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## 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 ## NCERT Solutions for Class 7 Maths Chapter 1 Integer                 #### Summery

We have shared a detailed introduction of Class 7 Maths Chapter 1 Integer. If you have any questions regarding Integer please let me know through comment. It is the best way to communicate with each other regarding problems and solutions.  Don’t forget to suggest our channel to someone who needs it: – http://bit.ly/2IaobbD