By studying this lesson, you will be able to, 

In this lesson, the operations of addition, subtraction, multiplication and division, which you have learnt earlier will be studied more methodically 

3.1 Adding whole numbers 

The first vendor has 12 balloons and the second vendor has 13 balloons. By counting the balloons, we can find out that the total number of balloons that the two vendors have is 25. 

12 + 13 = 25

This answer can also be obtained by separately adding the two digits in the ones (units) place together, and the two digits in the tens place together. 

Let us explain this addition using two methods. 

(1) Let us add numbers together using counting frames. 

Let us represent the numbers 12 and 13 on two counting frames. 

Let us place all the counters in the ones place of these two counting frames in the ones place of another counting frame. Let us also place all the counters in the tens place of both counting frames in the tens place of the new counting frame. This is illustrated below. 

(2) Let us add the two numbers 12 and 13 by considering the value represented by the digit in each place of the numbers. 

The value represented by the digit in the tens place of the answer is 20. 20 is 2 tens. That is, the digit in the tens place of the answer is 2. 

Similarly, the value represented by the digit in the ones place of the answer is 5. 5 is 5 ones. That is, the digit in the ones place of the answer is 5. 

Since the digit in the tens place is 2 and the digit in the ones place is 5, the answer is 25. That is, 12 + 13 = 25 

Next, let us find the sum of the following numbers. 

Let us explain this addition using the following steps. 

(3) There are 486 boys and 658 girls in a certain school. How many students are there in total in this school? 

(4) In January, 1846 coconuts were plucked from the coconut trees in a certain estate and in March, another 1384 coconuts were plucked. How many coconuts were plucked in total during the two months? 

(5) The number of shoes manufactured by a certain company during the months January, February and March were 1395, 1426 and 1737 respectively. How many shoes were manufactured in total during the three months? 

(6) Nimal who is a businessman received an income of Rs 810 on the first day, an income of Rs 985 on the second day and an income of Rs 1130 on the third day. What was his total income during the three days?

 (7) If 974 milk bottles were collected at a certain collection centre on Monday, and if 103 more milk bottles were collected on Tuesday than on Monday, then how many bottles of milk were collected in total on the two days? 

3.2 Subtracting a smaller whole number from a given whole number 

The first figure shows 25 lamps which are lit. The second figure shows the same 25 lamps after 12 lamps had burnt out. By counting them, we can find out that there are 13 lamps which are lit in the second figure. 

We can also find the number of lamps which are lit in the second figure by subtracting 12 from 25. 

As in the case of addition, in subtraction too, we subtract the digits in the ones place and the digits in the tens place separately. 

Now, let us subtract 1896 from 6753. 

Let us write the numbers in the following manner so that the digits in each place are in the relevant columns. 

Let us explain this subtraction using the following steps. 

(3) If Nimal, who took 475 coconuts, was able to sell 297 of them, how many coconuts were remaining? 

(4) If there were 192 males in a gathering of 300 people, how many females were there? 

(5) In a certain factory, 1450 cars were manufactured in 2013 and 2325 cars were manufactured in 2014. How many more cars were manufactured in 2014 than in 2013? 

(6) Heshan received Rs 325 from his father and Rs 430 from his mother. If he bought a pair of slippers for Rs 149, and a book for Rs 225 from this money, how much money was left over? 

3.3 Multiplying whole numbers 

The figure depicts three groups of 5 guavas each. 

There are 15 guavas in total in these three groups. 

5 + 5 + 5 = 15 

“Three fives” is denoted as a multiplication in the form 5 × 3, That is 5 × 3 = 15 

Similarly, 

2 + 2 + 2 + 2 + 2 = 2 × 5 = 10 and 

10 + 10 + 10 + 10 = 10 × 4 = 40 

Let us explain the fact that 5 × 3 = 3 × 5 in the following manner. Three groups of five is 15. 

Let us separate 15 into groups of three each as below. 

A multiplication table of the whole numbers from 0 up to 9 is given below. 

The multiplication of two whole numbers, which are less than 10 can be performed using the above table. 

The product of 34 X 2 cannot be obtained directly from the above table. Let us find the product in cases. 

2 thirty fours is 34 + 34. That is, 68. 

This answer can also be obtained in the following manner. 

By multiplying the value represented by the digit in the ones place and the value represented by the digit in the tens place separately by 2, the value 68 is obtained. 

3.4 Multiplying a whole number by 10, by 100 and by 1000 

Let us consider the following products. 

2 × 10 is 10 twos. That is, 2 tens. Its value is 20. 

2 × 100 is 100 twos. That is, 2 hundreds. Its value is 200. 

2 × 1 000 is 1000 twos. That is 2 thousands. Its value is 2000. 

12 × 10 is 10 twelves. That is 12 tens. That is, 10 tens and 2 tens. 

Therefore, its value is 100 + 20 = 120. 

Accordingly, let us consider the following products. 

By examining the above products, the following facts are discovered. 

● The number obtained, when a number is multiplied by 10 can be obtained by placing 1 zero at the right end of the initial number. 

● The number obtained, when a number is multiplied by 100 can be obtained by placing 2 zeros at the right end of the initial number. 

● The number obtained, when a number is multiplied by 1000 can be obtained by placing 3 zeros at the right end of the initial number. 

3.5 Multiplication of whole numbers described further 

Let us consider 25 × 14. 

25 × 14 is 14 twenty fives. This 14 twenty fives can be considered as 10 twenty fives and 4 twenty fives. 

10 twenty fives is 250. 4 twenty fives is 100. Therefore, 14 twenty fives is 250 + 100, which is equal to 350. 

That is, 25 × 14 = 10 twenty fives + 4 twenty fives = 250 + 100 = 350 

What has occurred here is, that 25 has been multiplied by the value represented by each digit in 14 and the resulting values have been added together to obtain the answer. 

Accordingly, when multiplying 25 by 14, it can be written in the following way too. 

(4) In a certain hall, there are 35 rows containing 57 chairs each. How many chairs are there in total in the hall? 

(5) The price of a bag of rice is Rs 1225. What is the price of 75 such bags of rice? 

(6) The number of students who can travel in a school bus is 55. How many students can travel in 6 such buses? 

(7) A school student needs 8 exercise books. The price of an exercise book is Rs 48. The number of students in a certain class is 35. How much money in total is required to buy the exercise books needed for all 35 students? 

3.6 Dividing a whole number by another whole number 

The figures show the number of olives, two friends named Rasika and Sameera received, when 10 olives were divided equally between the two. 

Rasika and Sameera each received 5 olives. 

We describe how the olives were divided between the two of them as “10 divided by 2”. 

This is written as 10 ÷ 2. 

Accordingly, 10 ÷ 2 = 5. 

This can be clarified in the following manner too. 

There are 2 groups of five in 10. That is, 10 = 5 × 2. Therefore, a group has 5, when 10 is divided into two equal groups. 

That is, 10 ÷ 2 = 5. 

That is, 7 ÷ 2 is 3 with 1 remaining. How we obtain 7 ÷ 2, using the long division method is shown below. 

3.7 Dividing a whole number by 10, by 100 and by 1000 

Let us consider the following divisions. 

20 ÷ 10 means, “how many tens are there in 20?”. 

200 ÷ 100 means, “how many hundreds are there in 200?”. 

2000 ÷ 1000 means “how many thousands are there in 2000?”. 

Let us consider the following divisions accordingly. Let us find the value of 20 ÷ 10. 

Since, 2 ×10 = 20, we obtain 20 ÷ 10 = 2. Similarly, we have 

By observing the above divisions, the following facts are discovered. 

● When a number, which has a zero at the right end is divided by 10, the answer is obtained by removing that 0. 

● When a number, with 2 zeros at the right end is divided by 100, the answer is obtained by removing these 2 zeros. 

● When a number, with 3 zeros at the right end is divided by 1000, the answer is obtained by removing these 3 zeros. 

3.8 The division of whole numbers described further 

Let us find the value of 75 ÷ 5 using the long division method. 

Next, Let us find the value of 20 ÷ 5. 

Now, let us divide a number by a number with two digits. Let us consider the division of 38 by 12. 

Accordingly, when 38 is divided by 12, we obtain 3 with 2 remaining. 

(3) The van fare was Rs 10 800 for a journey made by 16 people. If this cost was met equally by fifteen of them, how much did each pay? 

(4) If 6480 chairs are to be distributed equally among 20 schools, how many chairs will each school get? 

(5) If the cakes of soap in 12 boxes, each containing 25 cakes of soap, are divided equally among 15 employees, how many cakes of soap will each employee get? 

Miscellaneous Exercise 

(1) The number of people who visited an art exhibition on the first three days of the exhibition was respectively 1320, 1567 and 1624. How many people in total visited the art exhibition on these three days? 

(2) A factory produced 3788 yoghurts during the first week and 4124 yoghurts during the second week. How many more yoghurts were produced in the second week than in the first week? 

(3) There are 10 identical book racks in a library. Each book rack contains 5 shelves. 30 books are placed on each of these shelves. How many books are there in total in the library in these 10 book racks? 

(4) A man needs to plant 152 coconut plants. However, he is able to plant only 8 per day. How many days will he require to plant all 152 of them? 

(5) It is required to bring 740 cement bags to a cement sales centre. The maximum number of cement bags that can be transported in a vehicle is 24. Find the number of trips the vehicle needs to make to bring all the cement bags to the centre.