NCERT Exemplar Solutions
Class 6 - Mathematics

Unit 3: Integers

The smallest natural number is zero.

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

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

The successor of the integer 1 is 0.

Every positive integer is larger than every negative integer.

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

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

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

All whole numbers are integers.

All integers are whole numbers.

Since 5 > 3, therefore −5 > −3.

Zero is less than every positive integer.

Zero is larger than every negative integer.

Zero is neither positive nor negative.

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

−2 is to the left of −5 on the number line.

The smallest integer is 0.

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

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

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

The sum of two negative integers is a positive integer.

The sum of three different integers can never be zero.

On the number line, −15 is to the ______ of zero.

On the number line, 10 is to the ______ of zero.

The additive inverse of 14 is ______.

The additive inverse of −1 is ______.

The additive inverse of 0 is ______.

The number of integers lying between −5 and 5 is ______.

(−11) + (−2) + (−1) = ______.

______ + (−11) + 111 = 130

(−80) + 0 + (−90) = ______.

______ −3456 = −8910

(−11) + (−15) ____ 11 + 15

(−71) + (+9) ____ (−81) + (−9)

0 ____ 1

−60 ____ 50

−10 ____ −11

−101 ____ −102

(−2) + (−5) + (−6) ____ (−3) + (−4) + (−6)

0 ____ −2

1 + 2 + 3 ____ (−1) + (−2) + (−3)

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

60. Compute each of the following:

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. \(0 - 2 - (-2)\)

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

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

62. Write the opposite of each of the following:

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

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?

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

Write the integer which is its own additive inverse.

Write six distinct integers whose sum is 7.

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

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

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

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

71. Using number line, how do you compare

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

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

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

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

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

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

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

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

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

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. \(0\)

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

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

82. Find the value of

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

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