Page 112 - ICSE Math 5

Introduction to oduction to
Intr

8
Ne
Negative Numbersgative Numbers

Learning Outcomes

Students will be able to learn:
 the idea of integers as counting numbers, zero and negatives of counting numbers.
 to represent integers on a number line.
 to compare integers using a number line.
 to arrange integers in ascending and descending orders.
 the rules for addition and subtraction of integers.

We are familiar with natural (counting) numbers and whole numbers, and their four fundamental
operations: addition, subtraction, multiplication and division. Let’s revise these numbers quickly
before we extend our number system to integers.

Natural Numbers and Whole Numbers

The numbers like 1, 2, 3, 4, … that we use on a daily basis are
called natural (counting) numbers. We know that 1 is the first
Remember
and the smallest natural number, and we can obtain any natural
All whole numbers
number by adding 1 to its previous number. When we include 0
are natural numbers,
in the series of these natural numbers, they become 0, 1, 2, 3, except 0.
4, … and are called whole numbers. So, 0 is the smallest whole
number. We cannot find the greatest natural or whole number
as they are infinite.
Natural and whole numbers can be represented on a straight line as shown below.

0 1 2 3 4 5 6 7 8 9 10 …

Natural numbers

Whole numbers
We know that we can subtract any smaller number from a larger number and find the difference.
Can we think of subtracting a larger number from a smaller number? Let’s say we have to subtract
4 from 3, i.e., 3 – 4 = ?, then we must find a number such that 4 + ? = 3. Since there is no such
whole number, we extend the number system to a new type of number system, i.e., integers.
Let’s know about these numbers.
Integers

The counting numbers, zero and negatives of counting numbers are called integers. For example,
the numbers …, –4, –3, –2, –1, 0, 1, 2, 3, 4, … are integers.

102