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) north

(c) east

(d) Loss of

(e) 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

(b) Here B indicates the position of

(c) Here C represents the position of

(d) Here D represents the

(e) Here E represents the

Q4 Adjacent figure is a vertical number line, representing integers. Observe it and locate the following points :

(a) If point D is , then which point is ?

(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:

(a) If D is a then F represents (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 and respectively.

(d) E has the least value of

(e) Decreasing order of all the points are-

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

A5: Place Temperature

Siachin below .................

Shimla below .................

Ahmedabad above .................

Delhi above .................

Srinagar below .................

(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 where temperatures are above .

Answer: (a)

Place	Temperature	Integer form
Siachin	below	-10
Shimla	below	-2
Ahmedabad	above	+30
Delhi	above	+20
Srinagar	below	-5

(b)

(c) The coolest pace is Siachin with -10

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

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

(a)

(b)

(c)

(d)

(e)

(f)

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 ( )

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

(c) 0 is right to the -1

(d) 10 is right to the -11

(e) 6 is right to the -6

(f) 1 is right to the -100

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

(a)

(b)

(c)

(d)

Answer: (a) The integers between are;

(b) Integers between are;

(c) Integers between are;

(d) Integers between are;

Q8 (a) Write four negative integers greater than

(b) Write four integers less than

Answer: (a) four negative integers greater than are;

(all negative integers wg=ho comes before -20)

(b) four integers less than are;
(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) is to the right of on a number line.

(b) is to the right of on a number line.

(c) A smallest negative integer is .

(d) is greater than

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

(b) False. is to the left side of on a number line

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

(d) False,
Correction; is smaller than

Q10 Draw a number line and answer the following:

(a) Which number will we reach if we move numbers to the right of

(b) Which number will we reach if we move numbers to the left of .

(c) If we are at on the number line, in which direction should we move to reach ?

(d) If we are at on the number line, in which direction should we move to reach

Answer: (a) if we move numbers to the right of we get 2.

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

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

(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) more than

(b) more than

(c) less than

(d) less than

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

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

Q2 Use number line and add the following integers :

(a)

(b)

(c)

(d)

(e)

(f)

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

Q3 Add without using number line :

(a)

(b)

(c)
(d)
(e)
(f)

Answer: In addition without using the number line, in this method, we have to split one number according to the other number such that .

Now,

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

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

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

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

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

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

Q4 Find the sum of:

(a)

(b)

(c)

(d)

Answer: It is known that the sum of .

Therefore,
(a) the sum of
= 137 + (-137) + (- 217)
= - 217

(b) the sum of
= -52 + 52 = 0

(c) the sum of
= (- 231) + (81) + (39 + 192 )
= (- 81) + (- 231) + (231)
= - 81

(d) the sum of
= - (50 + 200 ) + (300)
= - 250 + (250) + 50
= 50

Q5 Find the sum :

(a)

(b)

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

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

(b)
= 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)

(b)

(c)

(d)

(e)

(f)

Answer: It is known that the sum of .
So, we have to split the number in order to cancel out with other numbers.

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

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

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

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

(e)
= 23 + 12
= 35

(f)
= (- 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 - 3 - 6 = -9
RHS - 3 + 6 = +3
Hence LHS < RHS

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

Hence LHS > RHS

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

Hence LHS > RHS

(d) (– 25) – (– 42) _____ (– 42) – (– 25)
LHS - 25 + 42 = 17
RHS -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, . Therefore, the blank space should be + 8.

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

(c) 12 + (– 12) = ____
Since we know that, 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)
(b)
(c)
(d)

Answer: We already know that the sum of the additive inverse is Zero ( )

(a)

(b)

(c)

(d)