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propErtiEs of Division

1. division of a number by 1: When a number is divided by 1, the quotient is the number
itself.

examples: (a) 5 ÷ 1 = 5 (b) 10 ÷ 1 = 10 (c) 28 ÷ 1 = 28

2. division of a number by itself: When a number is divided by itself, the quotient is 1.

examples: (a) 12 ÷ 12 = 1 (b) 26 ÷ 26 = 1 (c) 64 ÷ 64 = 1

3. division of zero by any number: When 0 is divided by any number (except 0) gives

the quotient 0.
Note
example: 0 ÷ 14 = 0 Division of any number by 0
is not defined. That is, 15 ÷
0 = Not defined.
long Division

We have learnt to express a division fact like 15 ÷ 3 = 5 as 3 15 5
15
0

long Division

Without remainder With remainder

Quotient example: Quotient example:
Divisor Dividend 3 6 2 Divisor Dividend 4 9 2
6 8
0 Remainder 1

Here, we can see that 2 × 3 + 0 = 6

2 × 4 + 1 = 9

That means, Quotient × Divisor + Remainder = Dividend

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

checking Division

Division can be checked by using the following relation.
Quotient × Divisor + Remainder = Dividend

90 Mathematics-3