13. Ways to Multiply and Divide

Maniratnam’s daughter Bela has learnt another method to multiply. She wrote like this and showed it to Bhanu, her brother.

Now Bhanu tried to find the salary of a minister for the month of January. He wanted to multiply 195 × 31.

To multiply by 30 I first write a zero here. Then I only have to multiply by 3.

Practice time

1) Use Bela s method to multiply these numbers. ’

a) 32 × 46

b) 67 × 18

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

* 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.

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

* Now find the salaries of the minister and horse rider for 1 year.

b) If Soha’s heart beats 72 times in one minute, how many times does it beat in one hour?

1. Now find out how many times it beats in one day.

2. Count your own heart beats to find out how many times your heart beats in one week.

Guess how many times it beats in one year.

c) A baby elephant drinks around 12 L of milk every day. How much milk will it drink 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 in how many days your family would use 200 L milk. How much milk would the baby blue whale drink in eight months?

Karunya — The Landlord

Karunya bought three fields.

* Find the area of all the three fields.

Field (A) _____ square metre.

Field (B) _____ square metre.

Field (C) _____ square metre.

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.

Hum, did he spend more than a lakh of rupees!

Oh! He does not give them the minimum wage?

And why does he pay less to Thulasi and more to her husband? Discuss.

I saw this in the newspaper.

Governments of different states have said that farmworkers should not be paid less than this salary for a day's work.

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?

Farmers in Vidarbha (Maharashtra)

Practice time

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 a 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?

Oh God! Water costs more than milk!! In the city people buy water for Rs 12 per litre!

Division

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 started this way.

Now you complete it.

Will both of them get the same answer? Discuss.

Practice time

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 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—correctit. Discuss.

Ans. We need 39 buses.

Ans. We need 40 buses.

Giving children the opportunity to find and discuss the errors in these examples will help their own understanding about the different steps for division. In A) a very common error has been given in which children either forget or do not understand the remainder. In B) there is a simple error of multiplication but there is also a more interesting question of whether the child has shown one extra bus for one remaining child.

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 1litre = Rs 47

Litres of petrol she can buy = Rs 1000 ÷ Rs 47 = ?

Isha can buy _____ litres of petrol.

Find out

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

Children's Day 

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?

Shivangi did it by a shortcut way.

I learnt it after a lot of practice. In this you have to remember many things.

Shivangi's Way

I know that I have to divide 969 with 4. But I first only look at 9. I put an arrow to remember to bring down 6.

How did you start with 9?

Iru

So now you only look at 16%4? What after that?

I remember to bring down 9 and divide by 4.

But then you are left with 1.

Yes! This is the remainder. 1 pencil is left.

Oh! I can't remember so many things. I will do it my way.

Brain Teaser

* 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

❈ 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?

1. There are 28 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?

2. 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?

Such exercises will help children understand the strategies to make questions related to the concepts of division and multiplication.

Practice Time

1) Do these divisions. Check your results by multiplication.

a) 438 ÷ 9 d) 900 ÷ 10

b) 3480 ÷ 12 e) 678 ÷ 6

c) 450 ÷ 7 f ) 2475 ÷ 11

2) Solve the given sums and colour the answers in the grid given below. See what you find.

21 × 16 15 × 7 93 × 2 17 × 5 10 × 10

26 × 26 77 × 10 50 × 10 11 × 11 59 × 7 31 × 19

85 × 30 64 × 42 3200 ÷ 40 19 × 3 248 ÷ 8

432 ÷ 18 729 ÷ 9 825 ÷ 5 221 ÷ 13 576 ÷ 12

288 ÷ 4 869 ÷ 11 847 ÷ 7 981 ÷ 3 475 ÷ 19