Page 90 - Maths Class 06

Integers
The whole numbers greater than zero are called positive integers denoted by 1, 2, 3, 4, 5…. . These
numbers are to the right of zero on the number line. Positive integers can be written with or without a
sign. Whole numbers less than zero are called negative integers denoted by –1, –2, –3, –4,… . These
numbers are to the left of zero on the number line.
The collection of whole numbers and the negative numbers is known as
NOTE
integers. Integers comprise of whole numbers and their opposites. The
integer zero is neither positive nor negative. Integers = Positive numbers,
Suppose the colours represent the collection of numbers written against negative numbers and 0.
them.
Yellow—Integers, Green—Whole numbers, Orange—Number zero.

Blue—Natural numbers.
Black—Negative numbers.

The numbers read so far can be represented diagrammatically.

Repre sen ta tion of Inte gers on Number Line
Draw a line and mark a point almost in the middle of it. Call it 0. Set off equal distances on right hand as
well as on left hand side of 0. On the right hand side, we label the points of division as 1, 2, 3, 4, 5, etc.
while on the left hand, these are labelled as -1, -2, -3 , -4, -5 etc. as shown below.

–5 –4 –3 –2 –1 0 1 2 3 4 5

Clearly 1 and -1 are at equal distances from 0 ; but in opposite directions. Similarly, 2 and -2 are at equal
distances from 0; but in opposite directions and so on.

Hence, every integer can be represented on the number line. As a convention, we represent positive
integers on the right hand of 0 and the negative numbers on the left hand of 0.
Ordering of Integers

Any number on the number line is greater than any other number appearing on its left; and any number
on the number line is less than any other number appearing on its right.
Looking at the number line, we observe that:
1. every integer has a successor and also a predecessor.

2. every positive integer is greater than zero; and also greater than every nega tive integer.
3. zero is greater than every negative integer.

4. the greater integer, the lesser is its oppo site.
e g. ., 4 3> but - < -4 3
Absolute Value of an Integer

Consider the integer +3 on the number line. It is at a distance of 3 units from 0 to the right. -3 is also at a
distance of 3 units from 0, but in the opposite direction, i e. . to the left. The common number 3 involved in
both +3 and -3 is called the magnitude or the absolute value of these two integers. If we denote the
magnitude of an integer by the symbol | | , then |+ 3 |= 3 and |- 3 |= 3.

Mathematics-6 90