Integers RS Aggrawal ICSE Class-7th Mathematics Solutions  Goyal Brothers Prakashan Chapter-1. We provide step by step Solutions of Exercise / lesson-1 Integers for ICSE Class-7 RS Aggarwal Mathematics  . Our Solutions contain all type Questions with Exe-1 A, Exe-1 B Exe-1 C   Exe-1 D, Exe-1 E, Exe-1 F (MCQ), Mental Maths to develop skill and confidence. Visit official Website for detail information about ICSE Board Class-7 Mathematics.

 Board ICSE Publications Goyal brothers Prakshan Subject Maths Class 7th Chapter-1 Integers Writer RS Aggrawal Book Name Foundation Topics Solution of Exe-1 A, Exe-1 B Exe-1 C   Exe-1 D, Exe-1 E, Exe-1 F (MCQ), Mental Maths Academic Session 2021-2022

## Integers RS Aggrawal ICSE Class-7th Mathematics Solutions  Goyal Brothers Prakashan Chapter-1

–: Select Topics :–

Notes on Integers

Exe-1 A,

Exe-1 B,

Exe-1 C ,

Exe-1 D,

Exe-1 E,

MCQ Exe-1 F,

Mental Maths

### Introduction to Integers

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

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

#### 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: 63=+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: +63=2

#### 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)+(4)=34=7

When one positive and one negative integers are added, we take their difference and place the sign of the bigger integer.
Example : (7)+(2)=5

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

#### 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)×(3)=6 and (2)×(+3)=6

Product of even number of negative integers is positive and product of odd number of negative integers is negative.

### Exercise – 1 AIntegers RS Aggrawal ICSE Class-7th Mathematics Solutions  Goyal Brothers Prakashan

Page 10-11

#### Question 1

write all integers between :

(i)………….

………………

#### Questions 2

compare the integer :

(i)………….

………………

…………………..

…………………..

…………………..

#### Question 6

fill in the blanks………….

(i)………….

………………

### Integers Exe-1 B of RS Aggrawal for ICSE Class-7th Mathematics Solutions  Goyal Brothers Prakashan

Page 13-14

(i)………….

………………

(i)………….

………………

……………………….

………………………..

………………………

#### Question 10

find predecessor of :

(i)………….

………………

### RS Aggrawal ICSE Class-7th Mathematics Solutions  Goyal Brothers Prakashan Integers Exercise – 1 C

Page 18

find product :

(i) 18 x 4

………………

find product

(i)………….

………………

#### Question 3

verify following :

(i)………….

………………

…………………….

…………………….

……………………

#### Question 9

the product of two integers is -120 . If one number is 15, find the others.

### Exercise – 1 D,Integers RS Aggrawal ICSE Class-7th Mathematics Solutions  Goyal Brothers Prakashan

Page 19

simplify :

5{(-6) + (12/4)}

#### Question 2

10 – {56/(-16 + 9)}

……………………

……………………

…………………..

#### Question 7

10 – [8 – {11 + 30/(4 – 5¯-7¯)}]

### RS Aggrawal ICSE Class-7th Mathematics Solutions  Goyal Brothers Prakashan Integers Exercise – 1 E

Page 29

#### Question 1

By how much does 5 exceed -5 ?

#### Question 2

How much -7 less than -1?

…………………….

………………………..

………………………..

#### Question 12

A class of 36 student contributed …………………. what amount was spent on the picnic ?

### Exercise – 1 F (MCQ)

Page 20

#### Question 1

The absolute value of 5 is

…………………

……………………..

…………………….

#### Question 5

The value of (-7) x 6 + (-7) x 14 is

…………………

### Mental Maths

Page 21

#### Question 1

Fill in the blanks :

(i) Negative.

(ii) Zero

(iii) Distributive

(iv) Negative

(v) Opposite

#### Question 2

Write true and false :

(i) False

(ii) False

(iii) False

(iv) True

(v) False

(vi) True

–: End of Integers RS Aggrawal ICSE Class-7th Solutions :–

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