Page 89 - Maths Class 06

Negative Numbers and Integers

Introduction

As read in the previous chapters, the natural numbers are the counting numbers; the whole numbers are
collection of all natural numbers along with zero. If we subtract 5 from 9 the result is 4 which is again a
whole number but what, if we want to subtract 9 from 5? There are no set of numbers that can represent
such numbers. Thus we need to extend our number system.

Negative Numbers
We have also learnt the representation of whole numbers on number line as shown below:

0 1 2 3 4 5 6 7 8

We know a line extends in both directions. the numbers to the right of the zero are the natural numbers 1,
2, 3, 4, 5… in the increasing order (greater than zero). Are there any numbers to the left of the zero?
We extend the number line to the left of zero to represent numbers which are smaller than 0. Such
numbers are called negative numbers. You must have read about negative numbers in weather reports.
The temperature in Ladhak is – 4°C means that temperature is ‘4 degrees below zero’. The counting
numbers 1, 2, 3 and so on, are all positive numbers.

–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8

The negative and positive numbers indicates the opposite of each other. The distance above the sea level
is denoted by positive number whereas the distance below sea level is denoted by negative number. If a
positive number is distance up, then a negative number is distance down. If the profit is positive, the loss
is negative. The credit is denoted by positive number and debit is denoted by a negative number. If the
positive indicates north then negative indicates the south direction.

Let us place a mirror on the number zero. The image of the natural numbers 1, 2, 3 can be seen as shown
below:

–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8

The image of number 1 can be represented as – 1, the image of number 2 as – 2, 3 as – 3 and so on… since
– 1 is placed one unit to the left of zero, it represents 1 unit less than 0.
Similarly, – 2 is 2 less than zero… and so on. Negative numbers are NOTE
represented by placing minus sign in front. For example, – 4 represents a For each positive integer,
negative quantity that is 4 units less than zero and is pronounced as there is a negative integer.
“minus four”.
89 Mathematics-6