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NCERT Solutions for Class 6 Maths Chapter 6 Integers

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

(c) 80 \; m east

(d) Loss of Rs \; 700

(e) 100\; m above sea level

Answer: The opposites are-

(a) Decrease in weight

(b) 30 km south

(c) 326 AD

(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.

(c) A deposit of rupees two hundred.

(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

(c) A deposit of rupees two hundred. In integer form, it can be written as-

+ 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

(c) + 8

(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 +51595479489301
15954794961961595479489641

(b) Here B indicates the position of -101595479489982
15954794965471595479490335
(c) Here C represents the position of +81595479490686
15954795005701595479491003
(d) Here D represents the -11595479491326
15954795009841595479491644
(e) Here E represents the -61595479491974
15954794995501595479492323

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?

(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

Answer:

15954796666401595479662960
(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)

(c) Integers for point B and E are +4 and -10 respectively.

(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.

15954798245341595479820328
(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)
15954806618461595480657752
(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

(c) 0,-1

(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 )

(c) 0 is right to the -1 (0 > -1)

(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

(c) -8 \; and\; -15

(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,

(c) Integers between -8 \; and\; -15 are;

-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.

(c) A smallest negative integer is -1 .

(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

(c) False,
Correction-There is no smallest negative integer

(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 .

(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?

Answer: (a) if we move 41595481545033 numbers to the right of -2.1595481545403 we get 2.
15954815544431595481545758
(b) if we move 51595481546099 numbers to the left of 11595481546471 we get -4
15954815551571595481546834
(c) If we are at -81595481547172 on the number line, we should move 5 number to the -81595481547519 left side on the number line.
15954815557611595481547870
(d) If we are at -61595481548224 on the number line, then we should move 5 number right to the -61595481548594 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

(c) 6 less than 2

(d) 3 less than -2

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

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

Q2 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)

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.
15954825497451595482547315

Q3 Add without using number line :

(a) 11+(-7)

(b) (-13)+(+18)

(c) (-10)+(+19)
(d) (-250)+(+150)
(e) (-380)+(-270)
(f) (-217)+(-100)

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

(c) (-10)+(+19)
= (- 10) + (10) + 9
= 9

(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

(c) -312,\; 39\; and\; 192

(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

(c) the sum of -312,\; 39\; and\; 192
= (- 231) + (81) + (39 + 192 )
= (- 81) + (- 231) + (231)
= - 81

(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)

(c) (-15)-(-18)

(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

(c) (-15)-(-18)
= (- 15) + 18
= (- 15) + (15) + 3
= 0 + 3 = 3

(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)

(c) 45 – (– 11) ______ 57 + (– 4)

(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

(c) 45 – (– 11) ______ 57 + (– 4)
LHS \Rightarrow 45 + 11 = 66
RHS \Rightarrow 57 - 4 =53

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

(c) 12 + (– 12) = ____

(d) (– 4) + ____ = – 12

(e) ____ – 15 = – 10

Answer: a) (– 8) + _____ = 0
Since we know that, gif-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)

(c) 12 + (– 12) = ____
Since we know that, gif-a +a =0 So, the answer is Zero (0)

(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


(c) (-7)+(-8)+(-90)
\\= (-7)-(8)-(90)\\ =-(7+8+90)\\ =-(105)


(d) 50-(-40)-(-2)
= 50 +40 +2
=92

 
Responsive Table
Chapter No. Chapter Name
Chapter 1 NCERT Solutions for class 6 maths chapter 1 Knowing Our Numbers
Chapter 2 NCERT solutions for class 6 maths chapter 2 Whole Numbers
Chapter 3 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 NCERT solutions for class 6 maths chapter 5 Understanding Elementary Shapes
Chapter 6 NCERT solutions for class 6 maths chapter 6 Integers
Chapter 7 NCERT Solutions for class 6 maths chapter 7 Fractions
Chapter 8 NCERT solutions for class 6 maths chapter 8 Decimals
Chapter 9 NCERT solutions for class 6 maths chapter 9 Data Handling
Chapter 10 NCERT solutions for class 6 maths chapter 10 Mensuration
Chapter 11 NCERT Solutions for class 6 maths chapter 11 Algebra
Chapter 12 NCERT solutions for class 6 maths chapter 12 Ratio and Proportion
Chapter 13 NCERT solutions for class 6 maths chapter 13 Symmetry
Chapter 14 NCERT Solutions for class 6 maths chapter 14 Practical Geometry

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