The collection of natural numbers, their negatives and zero are called integers. …, –4, –3, –2 and –1 are negative integers while 1, 2, 3, 4,… are positive integers.
Integers can be represented on a number line by taking equal distance between two consecutive integers. ‘Zero’ should be in between the positive and negative integers. Numbers on the left side of zero are negative Integers. Numbers on the right side of zero are positive Integers.
Ordering of integers:
Negative integers are written on the left hand side of 0 and positive integers are written on the right hand side of 0.
Integer occurring on the right hand side is greater than that on the left.
Every positive integer is greater than negative integer.
Zero is always less than every positive integer.
Zero is always greater than every negative integer.
The greater the positive integer, the lesser is its negative integer.
On a number line, the number increases towards the right of 0 and decreases towards the left of 0.
Addition of integers:
Two positive integers are added directly. Two negative integers are also added directly, but the answer takes a minus (–) sign.
When one positive and one negative integer are added, the numbers are subtracted as whole numbers by considering the numbers without their sign and the answer is written with the sign of greater integer.
Negative of an integer is called additive inverse of that number.
The subtraction of an integer is the same as the addition of its additive inverse.
Addition and subtraction on number line:
To add two integers (both positive, both negative or one positive and one negative) on the number line, both positive and negative integers with zero are marked first and then addition is shown.
When the second number is positive, move in the right direction.
When the second number is negative, move in the left direction.
For subtracting numbers on number line, two cases arise:
When a positive number is subtracted from a positive or negative number, move in the left direction.
When a positive number is subtracted from a positive or negative number, move in the right direction.