NCERT Solutions for Class 6 Maths Chapter 6 Integers

Updated on Apr 14, 2020 - 4:06 p.m. IST by Safeer PP

NCERT solutions for class 6 maths chapter 6 Integers- You have studied about whole numbers and natural numbers in the second chapter of this class. Now we are going to study integers in this chapter. Before discussing the integers you must have cleared concepts regarding natural numbers and whole numbers. CBSE NCERT solutions for class 6 maths chapter 6 Integers is covering the solutions of each question of the integer. Natural numbers are the collection of 1, 2, 3, 4, 5,..... If you include number 0 (zero) to this collection you get a new collection of numbers known as whole numbers. So, the whole number is the collection of 0, 1, 2, 3, 4,... You have studied these numbers in the second chapter. 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. Integers are the collection of numbers between negative infinity to positive infinity ( – 3, – 2, – 1, 0, 1, 2, 3). Numbers 1, 2, 3,.... called positive numbers are the positive integers and – 1, – 2, – 3, ... called negative integers. Solutions of NCERT for class 6 maths chapter 6 Integers are there to assist you while solving the unsolved problems. 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. If you need NCERT Solutions for other classes and subjects then you click on the given link. All the exercises are listed below.

Exercise 6.1

Exercise 6.2

Exercise 6.3

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 :

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 $+5$

(b) Here B indicates the position of $-10$

(c) Here C represents the position of $+8$

(d) Here D represents the $-1$

(e) Here E represents the $-6$

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:

(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.

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.

(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)

(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 $4$ numbers to the right of $-2.$ we get 2.

(b) if we move $5$ numbers to the left of $1$ we get -4

(c) If we are at $-8$ on the number line, we should move 5 number to the $-8$ left side on the number line.

(d) If we are at $-6$ on the number line, then we should move 5 number right to the $-6$ 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

(b) $5$ more than $-5$
The answer is 5 + (-5) = 0

(c) $6$ less than $2$
the answer is 2 - 6 = -4

(d) $3$ less than $-2$
The answer is 3 + (-2) = 1

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.

(b) $5+(-11)$
Initially, move 0 to 5 and then 11 number left to the 5 on the number line.

(d) $(-5)+10$
Initially, move 0 to -5 and then 2 number right to the -5 and again moves 10 number right to the -5

(e) $(-1)+(-2)+(-3)$
Initially, move 0 to -1 and then 2 number left to the -1 and again move 3 number left to the -3

(f) $(-2)+8+(-4)$
First, move 0 to -2 and then -2 to 8 number right on the number line and then move 4 numbers left to the 6

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

NCERT solutions for class 6 mathematics chapter-wise

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

NCERT solutions for class 6 subject wise

NCERT Solutions for class 6 maths

Solutions of NCERT for class 6 science

How to use NCERT solutions for class 6 maths chapter 6 Integers?

Please ensure that you have clear concepts of chapter 2 Whole Numbers.
Learn the concepts of integers using the NCERT textbook.
Take a look through some examples to understand these concepts' application.
Apply these concepts while solving these exercises.
If you feel trouble in solving any question you can take the assistance of NCERT solutions for class 6 maths chapter 6 Integers.

Keep working hard and happy learning!

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NCERT Solutions for Class 6 Maths Chapter 6 Integers

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NCERT solutions for class 6 maths chapter 6 Integers Exercise: 6.2

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NCERT solutions for class 6 maths chapter 6 Integers Exercise: 6.3

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NCERT solutions for class 6 mathematics chapter-wise

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How to use NCERT solutions for class 6 maths chapter 6 Integers?

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