**Fundamental operations on integers :**

In Math, The whole numbers and negative numbers together are called integers. The set of all integers is denoted by Z.

Z = {... - 2, - 1,0,1,2, ...}, is the set of all integers

Here, we are going to see, how the four fundamental operations in math (Addition, Subtraction, Multiplication and Division) work on integers.

Sum of two integers is again an integer.

For example,

i) 10 + (- 4) = 10 - 4 = 6

ii) 8 + 4 = 12

iii) 6 + 0 = 6

iv) 6 + 5 = 11

v) 4 + 0 = 4

To subtract an integer from another integer, add the additive inverse of the second number to the first number.

For example,

i) 5 – 3 = 5 + (addditive inverse of 3) = 5 + (– 3) = 2.

ii) 6 – (– 2) = 6 + (addditive inverse of (– 2)) = 6 + 2 = 8.

iii) (– 8) – (5) = (– 8) + (– 5) = – 13.

iv) (– 20) – (– 6) = – 20 + 6 = – 14.

In the previous class, we have learnt that multiplication is repeated addition in the set of whole numbers. Let us learn about it now in the set of integers.

**Rules :**

1. The product of two positive integers is a positive integer.

2. The product of two negative integers is a positive integer.

3. The product of a positive integer and a negative integer is a negative integer.

For example,

i) 5 x 8 = 40

ii) (- 5) x (- 9) = 45

iii) (- 15) x 3 = -(15 x 3) = - 45

iv) 12 x (- 4) = -(12 x 4) = - 48

We know that division is the inverse operation of multiplication.

Positive integer / Positive integer = Positive number

Negative integer / Negative integer = Positive number

Negative integer / Positive integer = Negative number

Positive integer / Negative integer = Negative number

For example,

250 / 50 = 5

(-144) / (-12) = 12

(-120) / 20 = -6

100 / (-25) = -4

Division of any number (except 0) by zero is meaningless because division by zero is not defined.

After having gone through the stuff given above, we hope that the students would have understood "Fundamental operations on integers".

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