# NCERT Solutions for Class 6 Mathematics Chapter 6

Class 6 students who are looking for NCERT Solutions for Class 6 Mathematics Chapter 6 Integers can find accurate answers to the textbook questions on Extramarks. NCERT Solutions for Class 6 Mathematics Chapter 6 are prepared by subject matter experts to assist students in solving exercises in a smooth and quicker way. These answers adhere to the revised guidelines by  CBSE, making them reliable and accurate  resources  which students can depend on. .

Students can also refer to the NCERT Solutions for Class 6 Mathematics Chapter 6 if they have any doubts while solving these exercises.

## NCERT Solutions for Class 6 Mathematics Chapter 6 - Integers

Integers are a collection of whole numbers and negative numbers. Chapter 6 starts with a conditional problem before moving on to the concept of negative numbers. As students proceed through the chapter, they will encounter new concepts such as integer representation on a number line, integer ordering and addition, integer subtraction, and so on.

### NCERT Solutions for Class 6 Mathematics Chapter 6 - Integers

NCERT Solutions for Class 6 Mathematics Chapter 6 are a must-have study resource for students to prepare well for their exams. These solutions are written in a straightforward manner, allowing students to effectively grasp fundamental as well as difficult concepts. These solutions can be accessed easily on Extramarks.

### NCERT Class 6 Mathematics Solutions Topic-Wise Discussion

Chapter 6 discusses Integers. There are a total of 4 sub-sections in the chapter.

• Introduction
• Integers
• Addition of Integers
• Subtraction of Integers with the Help of a Number Line.

Introduction

This section begins with an overview and is illustrated with several examples. It tells the story of Sunita, a young girl who wants ten bananas for her picnic but only has eight. As a result, she borrows two from her next-door neighbour. Sunita needs to return two bananas to her neighbour, according to this example. Many other examples in this chapter expose students to the concept of integers.

The numerous indicators associated with numbers and what they mean are then discussed.

Integers

Students are already familiar with natural numbers, which are positive integers. In this subsection, they will learn about negative integers.

The use of diverse figures aids students in better understanding the concepts of whole numbers, natural numbers, negative numbers, and integers. After that, they learn how to use a single line to represent a variety of integers.

The next step is ordering of integers, in which students learn how to arrange integers according to their value.

Students learn how to add two integers through an engaging example in this section. Mohan is a young boy whose house has steps leading to the terrace and godown. The steps leading to the terrace are positive numbers, while those leading to the godown are negative integers, and the ground level is zero. They can learn how to count numbers by moving up and down the stairs in this manner. There are also examples that use dice, tiles, and buttons to further simplify the concept.

#### Subtraction of Integers  with  the Help of a  Number Line

After learning how to add integers, students learn how to subtract them using a single line. This process can be done in a variety of ways, which are detailed in this section.

#### We cover all exercises in the chapter given below

Students should practise as many questions from this chapter as possible. This is because solving these questions helps them gauge their understanding of the chapter. Extramarks has answers to all the textbook questions. Students can improve their preparations by using our NCERT Solutions for Class 6 Mathematics Chapter 6. Extramarks, one of India's leading e-learning platforms, provides students with accurate and dependable learning materials. No wonder students have complete trust and faith in Extramarks.

#### Why NCERT Solutions For Class 6 Mathematics Chapter 6 Integers are a must-read?

Here are some more benefits of referring to NCERT solution for Class 6 Mathematics:

• The language in the solutions is clear and aids students in better understanding of the concepts.
• Individuals can use solutions to clear their doubts immediately because of the simple yet informative explanation given for each answer.
• The use of bullet points, graphs, charts, and other visual aids enhances the learning experience.
• NCERT Solutions for Class 6 Mathematics Chapter 6 are made by subject matter experts as per the latest CBSE guidelines.

Q.1 Write opposites of the following :
(a) Increase in weight
(b) 30 km north
(c) 80 m east
(d) Loss of Rs. 700
(e) 100 m above sea level

Ans.

(a) Decrease in weight

(b) 30 km south

(c) 80 m west

(d) Profit of Rs. 700

(e) 100 m below sea level

Q.2 Represent the following numbers as integers with appropriate signs.
(a) An aeroplane is flying at a height two thousand metre above the ground.
(b) A submarine is moving at a depth, eight hundred metre below the sea level.
(c) A deposit of rupees two hundred.
(d) Withdrawal of rupees seven hundred.

Ans.

1. +2000
2. – 800
3. + 200
4. –700

Q.3 Represent the following numbers on the number line :
(a) +5 (b) –10 (c) +8
(d) –1 (e) –6

Ans.

(a) (b) (c) (d) (e) Q.4 Adjacent figure is a vertical number line, representing integers. Observe it and locate the following points :
(a) If point D is + 8, then which point is – 8?
(b) Is point G a negative integer or a positive integer?
(c) Write integers for points B and E.
(d) Which point marked on this number line has the least value?
(e) Arrange all the points in decreasing order of value. Ans.

(a) If point D is +8, then –8 is represented by F.

(b Point G is a negative integer.

(c) Point B is represented by the integer +4 and point E is represented by the integer –10.

(d) Point E is farthest towards negative, so it has least value.

(e) The points arranged in decreasing order of their values are given as follows:

D, C, B, A, O, H,G, F, E.

Q.5 Following is the list of temperatures of five places in India on a particular day of the year.
Place Temperature
Siachin 10°C below 0°C ……………..
Shimla 2°C below 0°C ……………..
Ahmedabad 30°C above 0°C ……………..
Delhi 20°C above 0°C ……………..
Srinagar 5°C below 0°C ……………..

(a) Write the temperatures of these places in the form of integers in the blank column.
(b) Following is the number line representing the temperature in degree Celsius. Plot the name of the city against its temperature.
(c) Which is the coolest place?
(d) Write the names of the places whose temperatures are above 10°C.

Ans.

(a)
Place Temperature
Siachin 10°C below 0°C –10°C
Shimla 2°C below 0°C –2°C
Ahmedabad 30°C above 0°C 30°C
Delhi 20°C above 0°C 20°C
Srinagar 5°C below 0°C –5°C

(b) (c) Siachin is the coolest place.
(d) Ahmedabad and Delhi are the places whose temperatures are above 10°C.

Q.6 In each of the following pairs, which number is to the right of the other on the number line?
(a) 2, 9 (b) – 3, – 8 (c) 0, – 1
(d) – 11, 10 (e) –6, 6 (f) 1,–100

Ans.

(a) Since 9 > 2 so it will lie to the right of the other on the number line.

(b) Since –3 > –8 so it will lie to the right of the other on the number line.

(c) Since 0 > –1 so it will lie to the right of the other on the number line.

(d) Since 10 > –11 so it will lie to the right of the other on the number line.

(e) Since 6 > –6 so it will lie to the right of the other on the number line.

(f) Since 1 > –100 so it will lie to the right of the other on the number line.

Q.7 Write all the integers between the given pairs (write them in the increasing order.
(a) 0 and – 7 (b) –4 and 4
(c) –8 and –15 (d) –30 and –23

Ans.

(a) Integers lying between 0 and –7 are

–6, –5, –4, –3, –2, –1.

(b) Integers lying between –4 and 4 are

–3, –2, –1, 0, 1, 2, 3.

(c) Integers lying between –8 and –15 are

–14, –13, –12, –11, –10, –9.

(d) Integers lying between –30 and –23 are

–29, –28, –27, –26, –25, –24.

Q.8 (a)Write four negative integers greater than –20.
(b)Write four negative integers less than –10.

Ans.

(a) Four negative integers greater than –20 are

–19, –18, –17 and –16.

(b) Four negative integers less than –10 are

–11, –12, –13 and –14.

Q.9 For the following statements, write True (T) or False (F). If the statement is false, correct the statement.
(a) – 8 is to the right of – 10 on a number line.
(b) – 100 is to the right of – 50 on a number line.
(c) Smallest negative integer is – 1.
(d) – 26 is greater than – 25.

Ans.

(a) Since –8 > –10, so it is to the right of number line. Hence, the statement is True.

(b) The statement is False as –100 is to the left of –50 on a number line.

(c) The statement is False. The correct statement is largest negative integer is –1.

(d) The statement is False. The correct statement is –26 is smaller than –25.

Q.10 Draw a number line and answer the following :
(a) Which number will we reach if we move 4 numbers to the right of – 2?
(b) Which number will we reach if we move 5 numbers to the left of 1?
(c) If we are at – 8 on the number line, in which direction should we move to reach – 13?
(d) If we are at – 6 on the number line, in which direction should we move to reach –1?

Ans.

(a)
We will reach at 2, if we move 4 numbers to the right of –2. (b)
We will reach –4, if we move 5 numbers to the left of 1. (c)
We should move to the left to reach –13 from –8. (d)
We should move to the right to reach –1 from –6. Q.11 Using the number line write the integer which is :
(a) 3 more than 5
(b) 5 more than –5
(c) 6 less than 2
(d) 3 less than –2

Ans.

(a)
The number 3 more than 5 is 8. (b)
The number 5 more than –5 is 0. (c)
The number 6 less than 2 is –4. (d)
The number 3 less than –2 is –5. Q.12 Use number line and add the following integers :
(a) 9 + (– 6)
(b) 5 + (– 11)
(c) (– 1) + (– 7)
(d) (– 5) + 10
(e) (– 1) + (– 2) + (– 3)
(f) (– 2) + 8 + (– 4)

Ans.

(a) 9 + (–6) (b) 5 + ( –11) (c) (–1) + (–7) (d) (–5) + 10 (e) (–1) + (–2) + (–3) (f) (–2) + 8 + (–4) Q.13 Add without using number line :
(a) 11 + (– 7) (b) (– 13) + (+ 18)
(c) (– 10) + (+ 19) (d) (– 250) + (+ 150)
(e) (– 380) + (– 270) (f) (– 217) + (– 100)

Ans.

$\begin{array}{l}\text{(a)}11+\left(-7\right)\\ \text{}=11-7\\ \text{}=4\\ \text{(b)}-13+\left(+18\right)\\ \text{}=-13+18\\ \text{}=5\\ \text{(c)}\left(-10\right)+\left(+19\right)\\ \text{}=-10+19\\ \text{}=9\\ \text{(d)}-250+\left(+150\right)\\ \text{}=-250+150\\ \text{}=-100\\ \text{(e)}-380+\left(-270\right)\\ \text{}=-380-270\\ \text{}=-650\\ \text{(f) (}-217\right)+\left(-100\right)\\ \text{}=-217-100\\ \text{}=-317\end{array}$

Q.14 Find the sum of :
(a) 137 and – 354 (b) – 52 and 52
(c) – 312, 39 and 192 (d) –50,–200 and 300

Ans.

(a) 137 + (–354)
= 137 – 354
= –217

(b) –52 + 52
= 0

(c) (–312) + 39 + 192
= –312 + 39 + 192
= –81

(d) (–50) + (–200) + 300
= –50 – 200 + 300
= –250 + 300
= 50

Q.15 Find the sum :
(a) (– 7) + (– 9) + 4 + 16
(b) (37) + (– 2) + (– 65) + (– 8)

Ans.

(a) (–7) + (–9) + 4 + 16
= –7 – 9 + 4 +16
= –16 + 20
= 4

(b) 37 + (–2) + (–65) + (–8)
= 37 – 2 – 65 – 8
= 37 – 75
= – 38

Q.16 Find
(a) 35 – (20) (b) 72 – (90)
(c) (– 15) – (– 18) (d) (–20) – (13)
(e) 23 – (– 12) (f) (–32) – (– 40)

Ans.

(a) 35 – 20

= 15

(b) 72 – 90

= –18

(c) (–15) – (–18)

= –15 + 18

= 3

(d) (–20) – (13)

= –20 –13

= –33

(e) 23 – (–12)

= 23 + 12

= 35

(f) (–32) – (–40)

= –32 + 40

= 8

Q.17 Fill in the blanks with >, < or = sign.
(a) (– 3) + (– 6) ______ (– 3) – (– 6)
(b) (– 21) – (– 10) _____ (– 31) + (– 11)
(c) 45 – (– 11) ______ 57 + (– 4)
(d) (– 25) – (– 42) _____ (– 42) – (– 25)

Ans.

(a) (– 3) + (– 6) ______ (– 3) – (– 6)
–3 – 6 ______ –3 + 6
–9 ______ 3
Hence, (– 3) + (– 6) __<___ (– 3) – (– 6)

(b) (– 21) – (– 10) _____ (– 31) + (– 11)
–21 + 10 _____ –31 – 11
–11 _____ –42
Hence, (– 21) – (– 10) __>__ (– 31) + (– 11)

(c) 45 – (– 11) ______ 57 + (– 4)
45 + 11 ____ 57 – 4
56 ____ 53
Hence, 45 – (– 11) __>__ 57 + (– 4)

(d) (– 25) – (– 42) _____ (– 42) – (– 25)
–25 + 42 _____ –42 + 25
17 _____ –17
Hence, (– 25) – (– 42) __>__ (– 42) – (– 25)

Q.18 Fill in the blanks.
(a) (– 8) + _____ = 0
(b) 13 + _____ = 0
(c) 12 + (– 12) = ____
(d) (– 4) + ____ = – 12
(e) ____ – 15 = –10

Ans.

(a) (– 8) + __8___ = 0

(b) 13 + __(–13)_ = 0

(c) 12 + (– 12) = __0__

(d) (– 4) + __(–8)__ = – 12

(e) __5__ – 15 = –10

Q.19 Find
(a) (– 7) – 8 – (– 25)
(b) (– 13) + 32 – 8 – 1
(c) (– 7) + (– 8) + (– 90)
(d) 50 – (– 40) – (– 2)

Ans.

1. (– 7) – 8 – (– 25)

= –7 –8 + 25

=–15 + 25

= 10

1. (– 13) + 32 – 8 – 1

= –13 + 32 – 8 – 1

= –22 + 32

= 10

1. (– 7) + (– 8) + (– 90)

= –7 – 8 – 90

–105

1. 50 – (– 40) – (– 2)

= 50 + 40 + 2

= 92.

Q.20 Find
(a) (– 7) – 8 – (– 25)
(b) (– 13) + 32 – 8 – 1
(c) (– 7) + (– 8) + (– 90)
(d) 50 – (– 40) – (– 2)

Ans.

(a) (– 7) – 8 – (– 25)
= –7 –8 + 25
= –15 + 25
= 10

(b) (– 13) + 32 – 8 – 1
= –13 + 32 – 8 – 1
= –22 + 32
= 10

(c) (– 7) + (– 8) + (– 90)
= –7 – 8 – 90
–105

(d) 50 – (– 40) – (– 2)
= 50 + 40 + 2
= 92.

Q.21 Find
(a) (– 7) – 8 – (– 25)
(b) (– 13) + 32 – 8 – 1
(c) (– 7) + (– 8) + (– 90)
(d) 50 – (– 40) – (– 2)

Ans.

(a) (– 7) – 8 – (– 25)

= –7 –8 + 25

= –15 + 25

= 10

(b) (– 13) + 32 – 8 – 1

= –13 + 32 – 8 – 1

= –22 + 32

= 10

(c) (– 7) + (– 8) + (– 90)

= –7 – 8 – 90

= –105

(d) 50 – (– 40) – (– 2)

= 50 + 40 + 2

= 92

##### FAQs (Frequently Asked Questions)
1. What are the various integer types?

Integers are divided into three categories. The following are — (a) Positive integers: Positive numbers are represented with a positive sign, but this is not always the case. (1) Positive integers: Represented by a negative sign in front of them, which is required. (2) Negative integers: Represented by a negative sign in front of them, which is mandatory. -1, -10, -100, and so on, as well as (c) Zero: Zero is neither negative nor positive, although it is counted as an integer.

2. What are the advantages of using NCERT Solutions?

Students can boost their exam preparations by using NCERT Solutions. Every topic is presented in a clear and lucid manner, allowing students to understand various topics explained in the answers in a better way. The use of graphs and charts also makes learning more interesting and engaging.

3. How many exercises are there in Chapter 6 of Class 6 Mathematics?

There are a total of three exercises in this chapter, each focussing on the various aspects of integers. Each of these exercises carry:-

Exercise 6.2 – 10 questions

Exercise 6.2 – 5 questions

Exercise 6.3 – 4 questions

4. What are the different types of operations you can do with integers?

All four operations – addition, subtraction, multiplication, and division can be done with integers. To solve integers, students must follow rules and learn about their properties.