NCERT Class 7 Maths Chapter 1 Integer Introduction
Today we are going to share the Introduction and Solution of NCERT book for Class 7 Maths Chapter 1. We have shared two versions of NCERT Solution Class 7 Maths Chapter 1 Integer first in Text and Vide. Video is very important for all students who are studying in class 7 and want proper clarification and understanding maths. I recommend watching the video for proper learning Class 7 Maths Chapter 1 Integer.
Class 7 Maths Chapter 1 Integer
Introduction of Integers
Properties of Addition and Subtraction of Integers
Multiplication of Integers
Multiplication of a Positive and Negative Integer
Multiplication of two Negative Integer
Properties of Multiplication of Integers
Division of Integers
Properties of Division of Integers
Introduction of Integers
An integer is a whole number and negative number but not a fraction and decimal number. Integer denoted by Z. Integers are divided into two parts first is Negative Integers and second is Positive Integers.
For Example:
7 is integer
-5 is also an integer
3/2 is not an integer
3 is not an integer
Properties of Addition and Subtraction of Integers
Properties of Addition in Integers
Positive + Positive = Positive
5 + 3 = 8
Negative + Negative = Negative
(-5)+ (-3) = -8
*Positive + Negative or *Negative + Positive
(-5) + 3 = -2
3 + (-5) = -2
(-3) + 5 = 2
5+ (-3) = 2
* Subtract the smaller number from the larger number, then use the sign of the larger number in the answer.
Properties of Subtraction in Integers
Negative – Positive = Negative
(-5) – 3 = -8
Positive – Negative = Positive
5 –(-3) = 5 + 3 = 8
*Negative – Negative = Negative + Positive
(-5) – (-3) = -5 + 3 = -2
(-3) – (-5) = -3 + 5 = 2
* Subtract the smaller number from the larger number, then use the sign of the larger number in the answer.
Multiplication of Integers
Multiplication of Integers
Positive X Positive = Positive
3 X 5 = 15
Negative X Negative = Positive
(-3) X (-5) = 15
Negative X Positive = Negative
(-3) X 5 = -15
Positive X Negative = Negative
3 X (-5) = -15
Division of Integers
Division of Integers
Positive ÷ Positive = Positive
15 ÷ 3 = 5
Negative ÷ Negative = Positive
(-15) ÷ (-3) = 5
Negative ÷ Positive = Negative
(-15) ÷ 3 = -5
Positive ÷ Negative = Negative
15 ÷ (-3) = -5
Commutative Property
Addition
If x = 3 and y = 5,
Working
x + y = 3+ 5 = 8 and Y + x = 5 + 3 = 8
Then
x + y = y+ x
Subtraction
If x = 3 and y = 5,
Not Working
x – y = 3 – 5 = -2 and Y – x= 5 – 3 = 2
then
x – y ≠ y – x
Multiplication
If x = 3 and y = 5,
Working
X x y = 3 x 5 = 15 and Y x X = 5 x 3 = 15
Then
x × y = y × x
Division
If x = 3 and y = 5,
Not working
X ÷ y = 3 ÷ 5 = 0.6 and Y ÷ x = 5 ÷ 3 = 1.66
then
x ÷ y ≠ y ÷ x
AssociativeProperty
Addition
If x = 3, y = 4 and z = 5,
Working
X + (y + z) = 3 + (4 + 5) = 3 + 9 = 12
( x + y) + z = (3 + 4) + 5 = 7 + 5 =12
Then
x + (y + z) = (x + y) +z
Subtraction
If x = 3, y = 4 and z = 5,
Not Working
(x -y) – z = (3-4)-5 = -1-5= -6
X-(y-z) = 3 – (4-5) = 3 – (-1) = 3 + 1 = 4
then
(x – y) – z ≠ x – (y – z)
Multiplication
If x = 3, y = 4 and z = 5,
Working
X x (y x z) = 3 x (4 x 5) = 3 x 20 = 60
(X x y) x z = (3 x 4) x 5 = 12 x 5 = 60
Then
x × (y × z) = (x × y) × z
Division
If x = 3, y = 4 and z = 5,
Not working
(x ÷ y) ÷ z = (3 ÷ 4) ÷ 5 = 0.75 ÷ 5 = 0.15
x ÷ (y ÷ z) = 3 ÷ (4 ÷ 5) = 3 ÷ 0.80 = 3.75
then
(x ÷ y) ÷ z ≠ x ÷ (y ÷ z)
IdentityProperty
Addition
If x = 3,
Working
X + 0 = 3 + 0 = 3
0 + x = 0 + 3 = 3
Then
x + 0 = 0 + x
Subtraction
If x = 3,
Not Working
x – 0 = 3 – 0 = 3
0 – x = 0 – 3 = -3
Then
x – 0 ≠ 0 – x
Multiplication
If x = 3,
Working
X x 1 = 3 x 1 = 3
1 x X = 1 x 3 = 3
Then
x × 1 = 1 × x
Division
If x = 3,
Not working
x ÷ 1 = 3 ÷ 1 = 3
1 ÷ x = 1 ÷ 3 = 0. 33
Then
x ÷ 1 ≠ 1 ÷ x
ClosureProperty
Addition
If x = 3 and y 5,
Working
X + y = 3 + 5 = 8
Then
x + y ∈ Z
Subtraction
If x = 3 and y 5,
Working
x – y = 3 – 5 = -2
Then
x – y ∈ Z
Multiplication
If x = 3 and y 5,
Working
X x y = 3 x 5 = 15
Then
x × y ∈ Z
Division
If x = 3 and y 5,
Not working
x ÷ y = 3 ÷ 5 = 0.6
Then
x ÷ y ∉ Z
Distributive Property
Integer Property
Addition
Multiplication
Subtraction
Division
Distributive Property
If x =3, y = 4 and z = 5,
x × (y + z) = 3 x (4 + 5) = 3 X 9 = 27
x × y + x× z = 3 X 4 + 3 X 5 = 12 + 15 = 27
x × (y − z) = 3 x (4-5) = 3 X (-1) = – 3
x × y − x × z = 3 x 4 – 3 x 5 = 12 – 15 = -3
x × (y + z) = x × y + x× z
x × (y − z) = x × y − x × z
Properties of Integers
Summery
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