NCERT Solutions for Class 6 Maths Chapter 6 Integers

Edited By Ramraj Saini | Updated on Nov 30, 2023 09:45 AM IST

NCERT Solutions for Class 6 Maths Chapter 6 provided here. The solutions are prepared by expet team at careers360 keeping in mind the latest CBSE syllabus 2023. Before discussing the integers you must have cleared concepts in NCERT regarding Natural Numbers and Whole Numbers. NCERT Class 6 solution for chapter 6 Integers is covering the solutions of each question of the integer. If you put the negative numbers and the whole numbers together, the new collection of numbers will look like –1, – 2, – 3,–4, –5,...... 0, 1, 2, 3, 4, 5,..., and this collection of numbers is known as Integers.

Latest: Important Maths Formulas for Class 6 - Chapterwise

This Story also Contains

NCERT Solutions for Class 6 Maths Chapter 6 Integers - Important Formula
NCERT Solutions for Class 6 Maths Chapter 6 Integers - Important Points
NCERT Solutions for Class 6 Maths Chapter 6 Integers
NCERT Solutions for Class 6 Maths Chapter 6 Integers (Intext Questions and Exercise)
NCERT Solutions for Class 6 Maths Chapter 6 Integers Exercise: 6.1
NCERT Solutions for Class 6 Maths Chapter 6 Integers Exercise: 6.2
NCERT Solutions for Class 6 Maths Chapter 6 Integers Exercise: 6.3
Integers Class 6 Maths Chapter 2-Topics
NCERT Solutions for Class 6 Mathematics Chapter-wise
Key features of NCERT Solutions for Class 6 Maths chapter 6

$NCERT Solutions for Class 6 Maths Chapter 6 Integers$

NCERT Solutions for Class 6 Maths Chapter 6 Integers

It is advisable that students must complete NCERT Syllabus for Class 6 Maths in time. This chapter contains a total of 19 questions in 3 exercises. NCERT solutions for Class 6 Maths chapter 6 Integers is covering every question in detail. Students must refer to the NCERT Class 6 Maths Books and solve as many questions as they can. If you need NCERT Solutions for other classes and subjects then you click on the given link.

NCERT Solutions for Class 6 Maths Chapter 6 Integers - Important Formula

Integers are numbers like -4, -3, -1, 0, 1, 2, 3, 4, and so on. They include both positive and negative whole numbers.
Positive integers are numbers like 1, 2, 3, 4, 5, and so on. They are greater than zero. Negative integers are numbers like -1, -2, -3, and so on. They are less than zero.
The number 0 is an integer that is neither positive nor negative. It is right in the middle of the number line.
If we imagine a number line, with 0 in the centre, all the numbers to the right of 0 are positive integers, and all the numbers to the left of 0 are negative integers.

Opposite numbers are two integers that have the same distance from 0 on the number line but are on opposite sides. For example, 3 and -3 are opposite numbers.
Integer + Opposite Integer =0
The absolute value of an integer is the numerical value of the integer without considering its sign. If the integer is positive or zero, the absolute value is the same as the number itself. If the integer is negative, the absolute value is its opposite (positive) value.

Operation	Rule	Result
Addition of integers	Same sign: Add the absolute values and keep the same sign	Integer with the same sign
		Absolute value is the sum of the absolute values
	Opposite signs: Take the difference between the absolute values and keep the sign of the greater absolute value	Integer with the sign of the addend (integer) that has a greater absolute value has a greater absolute value
		Absolute value is the difference between the absolute values

To subtract an integer b from another integer a, you can change the sign of b and add it to a.
- a - b = a + (-b)

If you subtract one integer (b) from another integer (a), the result (a - b) is also an integer.
All the properties that apply to whole numbers also apply to integers. The operations of addition, subtraction, multiplication, and division work the same way for integers as they do for whole numbers.

NCERT Solutions for Class 6 Maths Chapter 6 Integers - Important Points

Negative Numbers: Numbers with a negative sign that represent values below zero on the number line. They are used in various contexts such as temperature scales, water levels, oil levels, debit accounts, and outstanding dues.

Integers: The collection of numbers including negative numbers (e.g., -4, -3, -2, -1) and positive numbers (e.g., 1, 2, 3, 4). Negative integers refer to numbers below zero, and positive integers refer to numbers above zero.

Successor and Predecessor: Adding one to a given number yields its successor, while subtracting one yields its predecessor.

Addition of Integers: a) Same Sign: When adding two integers with the same sign, add them and maintain the same sign. Positive integers added together result in a positive integer, and negative integers added together result in a negative integer. b) Different Signs: When adding one positive and one negative integer, subtract the numbers as whole numbers (ignoring their signs) and use the sign of the integer with the greater absolute value. The bigger integer is determined by ignoring the signs. c) Subtraction: Subtracting an integer is equivalent to adding its additive inverse.

Number Line Representation: Addition and subtraction of integers can be visualized and demonstrated on a number line.

Free download NCERT Solutions for Class 6 Maths Chapter 6 Integers PDF for CBSE Exam.

NCERT Solutions for Class 6 Maths Chapter 6 Integers

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NCERT Solutions for Class 6 Maths Chapter 6 Integers (Intext Questions and Exercise)

NCERT Solutions for Class 6 Maths Chapter 6 Integers Exercise: 6.1

Q1 Write opposites of the following :

(a) Increase in weight

(b) $30 \; km$ north

(d) Loss of $Rs \; 700$

(e) $100\; m$ above sea level

Answer: The opposites are-

(a) Decrease in weight

(b) 30 km south

(d) profit of Rs 700

(e) 100 m below sea level

Q2 Represent the following numbers as integers with appropriate signs.

(a) An airplane is flying at a height two thousand meters above the ground.

(b) A submarine is moving at a depth, eight hundred metre below the sea level.

(d) Withdrawal of rupees seven hundred.

Answer: (a) An airplane is flying at a height two thousand meters above the ground. So it can be written as-
+2000m

(b) A submarine is moving at a depth, eight hundred meters below the sea level. In integers, it can be written as-
- 800m

+ Rs 200

(d) Withdrawal of rupees seven hundred. It can be written as-

- Rs 700

Q3 Represent the following numbers on a number line :

(a) + 5

(b) – 10

(d) – 1

(e) – 6

Answer: Draw a straight line and place a mark on it at a distance of the 1cm unit.

(a) Here A indicates the position of
1595479496196

(b) Here B indicates the position of
1595479496547
(c) Here C represents the position of
1595479500570
(d) Here D represents the
1595479500984
(e) Here E represents the
1595479499550

Q4 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?

(d) Which point marked on this number line has the least value?

(e) Arrange all the points in decreasing order of value

Answer:

1595479666640
(a) If D is a $+8$ then F represents $-8$ (by counting on the vertical number line)

(b) G is a negative integer because it is below than point zero (0)

(d) E has the least value of $-10$

(e) Decreasing order of all the points are-
$D>C>B>A>0>H>G>F$

Q5: Following is the list of temperatures of five places in India on a particular day of the year

A5: Place Temperature

Siachin $10^{\circ}C$ below $0^{\circ}C$ .................

Shimla $2^{\circ}C$ below $0^{\circ}C$ .................

Ahmedabad $30^{\circ}C$ above $0^{\circ}C$ .................

Delhi $20^{\circ}C$ above $0^{\circ}C$ .................

Srinagar $5^{\circ}C$ below $0^{\circ}C$ .................

(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.

1595479824534
(c) Which is the coolest place?

(d) Write the names of the places where temperatures are above $10^{\circ}C$ .

Answer: (a)

Place	Temperature	Integer form
Siachin	$10^{\circ}C$ below $0^{\circ}C$	-10 $^0C$
Shimla	$2^{\circ}C$ below $0^{\circ}C$	-2 $^0C$
Ahmedabad	$30^{\circ}C$ above $0^{\circ}C$	+30 $^0C$
Delhi	$20^{\circ}C$ above $0^{\circ}C$	+20 $^0C$
Srinagar	$5^{\circ}C$ below $0^{\circ}C$	-5 $^0C$

(b)
1595480661846
(c) The coolest pace is Siachin with -10 $^0C$

(d) The places where the temperature is above 10 $^0C$ are-
(i) Delhi 20 $^0C$
(ii) Ahmedabad 30 $^0C$

Q6 In each of the following pairs, which number is to the right of the other on the number line?

(a) $2,9$

(b) $-3,-8$

(d) $-11,1$

(e) $-6,6$

(f) $1,-100$

Answer: In a number line, if an integer is greater than another integer, then it is placed on the right side of the number line. So, by this information, we can quickly identify which number is on the right side, in the given following pairs.
(a) 9 is right to the 2 ( $9 > 2$ )

(b) -3 is right to the - 8 ( $-3 > -8$ )

(d) 10 is right to the -11 $(10 > -11)$

(e) 6 is right to the -6 $(6 > -6)$

(f) 1 is right to the -100 $(1 > -100)$

Q7 Write all the integers between the given pairs (write them in the increasing order.)

(a) $0 \; and\; -7$

(b) $-4 \; and\; 4$

(d) $-30 \; and\; -23$

Answer: (a) The integers between $0 \; and\; -7$ are;
$-6,-5,-4,-3,-3,-1$

(b) Integers between $-4 \; and\; 4$ are;
$-3,-2,-1,0,1,2,3,$

$-14,-13,-12,-11,-10,-9,$

(d) Integers between $-30 \; and\; -23$ are;

$-29,-28,-27,-26,-25,-24$

Q8 (a) Write four negative integers greater than $-20.$

(b) Write four integers less than $-10.$

Answer: (a) four negative integers greater than $-20.$ are;

$-19,-18,16,-9$ (all negative integers wg=ho comes before -20)

(b) four integers less than $-10.$ are;
$-19,-18,16,-11$ (integers which comes after the -10)

Q9 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.

(d) $-26$ is greater than $-25$

Answer: (a) True, ( $-8$ is greater than $-10$ so it comes on the right side)

(b) False. $-100$ is to the left side of $-50$ on a number line

(d) False,
Correction; $-26$ is smaller than $-25$

Q10 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 $1$ .

(d) If we are at $-6$ on the number line, in which direction should we move to reach $-1?$

Answer: (a) if we move numbers to the right of -2. we get 2.
1595481554443
(b) if we move numbers to the left of we get -4
1595481555157
(c) If we are at on the number line, we should move 5 number to the left side on the number line.
1595481555761
(d) If we are at on the number line, then we should move 5 number right to the on the number line.

NCERT Solutions for Class 6 Maths Chapter 6 Integers Exercise: 6.2

Q1 Using the number line write the integer which is :

(a) $3$ more than $5$

(b) $5$ more than $-5$

(d) $3$ less than $-2$

Answer: (a) $3$ more than $5$
The answer is 5 + 3 = 8

(a) more than The answer is 5 + 3 = 8 1595482151407

Q2 Use number line and add the following integers :

(a) $9+(-6)$

(b) $5+(-11)$

(d) $(-5)+10$

(e) $(-1)+(-2)+(-3)$

(f) $(-2)+8+(-4)$

Answer: Addition by using the number line method-
(a) $9+(-6)$
Initially, move 0 to 9 and then 6 number left to the 9 on the numberline.
1595482549745

Q3 Add without using number line :

(a) $11+(-7)$

(b) $(-13)+(+18)$

Answer: In addition without using the number line, in this method, we have to split one number according to the other number such that $a + (-a) = 0$ .

Now,

(a) $11+(-7)$ = 4 + (7)+ (-7) = 4

(b) $(-13)+(+18)$
= -13 + (13) + 5
= 5

(d) $(-250)+(+150)$
= (- 100) + (- 150) + (150)
= - 100

(e) $(-380)+(-270)$
= - (380 + 270 )
= - 650

(f) $(-217)+(-100)$
= - (217 + 100)
= - 317

Q4 Find the sum of:

(a) $137 \; and \; -354$

(b) $-52\; and\; 52$

(d) $-50,\; -200\; and\; 300$

Answer: It is known that the sum of $-a + (a) = 0$ .

Therefore,
(a) the sum of $137 \; and \; -354$
= 137 + (-137) + (- 217)
= - 217

(b) the sum of $-52\; and\; 52$
= -52 + 52 = 0

(d) the sum of $-50,\; -200\; and\; 300$
= - (50 + 200 ) + (300)
= - 250 + (250) + 50
= 50

Q5 Find the sum :

(a) $(-7)+(-9)+4+16$

(b) $(37)+(-2)+(-65)+(-8)$

Answer: It is known that the sum of $-a + (a) = 0$ .
Therefore,
(a) $(-7)+(-9)+4+16$
= - (9 + 7) + 4 + 16
= (- 16) + 4 + 16
= 4

Also we can split the 16 into (- 9 and -7 ).

(b) $(37)+(-2)+(-65)+(-8)$
= 37 + (- 37) + (- 28) + (-2) + (- 8)
= 0 - (37 + 28 + 8)
= - 73

NCERT Solutions for Class 6 Maths Chapter 6 Integers Exercise: 6.3

Q1 Find

(a) $35-(20)$

(b) $72-(90)$

(d) $(-20)-(13)$

(e) $23-(-12)$

(f) $(-32)-(-40)$

Answer: It is known that the sum of $-a + (a) = 0$ .
So, we have to split the number in order to cancel out with other numbers.

(a) $35-(20)$
= 15 + (- 20) + 20
= 15 + 0 = 15

(b) $72-(90)$
= 72 - (72) - 18
= 0 - 18 = -18

(d) $(-20)-(13)$
= - (20 + 13 )
= -33

(e) $23-(-12)$
= 23 + 12
= 35

(f) $(-32)-(-40)$
= (- 32) + 40
= (- 32) + (32) + 8
= 0 + 8
= 8

Q2 Fill in the blanks with or sign.

(a) (– 3) + (– 6) ______ (– 3) – (– 6)

(b) (– 21) – (– 10) _____ (– 31) + (– 11)

(d) (– 25) – (– 42) _____ (– 42) – (– 25)

Answer: (a) (– 3) + (– 6) ______ (– 3) – (– 6)
LHS $\Rightarrow$ - 3 - 6 = -9
RHS $\Rightarrow$ - 3 + 6 = +3
Hence LHS < RHS

(b) (– 21) – (– 10) _____ (– 31) + (– 11)
LHS $\Rightarrow$ - 21 +10 = -11
RHS $\Rightarrow$ -31 - 11 = -42

Hence LHS > RHS

(d) (– 25) – (– 42) _____ (– 42) – (– 25)
LHS $\Rightarrow$ - 25 + 42 = 17
RHS $\Rightarrow$ -42 + 25 = -17

Hence LHS > RHS

Q3 Fill in the blanks.

(a) (– 8) + _____ = 0

(b) 13 + _____ = 0

(d) (– 4) + ____ = – 12

(e) ____ – 15 = – 10

Answer: a) (– 8) + _____ = 0
Since we know that, $-a +a =0$ . Therefore, the blank space should be + 8.

(b) 13 + _____ = 0
The sum is zero. Therefore it should be additive inverse of 13. $\Rightarrow$ -13( is the answer)

(d) (– 4) + ____ = – 12
The integer in blank space should be -8

(e) ____ – 15 = – 10
The integer in blank space should be +5

Q4 Find
(a) $(-7)-8-(-25)$
(b) $(-13)+32-8-1$
(c) $(-7)+(-8)+(-90)$
(d) $50-(-40)-(-2)$

Answer: We already know that the sum of the additive inverse is Zero ( $a+ (-a) = 0$ )

(a) $(-7)-8-(-25)$
$\\= -7 -8 +25\\ =-(7+8)+(15)+10\\ =-15+(-15)+10\\ =0+10 =10$

(b) $(-13)+32-8-1 = (-13)+ 32 -(8+1)$
$\\= (-13)+ 32 -(9)\\ =-(13+9)+32\\ =(-22)+22+10\\ =0+10=10$

(d) $50-(-40)-(-2)$
$= 50 +40 +2$
$=92$

Integers Class 6 Maths Chapter 2-Topics

Integers
Addition of Integers
Subtraction of Integers with the help of a Number Line

Also Check -

NCERT Books and NCERT Syllabus here:

NCERT Solutions for Class 6 Mathematics Chapter-wise

Chapters No.	Chapters Name
Chapter - 1	Knowing Our Numbers
Chapter - 2	Whole Numbers
Chapter - 3	Playing with Numbers
Chapter - 4	Basic Geometrical Ideas
Chapter - 5	Understanding Elementary Shapes
Chapter - 6	Integers
Chapter - 7	Fractions
Chapter - 8	Decimals
Chapter - 9	Data Handling
Chapter -10	Mensuration
Chapter -11	Algebra
Chapter -12	Ratio and Proportion
Chapter -13	Symmetry
Chapter -14	Practical Geometry

Key features of NCERT Solutions for Class 6 Maths chapter 6

Thoroughly Designed Solutions: The NCERT Solutions for Class 6 Maths Chapter 6 are meticulously crafted to offer comprehensive and step-by-step explanations for every problem and concept addressed in the chapter.

Enhanced Conceptual Clarity: The main objective of NCERT Maths Class 6 Chapter 6 solutions is to enhance the students' conceptual clarity by presenting intricate concepts in a simplified manner, making it easier for them to grasp.

Inclusive Topic Coverage: The solutions for Maths Class 6 Chapter 6 encompass all essential topics and subtopics, leaving no aspect of the chapter unaddressed. This comprehensive approach ensures that students gain a thorough understanding of the entire chapter.

Focus on Exam Preparedness: With a focused approach towards exam preparation, the NCERT Class 6 Maths chapter number 6 solutions equip students with the necessary skills and strategies to tackle questions effectively and excel in their exams.

NCERT Solutions for Class 6 Subject Wise

NCERT Solutions for Class 6 Maths

NCERT Solutions for Class 6 Science

How to Use NCERT Solutions for Class 6 Maths Chapter 6 Integers?

Please ensure that you have clear concepts of integers questions for class 6.
Learn the concepts of integers using the NCERT textbook.
Take a look through some examples to understand these concepts' applications.
Apply these concepts while solving these exercises.
If you feel trouble solving any question you can take the assistance of NCERT Solutions for Class 6 .
Keep working hard and happy learning!

Frequently Asked Questions (FAQs)

1. Why Class 6 NCERT solutions of chapter integers is important?

The NCERT questions of Class 6 Mathematics are provided for practising the concepts studied in the chapter and also will help in exams. Also, chapter integers will be helpful in higher studies.

2. What are the concepts covered in Integers Class 6 NCERT Maths chapter?

The basic idea of integers and the concept of addition and subtraction of integers are the main concepts covered in the chapter Integers. The questions based on these concepts are solved in the NCERT solutions for Class 6 Maths chapter 6 Integers.

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NCERT Solutions for Class 6 Science Chapter 1 Food Where Does It Come From

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

NCERT Solutions for Class 6 Maths Chapter 13 Symmetry

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Option 1) $0.34\; J$	Option 2) $0.16\; J$
Option 3) $1.00\; J$	Option 4) $0.67\; J$

Option 1) $2,000 \; J - 5,000\; J$	Option 2) $200 \, \, J - 500 \, \, J$
Option 3) $2\times 10^{5}J-3\times 10^{5}J$	Option 4) $20,000 \, \, J - 50,000 \, \, J$

Option 1) $K/2\,$	Option 2) $\; K\;$
Option 3) $zero\;$	Option 4) $K/4$

Option 1) $11.2\, L\, H_{2(g)}$ at STP is produced for every mole $HCL_{(aq)}$ consumed	Option 2) $6L\, HCl_{(aq)}$ is consumed for ever $3L\, H_{2(g)}$ produced
Option 3) $33.6 L\, H_{2(g)}$ is produced regardless of temperature and pressure for every mole Al that reacts	Option 4) $67.2\, L\, H_{2(g)}$ at STP is produced for every mole Al that reacts .

Option 1) 0.02	Option 2) 3.125 × 10^-2
Option 3) 1.25 × 10^-2	Option 4) 2.5 × 10^-2

Option 1) decrease twice	Option 2) increase two fold
Option 3) remain unchanged	Option 4) be a function of the molecular mass of the substance.

Option 1) Molality	Option 2) Weight fraction of solute
Option 3) Fraction of solute present in water	Option 4) Mole fraction.

Option 1) twice that in 60 g carbon	Option 2) 6.023 × 10²²
Option 3) half that in 8 g He	Option 4) 558.5 × 6.023 × 10²³

Option 1) less than 3	Option 2) more than 3 but less than 6
Option 3) more than 6 but less than 9	Option 4) more than 9

NCERT Solutions for Class 6 Maths Chapter 6 Integers

NCERT Solutions for Class 6 Maths Chapter 6 Integers - Important Formula

NCERT Solutions for Class 6 Maths Chapter 6 Integers - Important Points

NCERT Solutions for Class 6 Maths Chapter 6 Integers

NCERT Solutions for Class 6 Maths Chapter 6 Integers (Intext Questions and Exercise)

NCERT Solutions for Class 6 Maths Chapter 6 Integers Exercise: 6.1

NCERT Solutions for Class 6 Maths Chapter 6 Integers Exercise: 6.2

NCERT Solutions for Class 6 Maths Chapter 6 Integers Exercise: 6.3

Integers Class 6 Maths Chapter 2-Topics

NCERT Solutions for Class 6 Mathematics Chapter-wise

Key features of NCERT Solutions for Class 6 Maths chapter 6

NCERT Solutions for Class 6 Subject Wise

How to Use NCERT Solutions for Class 6 Maths Chapter 6 Integers?

Frequently Asked Questions (FAQs)

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