Integers RS Aggrawal ICSE Class-7th Maths Goyal Brothers

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 CISCE 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

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–: 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 

 

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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

Closure under Addition and subtraction
For every integer $a$ and $b$,  $a+b$ and $a–b$ are integers.

Commutativity Property for addition
for every integer $a$ and $b$,  $a+b=b+a$

Associativity Property for addition
for every integer $a$,$b$ and $c$, $(a+b)+c=a+(b+c)$

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

Closure under Multiplication
For every integer $a$ and $b$, $a\times b=Integer$

Commutative Property of Multiplication
For every integer $a$ and $b$, $a\times b=b\times a$

Multiplication by Zero
For every integer $a$, $a\times 0=0\times a=0$

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

Associative property of Multiplication
For every integer $a$, $b$  and $c$,  $(a\times b)\times c=a\times (b\times c)$

Distributive Property of Integers
Under addition and multiplication,  integers show the distributive property.
i.e., For every integer $a$, $b$  and $c$,  $a\times (b+c)=a\times b+a\times c$

Division of Integers

When a positive integer is divided by a positive integer, the quotient obtained is a positive integer.
Example: $\frac{+6}{+3}=+2$

When a negative integer is divided by a negative integer, the quotient obtained is a positive integer.
Example: $\frac{-6}{-3}=+2$

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: $\frac{-6}{+3}=-2$ and Example: $\frac{+6}{-3}=-2$

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 : $(-3)+(-4)=-3-4=-7$

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

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 : $(+2)\times (+3)=+6$

Product of two negative integers is a positive integer.
Example :$(-2)\times (-3)=+6$

Product of a positive and a negative integer is a negative integer.
Example :$(+2)\times (-3)=-6$ and $(-2)\times (+3)=-6$

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

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Exercise – 1 A Integers 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 3

…………………..

…………………..

…………………..

 Question 6

fill in the blanks………….

(i)………….

………………

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

Page 13-14

Question 1

Add the following integers

(i)………….

………………

 Question 2

find the additive inverse of:

(i)………….

………………

Question 3

……………………….

………………………..

………………………

Question 10

find predecessor of :

(i)………….

………………

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

Page 18

Question 1

find product :

(i) 18 x 4

………………

 Question 2

find product

(i)………….

………………

Question 3

verify following :

(i)………….

………………

Question 4

…………………….

…………………….

……………………

 Question 9

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

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

Page 19

simplify :

Question 1

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

Question 2

10 – {56/(-16 + 9)}

Question 3

……………………

……………………

…………………..

Question 7

10 – [8 – {11 + 30/(4 – 5¯-7¯)}]

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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 3

…………………….

………………………..

………………………..

Question 12

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

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Exercise – 1 F (MCQ) 

Page 20

Multiple Choice Question

Question 1

The absolute value of 5 is

…………………

Question 2

……………………..

…………………….

Question 5

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

…………………

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Mental Maths

Page 21

Question 1

Fill in the blanks :

Answer

(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 :–

 

Return to- RS Aggarwal Solutions for ICSE Class-7 Goyal Brothers Prakashan

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