Division can be considered as sharing or grouping a number into equal parts.

for example:  $6 \div 2 = 3$
Here total 6 objects are divided into 2 groups, then how many objects will be there in each group?

We have to divide these 6 objects in two equal groups, so we will have two groups of three objects each.

We can also write it as $6 \div 2 = 3$ or
$\frac {6}{2} = 3$

Generally the sign '$\div$' is used for denoting division. It is also known as a process in which we will be doing repeated subtraction.
$6 \div 2$. Subtract 2 repeatedly from 6 so that you either get a zero or a number less than 2 at the end.

$6 - 2$ = $4 - 2$ = $2 - 2$ = 0
Here 2 is subtracted three times from 6 to get zero. It means 3 two's go in a six.
The order of operation is very important in division .

$6 \div 2$ is not same as $2 \div 6$

There are four terms that describe the four numbers involved in division.

Dividend: the number being divided.

Divisor: the number which divides the dividend

Quotient: the number of times the divisor will go in the dividend. (the whole number obtained after division)

Remainder: The remaining amount left over which is less than the divisor or too small to be divided by the divisor to get a whole number. Sometimes after division an amount is left over ,it is called as remainder.

Division and multiplication are opposite of each other, We can cross check division by multiplication.

$12 \div 6 =2$
$2 \times 6 = 12$.

Numbers can not be divided by zero as it is impossible to make zero groups of given number.When any number is divided by 1 the answer is the number itself. If you divide a number in 1 group then everything is in that group . When a number divided itself the answer is 1. And if you divide zero with any number the answer will be zero itself.

## How to do Division

### Solved Examples

Question 1: Dividing a 2 digit number by a single digit number.
Divide $42 \div 6$
Solution:

Place  6 outside the divisor bracket on its left and dividend under the bracket.

Observe the first digit of the dividend (42 ) and check if it is divisible by the divisor 6 . Since 4 is less than 6, it is not divisible by 6. Now consider its next digit and the 2 digit number formed i.e. 42. Check how many times can 6 go in 42.

In other words we have to find a number that times 6 gives 42.
$6 \times$ ___ = 42
6 times 7  = 42.

When 42 is divided by 6 we get 7.

Place 7 above the division bracket, subtract 42 from dividend .

Question 2: Division with remainder.
Divide 413 by 5
Solution:

Check the first number from right of the dividend , is 4 divisible by 5 ?
As 4 is less than 5 , the divisor, it can not be divided .so take the next digit and consider the number 41.
How many times can 5 go in 41?
$5 \times 8 = 40$ and $5 \times 9 = 45$. So we take $5 \times 8$. Write 8 above the division bracket and place 40 below 41. Subtract 40 from 41.

Remainder 1 is left after subtracting 40 from 41. Now bring down the next number 3 in-front of 1 to make the number 13.
Divide 13 by 5.
$5 \times 2 = 10$ and $5 |times 3 = 15$
So 5 can go 2 times in 13 to give a whole number
Place 2 on left of 8 on the top of the division bracket and place 10 below 13.

3 is left after subtracting 10 from 13 .
The quotient is 82 and remainder is 3
$413 \div 5 = 82$ R 3.