Integers Class 7 Notes: Chapter 1

Introduction to 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, … }

For more information on Number Systems, watch the below video.


Properties of Addition and Subtraction of Integers

Closure under Addition and subtraction
For every integer a and ba+b and ab are integers.

Commutativity Property for addition
for every integer a and ba+b=b+a

Associativity Property for addition
for every integer a,b and c, (a+b)+c=a+(b+c)
To know more about Addition and Subtraction of Integers, visit here.

Additive Identity & Additive Inverse

Additive Identity
For every integer a, a+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.

Additive inverse
For every integer a, a+(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 b, a×b=Integer

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

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

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

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

These properties make calculations easier.

To know more about “Properties of Multiplication of Integers”, visit here.

Division of Integers

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
To know more about Multiplication and Division of Integers, visit here.

The Number Line

Number Line

Representation of integers on a number line

Representation of integers on a number line

On a number line when we

(i) add a positive integer for a given integer, we move to the right.
Example : When we add +2 to +3, move 2 places from +3 towards right to get +5

(ii) add a negative integer for a given integer, we move to the left.
Example : When we add -2 to +3, move 2 places from +3 towards left to get +1

(iii) subtract a positive integer from a given integer, we move to the left.
Example: When we subtract +2 from -3, move 2 places from -3 towards left to get -5

(iv) subtract a negative integer from a given integer, we move to the right
Example: When we subtract -2 from -3, move 2 places from -3 towards right to get 1

To know more about Number Lines, visit here.

Addition and Subtraction of Integers

The absolute value of +7 (a positive integer) is 7
The absolute value of -7 (negative integer) is 7 (its corresponding positive integer)

Addition of two positive integers gives a positive integer.
Example : (+3)+(+4) +7

Addition of two negative integers gives a negative integer.
Example : (3)+(434=7

When one positive and one negative integers are added, we take their difference and place the sign of the bigger integer.
Example : (7)+(25

For subtraction, we add the additive inverse of the integer that is being subtracted, to the other integer.
Example : 56(7356+73 129

Introduction to Zero

Integers

Integers are the collection of numbers which is formed by whole numbers and their negatives. 
The set of Integers is denoted by Z or I. I =  { …, -4, -3, -2, -1, 0, 1, 2, 3, 4,… }

Properties of Division of Integers

Properties of Division of Integers

For every integer a,
(a) a÷0 is not defined
(b) a÷a

Note:  Integers are not closed under division
Example: (– 9) ÷ (– 3) = 2. Result is an integer.
and (3)÷(9)= 1/3. Result is not an integer.

Multiplication of Integers

Multiplication of Integers

Product of two positive integers is a positive integer.
Example : (+2)×(+3+6

Product of two negative integers is a positive integer.
Example :(2)×(3+6

Product of a positive and a negative integer is a negative integer.
Example :(+2)×(36 and (2)×(+36

Product of even number of negative integers is positive and product of odd number of negative integers is negative.
These properties make calculations easier.

Frequently Asked Questions on CBSE Class 7 Maths Notes Chapter 1 Integers

Q1

What is closure property?

Closure property of whole numbers under addition: The sum of any two whole numbers will always be a whole number, i.e. if a and b are any two whole numbers, a + b will be a whole number.

Q2

What are the properties of zero?

1. Zero is even 2. Zero is neither positive nor negative 3. Zero is an integer

Q3

What is the definition of inverse?

A term is said to be in inverse proportion to another term if it increases (or decreases) as the other decreases (or increases). of or relating to an inverse function.

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