# 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 2020-2021. 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

Class: 7 | Mathematics |

Chapter: 1 | Integers |

Exercise: 1.1 | Hindi and English Medium |

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

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

#### 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.

#### Addition of Integers

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.

##### 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

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.

##### 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

#### 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).

##### 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.

##### 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.

##### 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.