# NCERT Solutions for Class 7 Maths Chapter 1 Exercise 1.1

NCERT Solutions for Class 7 Maths Chapter 1 Exercise 1.1 (Ex. 1.1) Integers in Hindi and English Medium updated for academic session 2021-2022. Contents are available in PDF file format as well as video format free to use online or download free without any registration.

In class 7 math exercise 1.1 we will study about addition and subtraction of integers through daily life situations word problems. All the questions are easy to understand and solve.

## Class 7 Maths Chapter 1 Exercise 1.1 Solution

• ### CBSE NCERT Class 7 Maths Chapter 1 Exercise 1.1 Solution in Hindi and English Medium

 Class: 7 Mathematics Chapter: 1 Integers Exercise: 1.1 Hindi and English Medium

### Class 7 Maths Chapter 1 Exercise 1.1 Solution in Videos

Class 7 Maths Chapter 1 Exercise 1.1 Solution
Class 7 Maths Exercise 1.1 Question 1 Explanation

Class 7 Maths Exercise 1.1 Question 2-6 Explanation
Class 7 Maths Exercise 1.1 Question 7-8 Explanation
Class 7 Maths Exercise 1.1 Question 9 Explanation
Class 7 Maths Exercise 1.1 Question 10 Explanation

#### Various Types of Numbers

##### Natural number:

Counting numbers are called natural numbers.
Thus, 1, 2, 3, 4, 5, 6,……, etc., are all natural numbers.

##### Whole numbers:

All natural numbers together with 0 (zero) are called whole numbers. Thus, 0, 1, 2, 3, 4, …, etc., are whole numbers. Clearly, every natural number is a whole number but 0 is a whole number which is not a natural number.

##### Integers:

All natural numbers, 0 and negatives of counting numbers are called integers. Thus, …, -4, -3, -2, -1, 0, 1, 2, 3, 4, …, etc., are all integers.
(i) Positive integers: 1, 2, 3, 4, 5, …, etc., are all positive integers.
(ii) Negative integers: -1, -2, -3, -4, …, etc., are all negative integers.
(iii) Zero is an integer which is neither positive nor negative.

Rule 1. If two positive or two negative integers are added, we add their values regardless of their signs and give the sum their common sign.

### Class 7 Maths Exercise 1.1 Practice Questions

##### Add: (i) 36 and 27 (ii) -31 and -25

We have:
(i) + 36 (36 + 27 = 63)
+ 27
63

(ii) – 31 {(-31) + (-25) = – 56}
– 25
– 56

##### Add: (i) -47 + 18 (ii) (-29) + 52

Using the rule for addition of integers with unlike signs, we have:
(i) – 47 (- 47 + 18 = -29)
+ 18
– 29

(ii) – 29 (-29 + 52 = + 23)
+ 52
+ 23

##### Consider the integers (- 6), (- 8) and 5.

We have:
So, {(- 6) + (- 8)} + 5 = (- 14) + 5 = – 9
And, (- 6) + {(- 8) + 5} = (- 6) + (- 3) = – 9.
So, {(- 6) + (- 8)} + 5 = (- 6) + {(- 8) + 5)}.
Similarly, other examples may be taken up.

Rule 2. To add a positive and a negative integer, we find the difference between their numerical values regardless of their signs and give the sign of the integer with the greater value to it.

REMARK: In order to add two integers of unlike signs, we see which is more and by how much.

#### Properties of Addition of Integers

##### I. Closure Property of Addition:

The sum of two integers is always an integer.
Examples:
(i) 5 + 4 = 9, which is an integer.
(ii) 4 + (-8) = -4, which is an integer.
(iii) (-3) + (-8) = -11, which is an integer.
(iv) 15 + (-9) = 6, which is an integer.
Hence, the sum of two integers is always an integer.

##### II. Commutative Law of Addition:

If a and b are any two integers, then
a + b = b + a.

Examples:
(i) (- 4) + 9 = 5 and 9 + (- 4) = 5.
So, (- 4) + 9 = 9 + (- 4).
(ii) (- 5) + (- 8) = – 13 and (- 8) + (- 5) = – 13
So, (- 5) + (- 8) = (- 8) + (- 5).

##### III. Associative Law of Addition:

If a, b and c are any three integers, then
(a + b) + c = a + (b + c).

##### IV. Existence of Additive Identity:

For any integer a, we have:
a + 0 = 0 + a = a.
0 is called the additive identity for integers.
Examples:
(i) 9 + 0 = 0 + 9 = 9
(ii) (- 6) + 0 = 0 + (- 6) = (- 6)

##### V. Existence of Addition Inverse:

For any integer a, we have:
a + (- a) = (- a) + a = 0.
The opposite of an integer a is (- a).
The sum of an integer and its opposite is 0.
Additive inverse of a is (- a).
Similarly, additive inverse of (- a) is a.

Example:
We have: 5 + (- 5) = (- 5) + 5 = 0.
So, the additive inverse of 5 is (- 5).
And, the additive inverse of (- 5) is 5.

### Class 7 Maths Exercise 1.1 Important Questions

##### What is integers in maths class 7?

In Maths, integers are the numbers which can be positive, negative or zero, but cannot be a fraction. These numbers are used to perform various arithmetic operations, like addition, subtraction, multiplication and division. The examples of integers are, 1, 2, 5,8, -9, -12, etc.

##### What is called whole number?

In mathematics, whole numbers are the basic counting numbers 0, 1, 2, 3, 4, 5, 6, … and so on. Whole numbers include natural numbers that begin from 1 onwards. Whole numbers include positive integers along with 0.

##### Which is the smallest whole number?

The smallest whole number is “0” (ZERO).

##### Which is the smallest positive number?

So, the number 1 is the smallest positive integer.

##### How many problems are there in exercise 1.1 of class 7th Maths Chapter 1?

There are 10 problems in exercise 1.1 of class 7th Maths Chapter 1 (Integers). Question 8 having 4 parts, question 9 with five parts. All questions of this exercise are easy, interesting, and good. Only in question 10, some students face problems while solving. Students enjoy doing this exercise. All questions of this exercise are based on real-life examples.

##### What type of questions can come from exercise 1.1 of class 7th Maths in the school’s terminal exams?

Exercise 1.1 of class 7th Maths contains straightforward and nice questions. Most probably, fill in the blanks, true or false (yes or no), one-word answer, MCQ type questions can come from exercise 1.1 of class 7th Maths in the school’s terminal exams.

##### How many days required by students to prepare exercise 1.1 of class 7th Maths in 1-2 days?

Students can prepare exercise 1.1 of class 6th Maths in 1-2 days or not depends on student’s working speed, efficiency, capability, and many other things. But if they try hard to prepare exercise 1.1 of class 7th Maths in 1-2 days, they can easily do that because exercise 1.1 is not very lengthy.

##### Which questions of exercise 1.1 of 7th standard Maths have more chances to come in the terminal exam?

There are 10 problems in exercise 1.1 of class 7th Maths Chapter 1 (Integers). All problems of exercise 1.1 of 7th standard Maths are important and can come in the terminal exam. But, some problems of this exercise are most important. These problems are questions 6, 7, 9 (a), and 10. Questions 6, 7, 9 (a), and 10 of exercise 1.1 of class 7th Maths have more chances to come in the terminal exams compared to other questions of exercise 1.1 of class 7th Maths.             