NCERT Exemplar for Class 6 Maths Solutions Chapter 3 Integers

1. Write the correct answer from the given four options: Sania and Trapi visited Leh and Tawang respectively during winter. Sania reported that she had experienced –4°C on Sunday, while Trapi reported that she had experienced –2°C on that day. On that Sunday

(A) Leh was cooler than Tawang.

(B) Leh was hotter than Tawang.

(C) Leh was as cool as Tawang.

(D) Tawang was cooler than Leh.

Ans: Correct option - A

Because -4 is less than -2. It is representing that Leh was cooler than Tawang.

2. State whether each of the following statements is true or false:

(a) Every positive integer is greater than 0.

Ans:  True

Because we know that every positive integer is greater than 0.

(b) Every integer is either positive or negative.

Ans: False

Because an integer can be either positive, zero or negative.

3. Fill in the blank using  <,> or = to make the statement correct 3 + (–2) ____ 3 + (–3).

Ans: 3 + (–2) > 3 + (–3)

3+ (-2) =3-2=1

And 3+ (-3) =3-3=0

So, 1 is greater than 0.

4. Represent the following using integers with a proper sign:

(a) 3 km above sea level

Ans:  +3

Because see level is above 3km.

(b) A loss of Rs 500

Ans:   –500

Because there is a loss of Rs. 500.

5. Find the sum of the pairs of integers:

(a) – 6, – 4

Ans:  – 6 + (– 4) = – 6 – 4  = –10

(b) +3, – 4

Ans:  + 3 + (– 4) = + 3 – 4 = –1

(c) +4, –2

Ans: 4 + (–2) = 4 – 2 = 2

6.Find the sum of –2 and –3, using the number line.

Ans:  On the number line ,to add –2 and –3, , firstly we move 2 steps to the left of number 0,after reaching –2, we move 3 steps to the left of –2 and then we will reach to –5.

So, –2 + (–3) = - 2 – 3 =  – 5.

7.Subtract :

(i) 3 from –4

Ans– 4 - (–3) = – 4 - 3 = –7

(ii) 3 from –4

Ans:  – 4 – (–3) = – 4 + 3 = –1

8.Using the number line, subtract :

(a) 2 from –3

Ans:  To subtract 2 from –3 on number line, we move 2 steps to the left of – 3 and we will reach to –5.

So, –3 – 2 = –5.

(b) –2 from –3

Ans:  To subtract –2 from –3 on number line , we find that 2 is the additive inverse of –2.

So, here  we add 2 to –3 using the number line and reach at –1.

So, –3 – (–2) = –3 +  2  = –1

9. How many integers are there between –9 and –2 ?

Ans:  There are six integers between – 9 and –2 and the integers are –8, –7, –6, –5, –4 and –3.

10. Calculate: 1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9 – 10

Ans:  1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9 – 10 = (1 + 3 + 5 + 7 + 9) – (2 + 4 + 6 + 8 + 10) = 25 – 30 = –5.

11. The sum of two integers is 47. If one of the integers is – 24, find the other.

Ans:   Given, the sum of two integers =  47

And one integer =  –24

So, the required integer = 47 – (–24) = 47 + 24 = 71.

12. Write the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 in this order and insert ‘+ ‘or ‘–’ between them to get the result

(a) 5

Ans: To get 5

 0 + 1 – 2 + 3 – 4 + 5 – 6 + 7 –8 + 9 = 5

(b) –3

Ans:  To get -3

0 – 1 – 2 + 3 + 4 – 5 + 6 – 7 + 8 – 9 = –3

 13. Write five distinct integers whose sum is 5.

Ans:   5 + [2+ (–2)] + [3+ (–3)] = 5.

So, five distinct integers are 5, 2, –2, 3 and –3

Whose sum is 5.

In Questions 1 to 17 ,only one of the four Options is Correct.write the Correct one. 

1.Every integer less than 0 has the sign

(A) + 

(B) -

(C) x 

(D) +

Ans: Correct option - A

We know that every integer less than 0 has a negative sign.

2.The integer ‘5 units to the right.of 0 on the number line’ is

(A) + 5

(B) -5

(C) + 4 

(D)-4

Ans: Correct option - A

Because all the positive integers lie to the right of 0 on the number line.

3.The predecessor of the integer -1 is

(A) 0 

(B) 2

(C)-2 

(D) 1

Ans: Correct option - C

Predecessor of the integer -1 = -1-1=-2 

So, the predecessor of the integer -1 is -2.

4. Number of integers lying between -1 and 1 is

(A) 1 

(B) 2 

(C) 3 

(D) 0

Ans: Correct option - A

The integers lying between -1 and 1 are 0.

5.Number of whole numbers lying between-5 and 5 is 

(A) 10 

(B) 3 

(C) 4 

(D) 5

Ans: Correct option - D

The whole numbers lying between-5 and 5 = 0,1,2, 3 and 4.

6.The greatest integer lying between-10 and -15 is

(A)-10 

(B)-11 

(C)-15 

(D)-14

Ans: Correct option - B

-11 is the greatest among -11,-12,-13,-14.

7.The least integer lying between -10 and -15 is 

(A)-10 

(B)-11 

(C)-15 

(D) -14

Ans: Correct option - D

 Integers lying between -10 and-15 are -11,-12,-13,-14.

-14 is the least integer. 

8. On the number line, the integer 5 is located

(A) to the left of 0 

(B) to the right of 0

(C) to the left of 1 

(D) to the left of -2

Ans: Correct option - B

Integer 5 is positive so 5 will be to the right of zero.

9. In which of the following pairs of integers, the first integer is not on the left of the other integer on the number line?

(A) (-1,10) 

(B) (-3,-5)

(C) (-5.-3) 

(D) (-6,0)

Ans: Correct option - B

From  the number line we observe that -3 is on the right of -5.

10. The integer with a negative sign (-) is always less than 

(A) 0 

(B)-3 

(C)-1

(D)-2

Ans: Correct option - A

Because the negative integer is always less than 0.

11. An integer with a positive sign (+) is always greater than

(A) 0 

(B) 1 

(C)2 

(D) 3

Ans: Correct option - A

Because the positive integer is always greater than 0.

12. The successor of the predecessor of -50 is

(A)-48 

(B)-49 

(C)-50 

(D)-51

Ans: Correct option - C

The predecessor of -50 =-50-1=-51 

And the successor of -51 = -51 + 1 = -50

13. The additive inverse of a negative integer

(A) is always negative 

(B) is always positive 

(C) is the same integer 

(D) zero

Ans: Correct option - B

The additive inverse of a negative integer is always positive.

14. Amulya and Amar visited two places A and B, respectively in Kashmir and recorded the minimum temperatures on a particular day as $-4^{\circ} C$ at A and $-1^{\circ} C$ at B. Which of the following statements is true?

(A) A is cooler than B

(B) B is cooler than A

(C) There is difference of $2^{\circ} C$ in the temperature   

(D) The temperature at A is $4^{\circ} C$higher than that at B

Ans: Correct option - A

Given A= $-4^{\circ} C$ and B=$-1^{\circ} C$

We know that $-4^{\circ} C$ is less than$-1^{\circ} C$. So, A is cooler than B. 

15. When a negative integer is subtracted from another negative integer, the sign of the result 

(A) is always negative

(B) is always positive

(C) is never negative 

(D) depends on the numerical value of the integers

Ans: Correct option - D

Because the sign of the result depends on the numerical value of the integers.

16. The statement "When an integer added to itself, the sum is greater than the integer" is

(A) always true 

(B) never true

(C) true only when the integer is positive

(D) true for non-negative integers

Ans: Correct option - C

Because this is true only when the integer is positive.

17. Which of the following shows the maximum rise in temperature?

(A) $0^{\circ} C$ to $10^{\circ} C$ 

(B) $-4^{\circ} C$ to $8^{\circ} C$ 

(C) $-15^{\circ} C$ to $-8^{\circ} C$ 

(D) $-7^{\circ} C$ to $0^{\circ} C$

Ans: Correct option - B

Rise in temperature

(A) In $0^{\circ} C$ to $10^{\circ} C$ 

$10^{\circ} C -0^{\circ} C =10^{\circ} C$

(B) In $-4^{\circ} C$ to $8^{\circ} C$

$8^{\circ} C -(-4^{\circ} C) =8^{\circ} C +4^{\circ} C =12^{\circ} C$ 

(C) In $-15^{\circ} C$ to $-8^{\circ} C$

$-8^{\circ} C -\left(-15^{\circ} C \right)=-8^{\circ} C +15^{\circ} C =7^{\circ} C$

(D) In $-7^{\circ} C$ to $0^{\circ} C$

$0^{\circ} C -\left(-7^{\circ} C \right)=0^{\circ} C +7^{\circ} C =7^{\circ} C$ 

Maximum rise in temperature is option (B).

In Questions 18 to 39, state whether the given Statements are True or False

18. The smallest natural number is zero.

Ans: False

We know that the smallest positive natural number is 0.

19. Zero is not an integer as it is neither positive nor negative.

Ans: False

Zero is an integer.

20. The sum of all the integers between-5 and -1 is -6

Ans: False

Between -5 and -1 The integers are -4,-3 and -2.

Sum=(-4)+ (-3)+ (-2)=-4-3-2=-9

21. The successor of integer 1 is 0.

Ans: False

The successor of 1 = 1+1=2

22. Every positive integer is Larger than every negative integer.

Ans: True

Positive integers are always larger than every single negative integer.

23. The sum of any two negative integers is always greater than both the integers.

Ans: False

It is fundamental.

24. The sum of any two negative integers is always smaller than both the integers.

Ans: True 

It is fundamental.

25. The sum of any two positive integers is greater than both the integers.

Ans: True

It is fundamental.

26. All whole numbers are integers.

Ans: True 

Because we know, the collection of whole numbers form the set of integers.

27. All integers are whole numbers.

Ans: False

Because we know, integers are the collection of all whole numbers.

28. Since 5 > 3, therefore -5> -3

Ans: False 

Because in a number line a number from zero on the left, smaller is its value.

29. Zero is less than every positive integer.

Ans: True

Because zero is left to the positive integer.

30. Zero is larger than every negative integer.

Ans: True

Because zero is right to the positive integer.

31. Zero is neither positive nor negative.

Ans: True

Zero is neither positive nor negative.

32. On the number line, an integer on the right of a given integer is always larger than the integer.

Ans: True

Because according to the number line it is true.

33. -2 is to the left of-5 on the number line.

Ans: False

According to the number line -2 is to the right of -5.

34. The smallest integer is 0.

Ans: False

Because we know, all negative integers are less than 0. 

35. 6 and -6 are at the same distance from 0 on the number line. 

Ans: True

According to the number line, we can see that 6 and -6 are at the same distance from 0.

36. The difference between an integer and its additive inverse is always even.

Ans: True 

Let an integer be 1 and its additive inverse is -1. 

Difference between 1 and -1=1-(-1)=1+1=2,where 2 is an even number.

37. The sum of an integer and its additive inverse is always zero.

Ans: True

Let an integer be 1 and its additive inverse is -1. 

Sum of 1 and -1= 1+ (-1) = 1-1 = 0

38. The sum of two negative integers is a positive integer.

Ans: False

Let two negative integers be -1 and -2.

Sum of -1 and -2=-1+(-2)=-1-2=-3,where 3 is negative.

39. The sum of three different integers can never be zero.

Ans: False

Let the three integers be 1, 2 and 3.

Sum of them =1+2+3=6 ,is not zero.

In Questions 40 to 49, fill in the blanks to make the Statements True

40. On the number line, 15 is to the ……… of zero.

Ans: On the number line, 15 is to the left of zero.

41. On the number line, 10 is to the……..of zero.

Ans: On the number line, 10 is to the right  of zero.

42. The additive inverse of 14 is....... .

Ans:  The additive inverse of 14 is -14 .

43. The additive inverse of -1 is….. .

Ans:The additive inverse of -1 is 1.

44. The additive inverse of 0 is…...

Ans:The additive inverse of 0 is 0 .

45. The number of integers lying between -5 and 5 is…….

Ans: The number of integers lying between -5 and 5 is 9.

46. (-11)+ (-2)+(-1) =........

Ans: (-11)+ (-2)+(-1)=-11-2-1=-(11+2+1)

=-14 

47. …… +(-11)+111=130

Ans: 30 +(-11)+111=130

Let number is b 

So, b+ (-11)+ 111=130 

b=130-111 +11

b= 30

48. (-80) +0 +(-90)=........... +0+(-90)=2

Ans: -170

(-80) + 0 + (90)=-80+ 0-90 = -(80+90)=-170.

49. ……… -3456 = -8910 

Ans: -5454 -3456= -8910

Let number is b  

So, b-3456 = -8910 

b=-8910+ 3456 = -5454

In Questions 50 to 58, fill in the Blanks using '<, = or >

50. (-11)+(-15) _____11+15

Ans: L.H.S.= (-11)+ (-15)=-11-15= -26 

R.H.S.=11+15=26

So,  (-11)+(-15)<11+15.

51. (-71)+(+9)_____ (-81) + (-9)

Ans: L.H.S.= (-71) + (+9)=-71+9=-62 

R.H.S. =(-81) + (-9)=-81-9= -90 

So,(-71)+(+9)> (-81) + (-9).

52. 0____ 1

Ans: 0 < 1

 53. -60_____50 

Ans: -60 < 50

54. -10______ -11

Ans: -10 > -11

55.  -101______ -102

Ans: -101 > -102

56. (-2)+(-5)+(-6)____(-3) + (-4) + (-6)

Ans: L.H.S. = (-2) + (-5)+(-6)=-2-5-6= -13 

R.H.S. = (-3) + (-4) + (-6)=-3-4-6=-13 

So, -13=-13

57. 0 ____ -2

Ans: 0 > -2

58. 1+ 2+ 3_____ (-1)+(-2)+(-3)

Ans: L.H.S.= 1+2+3=6

R.H.S.= (-1) + (-2)+(-3)=-1-2-3= (1+2+3)=-6 

So,  1+ 2+ 3 > (-1)+(-2)+(-3).

59. Match the items of Column I with that of Column II.

Ans: 

60. Compute each of the following:

(a) 30+ (-25) + (-10)

Ans: 30+ (-25)+(-10)=30-25-10

=30-35

=-5

(b) (-20)+(-5) 

Ans: (-20) + (-5)=-20-5

= -25

(c) 70+ (-20) + (-30)

Ans: 70+ (-20)+(-30)= 70-20-30

= 70-50

=-20 

(d)-50+ (-60) +50

Ans: -50+ (-60)+50=-50-60+50

=-110+ 50

=-60

(e) 1+ (-2) + (-3) + (-4) 

Ans: 1+ (-2) + (-3) + (-4)=1-2-3-4

=1-9=-8

(f) 0+ (-5)+(-2)

And: 0+(-5)+(-2)=0-5-2

=0-7=-7

(g) 0-(-6)-(+6)

Ans: 0-(-6)-(+6) =6-6=0

(h) 0-2-(-2)

Ans: 0-2-(-2)=0-2+2=-2+2=0

61. If we denote the height of a place above sea level by a positive integer and depth below the sea level by a negative integer, then write the following using integers with the sign:

(a) 200 m above sea level 

Ans: 200 m above sea level = + 200 m

(b) 100 m below sea level

Ans: 100 m below sea level = -100 m

(c) 10 m above sea level 

Ans: 10 m above sea level = + 10 m

(d) Sea level

Ans: Sea level=0

62. Write the opposite to each of the following: 

(a) Decrease in size.

Ans:  Increase in size.

(b) Failure. 

Ans: Success.

(c) Profit of 10.

Ans:  Loss of 10.

(d) 1000 AD.

Ans:  1000 BC.

(e) Rise in water level.

Ans: Fall in water level.

(f) 60 km South.

Ans:  60 km North.

(g) 10 m above the danger mark of river Ganga

Ans:  10 m below the danger mark of river Ganga.

(h) 20 m below the danger mark of the river Brahmaputra.

Ans: 20 m above the danger mark of the river Brahmaputra. 

(i) Winning by a margin of 2000 votes

Ans:  Losing by a margin of 2000 votes.

(j) Depositing 100 in the bank account.

Ans: Withdrawing 100 from the bank account.

(k)  $20^{\circ} C$ rise in temperature.

Ans:$20^{\circ} C$ fall in temperature.

63. Temperature of a place at 12:00 noon was +$5^{\circ} C$. Temperature increased by $3^{\circ} C$ in the first hour and decreased by $1^{\circ} C$ in the second hour. What was the temperature at 2:00 pm?

Ans: Temperature at 12:00 noon=+$5^{\circ} C$

So, temperature at 1:00 pm = $5^{\circ} C$ + $3^{\circ} C$ = $8^{\circ} C

Also, temperature decreased so, the temperature at 2:00 pm =  $8^{\circ} C -  $1^{\circ} C =  $7^{\circ} C

64. Write the digits 0, 1, 2, 3,......, 9 in this order and insert + or -  between them to get the result 3.

Ans: To get result 3

0-1- 2- 3-4- 5- 6+ 7+8+9 = 3

65. Write the integer which is its own additive inverse.

Ans:  Zero (0) is the integer its own additive inverse.

66. Write six distinct integers whose sum is 7.

Ans: Let the six distinct integers = 1,2,-2, 3,-3 and 6. 

Sum = 1+ 2+(-2) + 3+ (-3) +6 = 7 

67. Write the integer which is 4 more than its additive inverse.

Ans: Let  2 is an integer and its additive inverse is -2. From the number line,2 is 4 more than its additive inverse.

So, the required integer is 2.

68. Write the integer which is 2 less than its additive inverse.

Ans: Let -1 be an integer and its additive inverse is 1. From the number line, -1 is 2 less than its additive inverse. 

So, the required integer is -1.

69. Write two integers whose sum is less than both the integers.

Ans:  Let -5 and -6 be two negative integers.

Sum=(-5)+(-6)=-5-6 =-11 

So, the sum of  them is less than both the integers.

70. Write two distinct integers whose sum is equal to one of the integers. On adding 0 (zero) to any other integer, we get the sum equal to that integer.

Ans: Let 5 and 0 be two distinct integers.

 Sum=3 + 0 = 3.

71. Using number line, how do you compare 

(a) two negative integers?

Ans: When we compare two negative integers using the number line, the number which is to the right on the number line , will be greater than the other number.

(b) two positive integers?

Ans:  When  we compare two positive integers using  the number line, the number which is to the right on the number line, will be greater than the other number.

(c) one positive and one negative integers?

Ans:  When we compare one positive and one negative integer using the number line,a positive integer will be greater than the negative integer.

72. Observe the following:

1+2-3+4+5-6-7+8-9 = -5 

Change one -  sign as + sign to get the sum 9.

Ans: If we replace -7 by +7

Than sum=1+2-3+4+5-6+7+8-9=9 

73. Arrange the following integers in the ascending order.

 -2,1, 0,-3,+4,-5

Ans: Ascending order= -5<-3<-2<0< 1<4

74. Arrange the following integers in the descending order.

0,-1,-4,-3,-6

Ans: Descending order = 0>-1>-2>-3>-4>-6

75. Write two integers whose sum is 6 and the difference is also 6.

Ans:  Let two integers 6,0.

Sum=6+0=6

Difference=6-0=6

So, the required two integers are 0 and 6.

76. Write five integers which are less than-100 but greater than - 150.

Ans: Integers are -101, -102, -103, -104 and -105. 

77. Write four pairs of integers which are at the same distance from 2 on the number line. 

Ans:  According to  the number line.Pairs are (1,3), (0, 4), (-1,5),(-2,6) 

78. The sum of two integers is 30. If one of the integers is -42, then find the other. 

Ans: Given, sum of two integers = 30 and one integer = -42 

Then the other integer = 30-(-42) = 30+ 42=72.

79. Sum of two integers is -80. If one of the integers is -90, then find the other. 

Ans: Given, sum of two integers = -80 and one integer= -90

Than the other integer =-80-(-90) = -80 +90 = 10

80. If we are at 8 on the number line, then in which direction should we move to reach the integer

(a) -5

Ans: When  we are moving to the left we will get  -5.

(b) 11

Ans: When we are moving to the  right we will get 11.

(c) 0?

Ans: When we are moving to the left we will get  0.

81. Using the number line, write the integer which is

(a) 5 more than-5.

Ans: 0

(b) 3 less than 2.

Ans: -1

(c) 2 less than-2.

Ans: -4

82. Find the value of 49-(-40)-(-3) + 69.

Ans:  Given ,49 - (-40) -(-3) +69= 49 + 40 + 3 + 69

= 161

83. Subtract -5308 from the sum [(- 2100) + (-2001)].

Ans:  The sum= [(-2100) + (-2001)] = [-2100-2001] = -4101 

Now, subtraction= - 4101-(-5308) =-4101+ 5308 = 1207

What are Ncert Exemplar Solutions For Class 6 Maths Chapter 3 Integers?

NCERT Exemplar Solutions for Class 6 Maths Chapter 3 covers all the exercise questions in the NCERT Exemplar textbook. We, at Vedantu, ensure that you receive the best NCERT Exemplar Solutions study materials that can help you succeed in your studies with a well-structured learning curve. These NCERT Model 6 Mathematics Solution Solutions are prepared by our well-trained and well-trained course specialists and are provided here to assist students in learning concepts quickly and accurately.

Chapter 3 - A whole number is a positive, negative, or zero number. This Chapter covers topics such as the addition of two negative integers, the addition of two positive integers, the additional contrast, and the comparison of two integers in the number line. Students can also see how one more than a given number gives a replacement and one less than a given number gives a precedent.

Key Topics For Ncert Exemplar Class 6 Maths Solutions Chapter 3

Introduction

The numbers to the right of zero are greater than zero and are positive numbers. The numbers to the left of zero are less than zero and are known as negative numbers. The positive numbers are represented by the symbol + in front of them and the negative is represented by the symbol in front of them.

Integers

A set of numbers that includes a set of positive, zero, and negative numbers are known as numbers. These positive and negative numbers are called positive numbers and negative integers respectively.

Therefore, it can be concluded that all natural numbers, whole numbers, zero and negative numbers can be called numbers and all numbers may not be in these categories.

Representation of the Integer on the Number Line

Draw a line from the line and mark the corresponding points. Mark one point as zero so the points on the right will be marked +1, +2, +3 etc. or simply 1, 2, 3 and so on. Points to the left of zero will be marked as -1, -2, and -3 and so on.

Ordering of Integers

In the number line, the number increases as we go to the right and decreases as we go to the left.

Addition of Integers

• Adds if there are two positive integers in question. You should also add if there are two negative numbers in the question, making sure that the sum takes a negative mark before the number.

• If you have one negative and one negative addition, you should always subtract, but the answer will take the big number symbol (ignore the number symbols, decide which is the largest number)

• When a positive number is added to a given number, it becomes greater than its actual value whereas when a negative number is added to a given number, it becomes less than its actual value.

Additive Inverse

A number added to a given number to make its value zero is known as its additive inverse of that number.

Subtraction of Integers

When a negative number is subtracted from a certain number, we get a larger number. Deleting a number is the same as the addition of its additional contrast.