Page 9 - Start Up Mathematics_7

1 Integers

“The essence of Mathematics lies in its freedom.”
—Georg Cantor

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, ... .

In the previous class, we have learnt about addition and subtraction of integers. In this lesson,
we will learn various properties of integers. These include closure, commutative, associative and
distributive property. Existence of identity element and inverse of an element will also be discussed.
We will also deal with multiplication and division of integers.
Let’s review what we have learnt in our previous class.

Natural Numbers
The numbers 1, 2, 3, 4, … are called natural numbers.

Whole Numbers

The numbers 0, 1, 2, 3, 4, … are called whole numbers.

Integers

The numbers …, –4, –3, –2, –1, 0, 1 , 2 , 3, 4, … are called integers.

Zero
The number 0 is an integer which is neither positive nor negative.

Modulus or Absolute Value
Modulus or absolute value of an integer is always positive. It represents the numerical value of
an integer (i.e., ignore sign). The absolute value of an integer a is denoted by |a| and is given by

 if ≥0
||a = 
 − a if 0

Representation of Integers on a Number Line
We represent integers on a number line as:

... –4 –3 –2 –1 0 1 2 3 4 ...

We have learnt addition and subtraction of integers using a number line in the previous class.