NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 3: Integers
Problems and Solutions

Questions 59 to 83 with detailed solutions and explanations.

Question. 59

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

Q59 table
Column IColumn II
(i) The additive inverse of +2(A) 0
(ii) The greatest negative integer(B) −2
(iii) The greatest negative even integer(C) 2
(iv) The smallest integer greater than every negative integer(D) 1
(v) Sum of predecessor and successor of −1(E) −1

Answer:

(i) → (B) −2

(ii) → (E) −1

(iii) → (B) −2

(iv) → (A) 0

(v) → (B) −2

Open

Question. 60

60. Compute each of the following:

Q60 list
  1. \(30 + (-25) + (-10)\)
  2. \((-20) + (-5)\)
  3. \(70 + (-20) + (-30)\)
  4. \(-50 + (-60) + 50\)
  5. \(1 + (-2) + (-3) + (-4)\)
  6. \(0 + (-5) + (-2)\)
  7. \(0 - (-6) - (+6)\)
  8. \(0 - 2 - (-2)\)

Answer:

(a) −5, (b) −25, (c) 20, (d) −60, (e) −8, (f) −7, (g) 0, (h) 0

Open

Question. 61

61. Using integers with appropriate signs, write the following:

Q61 statements
  1. 200 m above sea level
  2. 100 m below sea level
  3. 10 m above sea level
  4. Sea level

Answer:

(a) \(+200\), (b) \(-100\), (c) \(+10\), (d) \(0\)

Open

Question. 62

62. Write the opposite of each of the following:

Q62 list
  1. Decrease in size
  2. Failure
  3. Profit of Rs. 10
  4. 1000 A.D.
  5. Rise in water level
  6. 60 km south
  7. 10 m above the danger mark of river Ganga
  8. 20 m below the danger mark of the river Brahmaputra
  9. Winning by a margin of 2000 votes
  10. Depositing Rs.100 in the bank account
  11. 20°C rise in temperature

Answer:

(a) Increase in size, (b) Success, (c) Loss of Rs. 10, (d) 1000 B.C., (e) Fall in water level, (f) 60 km north, (g) 10 m below the danger mark, (h) 20 m above the danger mark, (i) Losing by a margin of 2000 votes, (j) Withdrawing Rs. 100 from the bank account, (k) 20°C fall in temperature

Open

Question. 63

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

Q63

Answer:

\(+7^{\circ}\text{C}\)

Open

Question. 64

64. Write the digits \(0,1,2,\ldots,9\) in this order and insert '+' or '−' between them to get the result 3.

Q64

Answer:

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

Open

Question. 65

Write the integer which is its own additive inverse.

Answer:

\(0\)

Open

Question. 66

Write six distinct integers whose sum is 7.

Answer:

\(-3,\,0,\,1,\,2,\,3,\,4\)   (sum: \(-3+0+1+2+3+4=7\))

Open

Question. 67

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

Answer:

\(2\)

Open

Question. 68

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

Answer:

\(-1\)

Open

Question. 69

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

Answer:

\(-2\) and \(-3\): sum = \(-5\)

Open

Question. 70

Write two distinct integers whose sum is equal to one of the integers.

Answer:

\(0\) and \(5\): \(0+5=5\)

Open

Question. 71

71. Using number line, how do you compare

  1. two negative integers?
  2. two positive integers?
  3. one positive and one negative integer?
Q71

Answer:

(a) The negative integer nearer to 0 (smaller absolute value) is greater.

(b) The integer to the right is greater (larger value).

(c) Any positive integer is greater than any negative integer.

Open

Question. 72

72. Observe: \(1+2-3+4+5-6-7+8-9=-5\). Change one ‘−’ sign as ‘+’ sign to get the sum \(9\).

Q72

Answer:

Change “−7” to “+7”.

Open

Question. 73

Arrange in ascending order: \(-2, 1, 0, -3, +4, -5\).

Answer:

−5, −3, −2, 0, 1, 4

Open

Question. 74

Arrange in descending order: \(-3, 0, -1, -4, -3, -6\).

Answer:

0, −1, −3, −3, −4, −6

Open

Question. 75

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

Answer:

6 and 0

Open

Question. 76

Write five integers which are less than \(-100\) but greater than \(-150\).

Answer:

−101, −110, −120, −130, −149

Open

Question. 77

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

Answer:

(1, 3), (0, 4), (−1, 5), (−2, 6)

Open

Question. 78

The sum of two integers is 30. If one integer is \(-42\), find the other.

Answer:

72

Open

Question. 79

Sum of two integers is \(-80\). If one of the integers is \(-90\), find the other.

Answer:

10

Open

Question. 80

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

  1. \(-5\)
  2. \(11\)
  3. \(0\)
Q80

Answer:

(a) Left, (b) Right, (c) Left

Open

Question. 81

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

  1. 4 more than \(-5\)
  2. 3 less than \(2\)
  3. 2 less than \(-2\)
Q81

Answer:

(a) \(-1\), (b) \(-1\), (c) \(-4\)

Open

Question. 82

82. Find the value of

\(49 - ( -40) - ( -3) + 69\).

Q82

Answer:

161

Open

Question. 83

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

Q83

Answer:

1207

Open

NCERT Exemplar Solutions Class 6 – Mathematics – Unit 3: Integers – Problems and Solutions | Detailed Answers