Facts about Division

We have already learned division by repeated subtraction, equal sharing/distribution and by short division method. Now, we will read some facts about division to learn long division.

I: Dividing a Number by 0:

1. If the dividend is ‘zero’ then any number as a divisor will give the quotient as ‘zero’. 

For example: If ‘zero’ sweets are to be distributed among 8 children, naturally no one will get any sweets. 


II: Dividing a Number by 1:

2. If the divisor is ‘1’ then any dividend will have the quotient equal to itself. 

Dividing a Number by 1

How many match sticks in the group?

Obviously, there are 10 match sticks in the group.

We can write this as 10 ÷ 1 = 10.

When we divide a number by 1, the quotient is the number itself.

For example: 4 ÷ 1 =  4

                    15 ÷ 1 = 15

                    50 ÷ 1 = 50


For example: There are 15 sweets; each child is to get 1 sweet. How many children get the sweets?


III: Dividing a Number by Itself:

3. When we divide 0 by a number, the quotient is always 0.

Dividing a Number by Itself

How many match sticks in each group?

We can see that there is 1 match stick in every group.

We can write this as

10 ÷ 10 = 1

When we divide a number by itself, the quotient is always 1.

For example: 4 ÷  4 = 1

                    15 ÷ 15 = 1

                    50 ÷ 50 = 1


IV: Dividing 0 by a Number:

4. When we divide 0 by a number, the quotient is always 0.

For example: 0 ÷   4 = 0

                      0 ÷ 15 = 0

                      0 ÷ 50 = 0


5. The product of the divisor and the quotient added to the remainder is always equal to the dividend.

(Divisor × Quotient) + Remainder = Dividend.

(d × q) + r = D

Note: Always find the product first and then add the remainder. (This helps us to check whether the division is done correct or not.)

Example: Divide 23 by 7

Division Facts

Checking:

(d × q) + r = D

(7 × 3) + 2 = 23

21 + 2 = 23

23 = 23

So, the division is correct.


6. In a division sum the remainder is always smaller than the divisor.

Example:

In the last example clearly we can see that the remainder (2) is less than the divisor (7).


7. Every divisor fact has two multiplication facts to verify it.

Example:

In division, 12 ÷ 6 = 2, two multiplication facts are 2 × 6 = 12 and 6 × 2 = 12.


8. The quotient and the divisor are always the factors of the dividend, if there is no remainder.

Example:

D

18

3


÷

×

d

3

6


=

=

q

6

18


9. The dividend is always a multiple of the quotient and divisor, if there is no remainder.

Example:

D

30

5

6


÷

×

×

d

5

6

5


=

=

=

q

6

30

30

Let us have a quick review of what we have learnt about division. Division is splitting into equal parts or groups. It is the result of “fair sharing”.

If 5 friends want to share 15 chocolates. How many chocolates will each of them get? Let us divide the chocolates equally amongst them.

Division Fact

15 divided by 5 is 3. They get 3 each.


Division With Remainder

When the given number of things cannot be shared equally something is left over. This is called the remainder.

Example:

Division With Remainder

Divide 16 toffees among three children.

Solution:

As 1 is smaller than 3 so we take 16 as dividend

                        3 × 5 = 15

Write 15 under 16 and subtract

                       16 - 15 = 1

So, Quotient 5, Remainder = 1

Therefore, each child gets 5 toffees and 1 toffee is left over.


SUMMARY

In a division sum like 15 ÷ 3 = 5, 15 is called the dividend, 3 is called the divisor and 5 is called the quotient.

• The number which is left undivided in division is called the remainder.

• When 0 is divided by a number, the quotient is 0.

• When a number is divided by 1, the quotient is the number itself.

• Division by 0 has no meaning.


Worksheet on Facts about Division:

1. Fill in the missing numbers:

(i) 5 ÷ 1 = _____

(ii) 0 ÷ 8 = _____

(iii) 17 ÷ _____ =1

(iv) _____ ÷ 1 = 9

(v) _____ ÷ 19 = 0

(vi) 81 ÷ _____ =1

(vii) 14 ÷ _____ =14

(viii) 26 ÷ 26 = _____

(ix) _____ ÷ 99 = 1


Answer:

1. (i) 5

(ii) 0

(iii) 17

(iv) 9

(v)  0

(vi) 81

(vii) 1

(viii) 1

(ix) 99 

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