# CBSE Class 7th Maths

## Integers

### Introduction to Numbers

Natural Numbers : The collection of all the counting numbers is called set of natural numbers. It is denoted by N = {1,2,3,4….}

Whole Numbers: The collection of natural numbers along with zero is called a set of whole numbers. It is denoted by W = { 0, 1, 2, 3, 4, 5, … }

## Properties of Addition and Subtraction of Integers

For every integer a and b,  a+b and ab are integers.

for every integer a and b,  a+b=b+a

for every integer a,b and c(a+b)+c=a+(b+c)

For every integer aa+0=0+a=a here 0 is Additive Identity, since adding 0 to a number leaves it unchanged.
Example : For an integer 2, 2+0 = 0+2 = 2.

For every integer aa+(a)=0 Here, a is additive inverse of a and a is the additive inverse of-a.
Example : For an integer 2, (– 2) is additive inverse  and for (– 2), additive inverse is 2. [Since + 2 – 2 = 0]

## Properties of Multiplication of Integers

### Properties of Multiplication of Integers

Closure under Multiplication
For every integer a and ba×b=Integer

Commutative Property of Multiplication
For every integer a and ba×b=b×a

Multiplication by Zero
For every integer aa×0=0×a=0

Multiplicative Identity
For every integer aa×1=1×a=a. Here 1 is the multiplicative identity for integers.

Associative property of Multiplication
For every integer ab  and c,  (a×b)×c=a×(b×c)

Distributive Property of Integers
Under addition and multiplication,  integers show the distributive property.
i.e., For every integer ab  and c,  a×(b+c)=a×b+a×c

These properties make calculations easier.

### Division of Integers

When a positive integer is divided by a positive integer, the quotient obtained is a positive integer.
Example: (+6) ÷ (+3) +2

When a negative integer is divided by a negative integer, the quotient obtained is a positive integer.
Example: (-6) ÷ (-3) +2

When a positive integer is divided by a negative integer or negative integer is divided by a positive integer, the quotient obtained is a negative integer.
Example: (-6) ÷ (+3) =2 and Example: (+6) ÷ (-3) 2

### Number Line

Representation of integers on a number line

On a number line when we add a positive integer for a given integer, we move to the right, add a negative integer for a given integer, we move to the left.