Integers are whole numbers and not fractions. They can be positive or negative. Even zero is an integer. The integers have been represented in a number line below. All the negative numbers are represented on the left side of the number line, and all the positive numbers are represented on the right side of the number line. 

E.g.:

To determine the operations, a few properties of integers must be taken into account to help us solve many problems and equations. It will simplify the series of equations quickly. The properties of integers apply to every type of operation, such as addition, subtraction, division, and multiplication. They are denoted with the letter Z. The five properties of operation are listed below:

• • Closure Property
  • Commutative Property
  • Associative Property
  • Identity Property
  • Distributive Propert

The properties of addition and subtraction of integers are explained in the table format:

 

The repeated addition of numbers is called the multiplication of integers. In other words, the process of repetitive addition of numbers, such as when a number is added to itself a specific number of times, is called the multiplication of integers. 

 

The multiplication of integers follows two rules:

Rule 1: The product of a positive integer always results in a positive number.

Rule 2: The product of a negative integer always results in a negative number. 

 

The product of the multiplication of two negative integers always results in positive integers. This happens because the two negative signs are cancelled out against each other, and they form a positive sign. 

In this part, the basic rules of the multiplication of integers have been explained with formulas. Below listed are the various properties of multiplication of integers that will help you in solving various multiplication problems:

• Closure property
• Commutative property
• Associative property
• Distributive property
• Multiplication by zero
• Multiplicative identity

The properties of the multiplication of integers are explained in the table format: 

 

Division of integers means the distribution of numbers. It is the opposite operation of multiplication. The rules of division are the same as the rules of multiplication, such as:

Rule 1: The division of two positive integers will always be positive.

Rule 2: The division of two negative integers will always be negative.

Rule 3: The division of one positive integer with one negative integer will always be negative.

The properties of the division of integers refer to the distribution of two or more integers. The division is the fourth mathematical operation. For the division of integers, you need to learn some basic properties, which have been listed below. The learning of such properties helps to solve division problems easily. 

• Closure property
• Commutative property
• Associative property
• Distributive property
• Identity property

The properties of the division of integers are explained in the table format: 

 

1. Fill in the blanks:

1. Sum of integer and its additive inverse is ____________
2. Sum of -22 and -44 is ______________
3. -36 ÷ (_______) =-9
4. _______ is absolute value of -998

 Solutions :

1. zero

2. -66

3. 4

4.  998

2. What are the 6 properties of the multiplication of integers?

    The 6 main properties of the multiplication of integers are Closure Property, Commutative Property, Associative Property,                Distributive Property, Identity Property, and Multiplication by Zero.

3. What are the four integer operations?

    The four basic integer operations consist of addition, subtraction, multiplication, and division.

4. What do you mean by the division of integers?

    The division of integers means equal grouping or dividing an integer into a specific number of groups. For example, -6 ÷ 2              means dividing -6 into 2 equal parts, which results in -3.

5. What are the five properties of operations?

    The five properties of operation are listed below:

• Closure Property

• Commutative Property

• Associative Property

• Identity Property

• Distributive Property

6. What are the rules of division in Integers?

    The rules of divisions are as follows: 

    Rule 1: The division of two positive integers will always be positive.

    Rule 2: The division of one positive integer with one negative integer will always be negative.

    Rule 3: The division of two negative integers will always be negative.

 

1. Is the Chapter 1 integers important for the Class 7 maths examination?

    Chapter 1 integers is important from the examination point of view as it carries 18 marks as a whole. The chapter comes under        Unit 4 and contributes 16% of the questions in the examination. So, students are advised to practise the chapter thoroughly to        get good grades. 

 2. Which topics are essential for Chapter 1 of NCERT Solutions?

     The important topics are as follows:

• Introduction of Integers

• Properties of Addition and Subtraction of Integers

• Multiplication of Integers

• Multiplication of a Positive and Negative Integers

• Multiplication of two Negative Integers

• Properties of Multiplication of Integers

• Division of Integers

• Properties of Division of Integers

3. What are the uses to learn from the NCERT Solutions for Chapter 1 integers?

    The uses are as follows:

• All the questions have answers in a detailed manner. 

• Students can download the PDF file for easy access to NCERT Solutions. 

• Figures are present in the solutions to understand the topics easily. 

4. Raj deposits INR 2,000 in a band account and withdraws INR 1,642 from the account the next day. If withdrawal is                represented by the negative integer, how will you determine or represent the deposit amount in the bank? Find the              balance of Raj’s account after the withdrawal.

    Sol: The withdrawal amount is represented by a negative integer.

    Deposit is a positive integer

    From the statement, we get.

    Total amount deposited = INR 2,000

    Amount withdrawn by Raj = INR 1642

    Balance = Amount deposited + amount withdrawn

                       = 2,000 + (-1,642)

                       = 2,000 – 1,642

                        = 358

    Hence, the balance of the bank account after withdrawal is INR 358