Class 7 Maths- Division of integers and its properties

Division of integers and its properties

An integer is a number that can be written without a fractional (e.g. 2/5, 7/9) or decimal component (2.345, 6.89).

For example, 21, 4, and −2048 are integers; 9.75, 5½, and Ö2 are not integers.

If we were to distribute 80 sweets among 40 children, we would give 2 sweets to each child as 80/40 = 2.

This explains division of integers (here 80 and 40 are both integers).

Division of whole numbers is an inverse process of multiplication.

Dividend: The number to be divided is called dividend (80 in the above example)

Divisor: The number which divides is called the divisor (40 in the above example)

Quotient: The result of division is called the quotient (2 in the above example)

Division of integers has the following properties:

(i) If ‘a’ and ‘b’ are integers, then a ÷ b is not necessarily an integer.

For example, 14 ÷ 4 = 3.5 where 14 and 4 are integers but 3.5 is not an integer.

(ii) If ‘a’ is an integer different from 0, then a ÷ a = 1; 9/9 = 1 etc.

(iii) For every integer a, we have a ÷ 1 = a

(iv) If a is non-zero integer, then 0 ÷ a = 0