
So the money spent on keeping the cow was Rs ___________
Money earned by selling the milk Rs ___________
Which is more — money spent on the cow or money earned form it? How much?
• Explain why she wanted to sell the cow.
• Kamla Bai paid Rs 5,500 for getting the cow.
The cost of the cow is Rs 17,500.
So, the amount government spent on the cow = Rs (17,500 – 5,500)
Hence, the government spent Rs 12,000 on one cow.
• Now, we know the money spent by the government for one cow is Rs 12,000
So, for 9 cows the money spent by the government would be = Rs 12,000 x 9
Hence, the government spent Rs 1, 08,000 on nine cows for nine people.
• Kamla Bai spends Rs 85 a day.
I month = 30 days
So, the money spent by Kamla Bai in one month = Rs 85 x 30
Hence, Kamla Bai will spend Rs 2,550 on the cow in one month.
• The cow gives 8 litres a day.
1 month = 30 days
So, the amount of milk the cow will give in one month = 8 L x 30
Hence, the cow will give 240 litres of milk in one month.
• The milk is sold at Rs 9 per litre.
Then, the selling price for 240 litres of milk = Rs 9 x 240
Hence, Kamla Bai will earn Rs 2,160 by selling 240 litres of milk in one month.
So, the money spent for keeping the cow was Rs 2,550
Money earned by selling the milk Rs 2,160
The money spent on the cow is more as compared to the money earned by the cow.
= Money spent for the cow – Money earned by selling milk
= Rs 2,550 – Rs 2,160
= Rs 390
Hence, the money spent on keeping the cow is Rs 390 more than the money earned by selling the milk.
• She wanted to sell the cow because she had to spend more money on the cow compared to her earnings by selling the milk of the cow.
(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?
(c) Ratiram is milk seller in the city. He sells 13 litres of milk everyday at Rs 23 per litre. How much does he earn?
(d) A farmer sells 1 litre of milk for Rs 11. In one month he sells 210 litres of milk. How much does he earn in a month?
(e) A company sells 1 litre of packed water for Rs 12. A shopkeeper buys 240 litres of packed water. How much does he pay?
(a) Sukhi is paid Rs 98 for working one day on a farm.
So, his earning if we works 52 days will be = Rs 98 x 52
Hence, Sukhi will earn Rs 5,096 by working in the farm for 52 days.
(b) Hariya pays back Rs 2,750 every month.
She has to pay the amount for a period of 2 years.
2 years = 2 x 12 months = 24 months
So, the money to be paid by Hariya in 24 months = Rs 2,750 x 24
Hence, Hariya will pay back Rs 66,000 in 2 years for the loan.
(c) The earnings of Ratiram by selling 1 litre of milk = Rs 23.
Then, the earnings of Ratiram by selling 13 litres of milk = Rs 23 x 13
Hence, Ratiram earns Rs 299 after selling 13 litre of milk every day.
(d) The farmer sells 1 litre of milk at Rs 11.
So, the earning of selling 210 litres of milk in one month = Rs 11 x 210
Hence, the farmer earns Rs 2,310 in a month by selling milk.
(e) Selling price of 1 litre of packed water = Rs 12
Then, the amount the shopkeeper has to pay for buying 240 litres of packed water = Rs 12 x 240
Hence, the shopkeeper has to pay Rs 2,880 for 240 litres of packed water.
Fun with multiplication
A) Look for the pattern and take this forward.
B) Each letter a, b, c stands for a number.
Take a = 1, then find what the numbers b and c will be.
Therefore, we have b = 2 and c = 3.
C) 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 find your age in that answer? How many times does your age show in the answer?
Now try this trick with other people.
Write your age: 10
Multiply it by 7: 10 x 7 = 70
Again multiply the answer by 13: 70 x 13 = 910
Multiply again that answer by 11: 910 x 11 = 10010
Yes, I can find my age in the final answer. My age appears two times in the answer.
D) Going round and round!
Do you find a pattern in all these answers? Discuss this with your friends.
No, we didn’t find any pattern in the answer.
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.
• Will both of them get the same answer? Discuss.
The answer calculated by her daughter = 500 + 500 + 90 + 8 = 1598
The answer calculated by her son = 1000 + 500 + 90 + 8 = 1598.
So, both the children get the same answer.
Therefore, Dolma has to pay a sum of Rs 1,598 every month for 6 months to her friend.
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
How Much Petrol?
Isha has Rs 1000 with her. She wants to buy petrol. One litre of petrol costs Rs 47. How many litres can she buy?
Money with Isha = Rs 1000
Cost of 1 litre = Rs 47
Litres of petrol she can buy = Rs 1000 ÷ Rs 47 =?
Isha can buy ________ litres of petrol.
Dividing Rs 1000 ÷ Rs 47 we have,
Remainder = 13
Hence, Isha can only buy 21 litres of petrol with Rs 1,000.
If Isha comes to your city, how much petrol can she buy with the same money?
The cost of petrol in my city = Rs 50
So, the number of litres of petrol Isha can buy with Rs 1000 = 1000 ÷ 50
Thus, Isha can buy 20 litres of petrol in my city.
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.
Complete Iru’s and Sreeni’s way of division. What is the answer you get?
In both the ways we got the same answer which is 242.
Hence, 242 students can get the colour pencils.
1. 576 books are to be packed in boxes. If one box has 24 books, how many boxes are needed?
Total number of books to be packed in boxes = 576
Number of books one box = 24
The number of boxes required to put 576 books = 576 ÷ 24
Hence, 24 boxes are required to pack 576 books.
2. 836 people are watching a movie in a hall. If the hall has 44 rows, how many people can sit in 1 row?
Total number of people watching movie in the hall = 836
Number of rows in the hall = 44
The number of people sitting in one row = 836 ÷ 44
Hence, 19 people are sitting in 1 row of hall.
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?
Total number of trees bought by gardener = 458
Number of trees planted in one row = 15
So, the number of rows he can plant = 458 ÷ 15
Thus, the gardener can plant 30 rows of apple trees and he’ll be left with 8 trees.
1. 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?
The life of the battery = 200 hours
She uses it all day and night, i.e. for 24 hours
So, the number of days the battery will run = 2000 ÷ 24
Thus, the battery will run for 83 days.
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?
Amount of water in 1 tank = 300 L
Then, the amount of water in 25 tanks = 25 x 300 L = 7500 L
The number of buckets that can be filled with one tank of water = 15
So, the number of buckets that can be filled with 25 tanks of water = 25 x 15
Hence, 375 buckets can be filled with 25 tanks of water.
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?
Number of laddoos in 1 kg = 28
Then, the number of laddoos in 12 kg = 28 x 12
Hence, there will be 336 laddoos in 12 kg,
Number of laddoos that can be packed in one box = 16
So, the number of boxes required to pack 336 laddoos = 336 ÷ 16
Hence, 21 boxes are needed to pack all the laddoos.
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 the plants?
Number of rooms in the school = 26
Number of plants in each room = 4
So, the total number of plants = 26 x 4 = 104
Number of cups needed for each plant = 2 cups
Then, the total number of cups required for 104 plants = 104 x 2 = 208
Hence, we need 208 cups of water for all the plants.
Make the Best Story Problem
Each line gives a story. You have to choose the question which makes the best story problem.
(1) A shopkeeper has 50 boxes. There are 48 fruits in one box.
Explain why (a) and (c) are not good choices.
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.
(3) A shopkeeper has 204 eggs. He puts them in egg trays. Each tray has 12 eggs.
(4) The cost of one book is Rs 47. Sonu buys 23 books.
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
(a) Quotient = 48, Remainder = 6 and Divisor = 9.
Divisor x Quotient + Remainder = 9 x 48 + 6 = 438 = Dividend
(b) Quotient = 290, Remainder = 0 and Divisor = 12.
Divisor x Quotient + Remainder = 12 x 290 + 0 = 3480 = Dividend
(c) Quotient = 64, Remainder = 2 and Divisor = 7.
Divisor x Quotient + Remainder = 7 x 64 + 2 = 450 = Dividend
(d) Quotient = 90, Remainder = 0 and Divisor = 10.
Divisor x Quotient + Remainder = 10 x 90 + 0 = 900 = Dividend
(e) Quotient = 113, Remainder = 0 and Divisor = 6.
Divisor x Quotient + Remainder = 6 x 113 + 0 = 678 = Dividend
(f) Quotient = 225, Remainder = 0 and Divisor = 11.
Divisor x Quotient + Remainder = 11 x 225 + 0 = 2475 = Dividend
2) Solve the given sums and colour the answers in the grid given below See what you find.
- 21 x 16
- 15 x 7
- 93 x 2
- 17 x 5
- 10 x 10
- 26 x 26
- 77 x 10
- 50 x 10
- 11 x 11
- 59 x 7
- 31 x 19
- 85 x 30
- 64 x 42
- 3200 ÷ 40
- 19 x 3
- 248 ÷ 8
- 432 ÷ 18
- 729 ÷ 9
- 825 ÷ 5
- 221 ÷ 13
- 576 ÷ 12
- 288 ÷ 4
- 869 ÷ 11
- 847 ÷ 7
- 981÷ 3
- 475 ÷ 19