Page 113 - ICSE Math 5

• The numbers …, –4, –3, –2, –1 are called negative numbers or negative integers.
• The numbers 1, 2, 3, 4, … are called positive numbers or positive integers.

• The number 0 is an integer but it is neither positive nor negative.

Representation of Integers on a Number Line

A number line is usually a horizontal or straight line on which counting numbers, zero and
negatives of counting numbers are marked at equal distances.

Let’s draw a number line to represent integers on it. Mark a point ‘0’ at the centre of the number
line drawn. Now mark points on the right as well as on the left of 0 at equal distances on the
number line. Label the points on the right side of 0 as 1, 2, 3, 4, 5, ... and on the left side as –1,
–2, –3, –4, –5, ... and so on.
We represent the integers on a number line as shown below.

… –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 …

Negative numbers Zero Positive numbers

It is clear from the above number line that 1 and –1 are marked at equal distance from 0 but
in opposite directions. Similarly, 2 and –2 are marked at equal distance from 0 but in opposite
directions and so on.

The numbers 1, 2, 3, 4, … that are represented on the right side of 0 are called positive numbers
or positive integers. These numbers are greater than 0 and can be written with or without a ‘+’
sign in front of them.
The numbers that are represented on the left side of 0 on the given number line are called
negative numbers or negative integers. These numbers are less than 0 and are negatives of
counting numbers. For example, –1, –2, –3 and –4 are negative numbers and are read as negative
one, negative two, negative three and negative four, respectively. Negative numbers are usually
written using a negative sign ‘–’ in front of the number. The greatest negative number is –1.
Let’s show some more integers like –9, –2, 4 and 7 on a number line.

–9 –2 4 7

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

Necessity of Negative Numbers

Negative numbers or negative integers are necessary in everyday life because these numbers
are a part of important calculations. These indicate oppositeness of situations like opposite
directions, height above the sea level and depth below the sea level, temperature above and
below zero degree, profits and losses in the business, and rise and fall in the prices of goods.

Let’s consider some real life examples to understand the necessity of positive and negative
numbers or integers.

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