Integers and Operations On Integers

Class 7 - Mathematics

1. When two positive integers are added, we get a positive integer.
e.g. 6 + 4 = 10

2. When two negative integers are added, we get a negative integer.
e.g.  -6 + (-3) = -9

3. When a positive and a negative integer are added, the sign of the sum is always the sign of the bigger number of the two, without considering their signs.
e.g.  45 + -25 = 20   and    -45 + 20 = -25

The additive inverse of any integer a is - a, and the additive inverse of (- a) is a.
e.g.  Additive inverse of (-15) = - (-15) = 15

Subtraction is the opposite of addition, and, therefore, we add the additive inverse of the integer that is being subtracted, to the other integer.
e.g.  23 - 43 = 23 + Additive inverse of 43 = 23 + (- 43) = - 20

5. Product of Integers
The product of a positive and a negative integer is a negative integer.
e.g. 2 × -3 = -6

The product of two negative integers is a positive integer.
e.g. -3 × -4 = 12

If the number of negative integers in a product is even, then the product is a positive integer.
e.g. -2 × -3 × -4 × -5 = +120

Similarly, if the number of negative integers in a product is odd, then the product is a negative integer
e.g. -1 × -1 × -1 = -1

6. Division of Integers
Division is the inverse operation of multiplication.

The division of a negative integer by a positive integer results in a negative integer
e.g. -12 ÷ 3 = -4

The division of a positive integer by a negative integer results in a negative integer
e.g. 12 ÷ -3 = -4

The division of a negative integer by a negative integer results in a positive integer.
e.g. -12 ÷ -3 = 4

7. Multiply Or Division By Zero Integer

For any integer p, p multiplied by zero or zero multiplied by p is equal to zero.
e.g. p × 0 = 0 × p = 0

For any integer p, p divided by zero is not defined, and zero divided by p is equal to zero, where p is not equal to zero.
e.g. p ÷ 0 = undefined
0 ÷ p = 0