Page 41 - ICSE Math 6

3 Negative Numbers and

Integers

Key Concepts

• Need for Negative Numbers • Ordering of Integers
• Connection of Negative Numbers in Daily Life • Absolute Value of an Integer
• Integers and their Representation on a Number Line • Addition and Subtraction of integers

Need for Negative Numbers

In Mathematics, the need to extend our number system arises, when we have to subtract a larger
number from a smaller number. To compute 3 – 5, we must find a number, say n, such that 5 + n = 3.
Since there is no such whole number, we extend the number system to integers.

The credit for inventing zero and negative numbers goes to the Indian mathematician Brahmagupta.
The first number used in counting is 1. The number that corresponds to 1 to the left of 0 on the number
line is negative one and is denoted by –1. It is opposite to +1. The same is true for other negative
numbers like –2, –3, –4, and so on.

Connection of negative numbers in daily life
Negative numbers are essential in everyday life. Their usefulness can be understood from the following
examples. The highest temperature ever recorded on Earth was 58°C in Libya and the coldest temperature
recorded was 89.2°C in Antarctica. Symbolically, the two temperatures can be denoted by +58°C and
–89.2°C respectively. Similarly, it is very easy to represent the highest point on the Earth, Mount
Everest which is 29,029 ft above sea level by +29,029 ft and the lowest point on the Earth, Dead Sea
which is 1,371 ft below sea level by –1,371 ft.
Note: The facts given above have been taken from Wikipedia.

Integers

The negative numbers …, –4, –3, –2, –1, along with whole numbers are called integers. In other
words, the numbers …, –4, –3, –2, –1, 0, 1, 2, 3, 4, ... are integers.

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

• The numbers 1, 2, 3, 4, … are called positive integers.
• The number zero is an integer which is neither positive nor negative.

Representation of integers on a number line
Let’s draw a line and mark any point ‘O’ on it. Consider this point ‘O’ as zero. Now mark points at
equal distances on the right as well as on the left of ‘O’. Label the points on the right side of 0 as 1,
2, 3, 4, 5, ..., etc., and on left side of 0 as –1, –2, –3, –4, –5, ..., etc.

Negative Numbers O Positive Numbers

… –5 –4 –3 –2 –1 0 1 2 3 4 5 ...

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