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NCERT Solutions for Class 7 Maths Chapter 1 – Integers

NCERT Solutions for Class 7 Maths Chapter 1 is about Integers. In this chapter, there are a total of 4 exercises and 33 questions. We will study the properties of Integers- Addition and Subtraction of Integers, Multiplication of Integers and Positive & Negative Integers. 

Try these NCERT Solutions for Class7 for Chapter 1 ‘Integers’, which are based on the latest CBSE approved syllabus. You can consider them as the most reliable study material for Class 7 Maths. We, at Instasolv, provide Chapter-wise Solutions of NCERT Class 7 Maths Book. These answers will help you in understanding the concepts of each Chapter. They will improve your speed of solving any question of any type based on integers for class 7 NCERT.

For the Maths subject in Class 7, we follow an approach where we explain the important elements and summarise each part and subpart of the Chapter. We will follow the same sequence as in the book so that it becomes easy to refer and understand. This will help you strengthen your concepts and help you in scoring higher marks in the exams.

NCERT Solutions for Class 7 Maths Chapter 1 Integers: Summary

1.1 Introduction – Integers are a bigger collection of numbers that contains whole numbers and negative numbers.

1.2 Recall On the number line positive numbers become bigger as you move to the right and smaller as you move to the left. The same concept is applied to negative numbers. As you go to the left, the numbers get smaller so -5 is smaller or less than -3 because -5 comes to the left of -3. We can also call this as ascending order to the right and descending order to the left. 

1.3 Property of Addition and Subtraction of Integers

1.3.1 Closure under Addition

The addition of any two integers, positive or negative, results in an integer. This is called closure property of addition. 

1.3.2 Closure under Subtraction

The subtraction or difference obtained in any two integers is also an integer. This is called closure property of subtraction

1.3.3 Commutative Property

Integers can be added in any order. For any two integers X and Y, X+Y = Y+X. This is the commutative property of addition of integers.

To note, subtraction of integers does not have commutative property so X-Y is not equal to Y-X

1.3.4 Associative Property

Just like addition in integers has commutative property and not subtraction. Similarly, an addition in integers has associative property. Here any grouping does not make a difference so for any three integers X, Y, and Z; (X+Y) + Z = X + (Y + Z) 

1.3.5 Additive Identity

Zero is an additive identity for integers. In other words, add zero to any integer and the result will be the same integer.

1.4 Multiplication of Integers 

1.4.1 Multiplication of  a Positive and Negative Integer

When one positive integer is multiplied by one negative integer, the result is a negative integer. One can multiply both numbers like positive integers and put a negative sign before the result.

1.4.2 Multiplication of Two Negative Integers

Multiplication of two negatives results in a positive. So two negative integers can be multiplied as two positive integers, the answer would be the same. 

1.4.3 Product of Three or More Negative Integers

Multiplication of two negatives results in a positive so If there are an even number of negatives the answer will be positive and an odd number of negatives the answer will be negative. 

1.5 Property of Multiplication of Integers

1.5.1 Closure under Multiplication

We have already understood what closure property is. So multiplication of any two integers will also result in an integer

1.5.2 Commutativity of Multiplication

The order does not matter. Multiply integers in any order and the result will not change. 

1.5.3 Multiplication by Zero

Any integer multiplied by zero will result in zero.

1.5.4 Multiplicative Identity

One is the multiplicative identity for integers. Any integer multiplied by one results in the same integer.

1.5.5 Associativity For Multiplication

Just like in addition, the grouping in which the integers are done does not change the result.

1.5.6 Distributive Property

For integers, multiplication has distributive property over addition. When one integer is multiplied to an addition of two integers, it is the same as multiplying the first integer independently with the other two integers and then adding the results. 

X x (Y + Z) = (X x Y) + (X x Z)

1.5.7 Making Multiplication Easier

Some more examples are given with a combination of all the properties so that the understanding becomes better. 

1.6 Division of Integers

The division is an inverse operation of multiplication. If X x Y = Z, then Z divided by X is equal to Y and Z divided by Y is equal to X. For each multiplication statement, there will be two division statements.

The division of one positive and one negative integer will result in a negative integer. If both integers are negative, the resulting answer will be a positive integer provided the denominator is not zero.

1.7 Properties of Division of Integers

  • The division is not commutative
  • Any number divided by zero does not give a finite answer and is meaningless
  • Zero divided by any integer is zero. Zero divided by Zero as explained above is also meaningless
  • 1 is the identity for the division. Any integer divided by one results in the same integer

Study Tips for NCERT Class 7 Maths  Chapter 1: Integers

Every student aims to get a high score in the exams. Instasolv recommends that you first read this chapter of CBSE NCERT textbook for Class 7 Maths.

Instasolv has provided above is a simple explanation and summary for each part and subpart of Chapter 1. Use this to develop a better understanding of all the concepts by class 7 maths chapter 1 exercise solutions.  

Thereafter, the suggested steps are: 

  1. If any concept is still not understood, ask the experts on the Instasolv app. 
  2. Do all the exercises, solved examples and self-practice questions on your own.
  3. Check your answers from the NCERT solutions for class 7 maths chapter 1 – Integers provided by Instasolv. 
  4. Identify the mistakes and note them so that you never repeat the same mistake.
  5. You can check your progress by keeping track of how many questions you are able to solve yourself without any mistakes.

Learning by rote is never recommended by the subject matter experts of Instasolv. In Maths the questions can be changed by simply changing the values. There are many variations possible to change the questions. Only someone with conceptual clarity can answer all the questions whichever way they are asked.

Practice will help improve your speed as well enabling you to attempt all questions and have enough time to check them for any errors. Follow the NCERT Solutions and tips provided by Instasolv and score maximum marks in your Maths exam.