We add equal groups to find the product of two numbers, ie multiply. That is, addition and multiplication are related.

In division, we subtract equal groups repeatedly.Hence, division and subtraction are related.

So, it is clear that multiplication and division are inverse operations or opposite operations.

We can define division in terms of missing factors in multiplication ,although division and multiplication are inverse operations.

Look at the following sets of fishes.

There are 9 fishes in each set.

We can write the multiplication fact associated with this as:

9 X 2 = ? or 2 X 9 =?

The product of the factors 9 and 2 can be found by adding the two equal groups.

9 + 9 = 18.

Therefore,

9 X 2 = 18 or 2 X 9 = 18.

This clearly shows that multiplication is repeated addition of equal groups.

Now, let us write the Division fact for the same situation:

18 ÷ 2 = ? or 18 ÷ 9 = ?

Thus, it is evident that

1)Multiplication and division are inverse operations

2)One multiplication fact known, will help us solve one other multiplication problem and also two other division problems.

Now look at the picture model above. Let us use the same model to solve the division fact that we have just written.

Here, this means that there are 18 fishes and we have to separate them into two equal groups.

We see that there are 9 fishes in each group. Hence,

18 ÷ 2 = 9

Now, let us take up the next division fact. With the same picture model shown above, we see that there are two groups of 9 fishes each.

Therefore,

18 ÷ 9 = 2

## Division-dividend, Divisor, Quotient and Remainder

## Example: Tilda has 12 cookies with her. She wants to share them with her 4 friends. How many cookies will each of Tilda's friends get ?

Now let us solve this problem using picture model.

First we have to know what are we supposed to find. Here we have to find the number of cookies each person gets.

Let us start by counting 12 cookies and then take four boxes, one for each friend.

Now, start putting a cookie in each box till no cookie is left out.

We see that there are 3 cookies in each box. Hence, each of Tilda's friends will get 3 cookies.

Now let us write the division sentence:

12 ÷ 4 = 3

Now, that we know what is division, let us the terms related to division.

There are three other most important terms in division.

Dividend

Divisor

3. Quotient

Division is an operation performed with two numbers: dividend and divisor and the result of division is quotient.

Now that we see another term “Remainder” , let us find out what is it?

## Division-dividend, Divisor, Quotient and Remainder

## Division with remainders

How many 2s are there in a 9?

Let us use picture model first.

Let us take 9 counters and separate them into groups of 2.

We see that one counter is left out.

There are 4 groups of 2s in 9 and one more counter.

9 ÷ 2 = 4

The one that is left out or the things that cannot be grouped are called the remainders.

So, remember: DIVIDEND = (DIVISOR X QUOTIENT) + REMAINDER.

This is useful in checking if the division is right.