The notion of a number is connected with the act of counting. So, the natural numbers 1, 2, 3, 4, 5, …… are also called counting numbers. We use ten symbols or digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to denote large numbers by using position of the digits in the given number.

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What are integers?

The negative numbers, zero and the natural numbers together are called integers.A collection of numbers which is written as …….. -4, -3, -2, -1, 0, 1, 2, 3, 4……… .These numbers are called integers.

For example:(i) -8, -2, 0, 2, 8(ii) -7, -1, 0, 5, 12(iii) -15, -9, 11, 21(iv) -10, -3, 0, 9, 14(v) -6, -4, 0, 7, 19

We usually represent numbers by making evenly spaced pointsone unit apart on a straight horizontal line which is called a number line. Theline extends indefinitely to the left and to the right. A point O on the line,called the origin corresponds to the number 0. So, point A at a distance of 9units to the right of zero represents the number 9 on the number line shownbelow. What lies on the left of 0? Let us think about some of the familiar things tounderstand about the positive number and the negative number.

We very often hear that the temperature during winter wentdown to -2°. We know that the temperature in -2° is very cold, it is colderthan 0°c. It means that -2 is smaller than 0. Let us see in a thermometer where-2 is located. It is marked below 0.

Tomeasure the depth below the ground level we use negative numbers. Here, 0indicated ground level. On a number line a number that is right to the 0 ispositive and a number left side to the 0 is negative. So, we have a new set ofnumbers -1, -2, -3, -4, -5, ….. These are known as the negative numbers. On the number line there are positive numbers, negativenumbers and 0. These are called integers. 0 is neither positive nor negative. The sign before thenumber indicates its direction to the right or left of 0. For example +5indicates that the number lies to the right of 0 and -5 indicates that thenumber lies to the left of 0. Thus, integers are also called directed numbers.If a number has no sign it means that it is a positive integer.

Negative Integers

The negative numbers ………. -5, -4, -3, -2, -1 are called negative integers.Thus, examples of negative integers are ……… -5, -4, -3, -2, -1.

Note:

We use the symbol ‘-’ to denote negative integers and the same symbol is used to indicate subtraction. But the context will always make it clear whether we mean negative integer or subtraction.

Positive Integers

The natural numbers 1, 2, 3, 4, 5, ……… are called positive integers.Thus, examples of positive integers are 1, 2, 3, 4, 5, ………. .

Note:

Positive integers are also written as +1, +2, +3, +4, +5, ………… however, the plus sign (+) is usually omitted and understood.

The number 0 is simply an integer. It is neither positive nor negative.

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● Integers

Representation of Integers on a Number Line.

Addition of Integers on a Number Line.

Rules to Subtract Integers.

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