NCERT Solutions for Class 7 Maths Chapter 1 Integers Introduction
Table of Contents
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 |
Associative Property
| 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) |
Identity Property
| 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 |
Closure Property
| 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
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