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

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Class 7 Maths Chapter 1 Exercise 1.1 Solution
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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.

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