# Integers Chapter 1 Class 7 Maths NCERT Textbook With Solutions PDF

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### Chapter 1: Integers

#### 1.1 INTRODUCTION

We have learned about whole numbers and integers in Class VI. We know that integers are from a bigger collection of numbers that contains whole numbers and negative numbers.

What other differences do you find between entire numbers and integers? In this chapter, we will study more about integers, their properties, and operations.

First, we will review and revise what we have done about integers in our previous class.

#### 1.2 RECALL

We know how to represent integers on a number line. Some integers are marked on the number line given below.

Can you write these marked integers in ascending order? The ascending order of these numbers is – 5, – 1, 3. Why did we choose – 5 as the smallest number? Some points are marked with integers on the following number line. Write these integers in descending order.

The descending order of these integers is 14, 8, 3, …
The above number line has only a few integers filled. Write appropriate numbers at each dot.

1. A number line representing integers is given below
–3 and –2 are marked by E and F respectively. Which integers are marked by B,
D, H, J, M and O?
2. Arrange 7, –5, 4, 0 and – 4 in ascending order and then mark them on a number
We have done addition and subtraction of integers in our previous class. Read the
following statements.
On a number line when we
(i) add a positive integer, we move to the right.
(ii) add a negative integer, we move to the left.
(iii) subtract a positive integer, we move to the left.
(iv) subtract a negative integer, we move to the right.
State whether the following statements are correct or incorrect. Correct those which
are wrong:
(i) When two positive integers are added we get a positive integer.
(ii) When two negative integers are added we get a positive integer.
(iii) When a positive integer and a negative integer are added, we always get a negative
integer.
(iv) Additive inverse of an integer 8 is (– 8) and additive inverse of (– 8) is 8.
(v) For subtraction, we add the additive inverse of the integer that is being subtracted,
to the other integer.
(vi) (–10) + 3 = 10 – 3
(vii) 8 + (–7) – (– 4) = 8 + 7 – 4

(i) Correct. For example:
(a) 56 + 73 = 129 (b) 113 + 82 = 195 etc.
Construct five more examples in support of this statement.
(ii) Incorrect, since (– 6) + (– 7) = – 13, which is not a positive integer. The correct
statement is: When two negative integers are added we get a negative integer.
For example,
(a) (– 56) + (– 73) = – 129 (b) (– 113) + (– 82) = – 195, etc.
Construct five more examples on your own to verify this statement.
(iii) Incorrect, since – 9 + 16 = 7, which is not a negative integer. The correct statement is :
When one positive and one negative integers are added, we take their difference
and place the sign of the bigger integer. The bigger integer is decided by ignoring the
signs of both the integers. For example:
(a) (– 56) + (73) = 17 (b) (– 113) + 82 = – 31
(c) 16 + (– 23) = – 7 (d) 125 + (– 101) = 24
Construct five more examples for verifying this statement.
(iv) Correct. Some other examples of additive inverse are as given below:
10 –10
–10 10
76 –76
–76 76
Thus, the additive inverse of any integer a is – a and additive inverse of (– a) is a.
inverse of the integer that is being subtracted, to the other integer. For example:
(a) 56 – 73 = 56 + additive inverse of 73 = 56 + (–73) = –17
(b) 56 – (–73) = 56 + additive inverse of (–73) = 56 + 73 = 129
(c) (–79) – 45 = (–79) + (– 45) = –124
(d) (–100) – (–172) = –100 + 172 = 72 etc.
Write atleast five such examples to verify this statement.
Thus, we find that for any two integers a and b,
a – b = a + additive inverse of b = a + (– b)
and a – (– b) = a + additive inverse of (– b) = a + b
(vi) Incorrect, since (–10) + 3 = –7 and 10 – 3 = 7
therefore, (–10) + 3 ≠ 10 – 3
(vii) Incorrect, since, 8 + (–7) – (– 4) = 8 + (–7) + 4 = 1 + 4 = 5
and 8 + 7 – 4 = 15 – 4 = 11
However, 8 + (–7) – (– 4) = 8 – 7 + 4

### NCERT Solutions Class 7 Maths Chapter 1 Integers

Q2. In a quiz, positive marks are given for correct answers and negative marks are given for incorrect answers. If Jack’s score in five successive rounds were 25, –5, –10, 15, 10. What was his total in the end?

Solution:
Jack’s scores in the five successive rounds are 25, –5, –10, 10 and 15 Total marks obtained by jack 25 5 10 10 15 ( ) ( )
25 5 10 10 15 35
– – = + − + − + +

= + +

Thus, jack obtained 35 marks in the quiz.

Q3. In Srinagar temperature was –5°C on Monday and then it was dropped by 2°C on Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday it rose up by 4°C. What was the temperature on this day?

Solution:
The temperature of Srinagar on Monday = –5°C
On Tuesday, it was dropped by 2°C.
Temperature on Tuesday = –5° C – 2° C = –7°C
On Wednesday, it rose up by 4°C
The temperature on Wednesday = –7°C+4°C= –3°C
Thus, the temperature on Tuesday was –7°C and on Wednesday was –3°C.