Class 6 Maths Chapter 6 Integers
Exercise – 6.1
1. Write opposites of the following:
(1) Increase in weight
(2) 30 km north
(3) 80 m east
(4) Loss of? 700
(5) 1 00 m above sea level
Solution: (1) Decrease in weight
(2) 30 km south
(3) 80 m west
(4) Profit of? 700
(5) 100 m below sea level
Read and Learn More Class 6 Maths Exemplar Solutions
2. Represent the following numbers as integers with appropriate signs.
(1) An aeroplane is flying at a height, two thousand metre above the ground.
(2) A submarine is moving at a depth, eight hundred metre below the sea level.
(3) A deposit of rupees two hundred.
(4) Withdrawal of rupees seven hundred.
Solution: (1) Two thousand metre above the ground = + 2000
(2) Eight hundred metre below the sea level = -800
(3) Deposit of two hundred rupees = + 200
(4) Withdrawal of seven hundred rupees = -700
3. Represent the following numbers on a number line:
(1) +5
(2) -10
(3) + 8
(4) -1
(5) -6
Solution: (1)
(2)
(3)
(4)
(5)
4. Adjacent figure is a vertical number A line, representing integers. Observe it and locate the following points:
(1) If point D is + 8, then which point is -8?
(2) Is point G a negative integer or a positive integer?
(3) Write integers for points 8 and E.
(4) Which point marked on this number line has the least value?
(5) Arrange all the points in decreasing order of value.
Solution: (1) We have, point D is +8.
Therefore, 16 steps to the down from D is -8 i.e., the point F.
(2) Point G is a negative integer.
(3) Point B is four steps down from point D.
Value of point B = +8- 4 = +4
Point E is eighteen steps down from point D.
Value of point E = +8- 18 = -10
(4) Since, point E is located in the bottom.
So, point E has the least value.
(5) Decreasing order of all the points is,
D, C,B, A,0, H,G, F,E
5. Following Is the list of temperatures of five places In India on a particular day of the year.
Place Temperature
Siachin 10°C below 0°C …………
Shimla 2°C below 0°C …………
Ahmedabad 30°C above 0°C …………
Delhi 20°C above 0°C …………
Srinagar 5°C below 0°C …………
(1) Write the temperatures of these places in the form of integers in the blank column.
(2) Following is the number line representing the temperature in degree Celsius
Plot the name of the city against its temperature.
(3) Which is the coolest place?
(4) Write the names of the places where temperatures are above 10°C.
Solution:
Place Temperature
(1) Siachin -10°C
Shimla -2°C
Ahmedabad + 30°C
Delhi + 20°C
Srinagar -5°C
(3) Siachin is the coolest place.
(4) Ahmedabad and Delhi have temperature above 10°C.
6. In each of the following pairs, which number is to the right of the other on the number line?
(1) 2, 9
(2) -3,-8
(3) 0,-1
(4) -11,10
(5) -6,6
(6) 1,-100
Solution: (1) 9 is right to 2
(2) -3 is right to -8
(3) 0 is right to -1
(4) 10 is right to -11
(5) 6 is right to -6
(6) 1 is right to -100
7. Write all the integers between the given pairs (write them in the increasing order.)
(1) 0 and-7
(2) -4 and 4
(4) -30 and -23
(3) -8 and -15
Solution: (1) The integers between 0 and -7 are -6, -5, -4, -3, -2, -1
(2) The integers between -4 and 4 are -3, -2, -1,0, 1,2, 3
(3) The integers between-8 and -15 are -14, -13, -12, -11, -10, -9
(4) The integers between -30 and -23 are -29, -28, -27, -26, -25, -24
8. (1) Write four negative integers greater than -20.
(2) Write four integers less than- 1 0.
Solution: (1) There are 19 negative integers which are greater than -20. Four of them are -19, -18, -17, -16
(2) There are infinite integers which are less than -10. Four of them are -11, -12, -13, -14
9. For the following statements, write True (T) or False (6). If the statement is false, correct the statement.
(1) – 8 is to the right of- 1 0 on a number line.
(2) – 100 is to the right of – 50 on a number line.
(3) Smallest negative integer is -1.
(4) – 26 is greater than- 25
Solution: (1) True
(2) False
Since -100 is to the left of -50 on the number line.
(3) False
Since -1 is the greatest negative integer.
(4) False
Since -26 is less than -25.
10. Draw a number line and answer the following :
(1) Which number will we reach if we move 4 numbers to the right of- 2.
(2) Which number will we reach if we move 5 numbers to the left of 1.
(3) if wc arc at- 8 on the number line, in which direction should we move to reach – 1 3?
(4) If we are at- 6 on the number line, in which direction should we move to reach – 1 ?
Solution: (1)
Thus, we will reach 2 if we move 4 numbers to the right of -2.
(2)
Thus, we will reach -4 if we move 5 numbers to the left of 1.
(3)
Thus, we should move 5 numbers to the left of-8 to reach -13.
(4)
Thus, we should move 5 numbers to the right of -6 to reach -1.
Exercise – 6.2
1. Using the number line write the integer which is:
(1) 3 more than 5
(2) 5 more than -5
(3) 6 less than 2
(4) 3 less than -2
Solution: (1)
Thus, 3 more than 5 is 8.
(2)
Thus, 5 more than -5 is 0.
(3)
Thus, 6 less than 2 is -4.
(4)
Thus, 3 less than -2 is -5.
2. Use number line and add the following integers :
(1) 9 + (-6)
(2) 5 + (-11)
(3) (-1) + (-7)
(4) (- 5) + 10
(5) (- 1 ) + (- 2) + (- 3)
(6) (- 2) + 8 + (- 4)
Solution: (1)
Thus, 9 + (-6) = 3
(2)
Thus, 5 + (-11) = -6
(3)
Thus, (-1) + (-7) = -8
(4)
Thus, (-5) + 10 = 5
(5)
Thus, (-1) + (-2) + (-3) = -6
(6)
Thus, (-2) + 8 + (-4) = 2
3. Add without using number line:
(1) 1 1 + (- 7)
(2) (-13) + (+18)
(3) (-10) + (+19)
(4) (-250) + (+150)
(5) (- 380) + (- 270)
(6) (- 21 7) + (- 1 00)
Solution: (1) 11+ (-7) -11-7=4
(2) (-13) + (+18)= -13 + 18 =5
(3) (-10) + (+19)= -10 + 19 =9
(4) (-250) + (+150) = -250 + 150 = -100
(5) (-380) + (-270) = -380- 270 = -650
(6) (-217) + (-100) = -217 -100 = -317
4. Find the sum of:
(1) 137 and -354
(2) -52 and 52
(3) -31 2, 39 and 192
(4) -50, -200 and 300
Solution: (1) 137 + (-354) = 137- 354 = -217
(2) -52 + 52 = 0
(3) -312 + 39 + 192 = -312 + 231 =-81
(4) -50 + (-200) + 300 = -50 -200 + 300 = -250 + 300 = 50
5. Find the sum:
(1) (- 7) + (- 9) + 4 + 16
(2) (37) + (-2) + (-65) + (-8)
Solution: (1) (-7) + (-9) + 4 + 16
=-7-9 + 4 + 16
= -16 + 20 = 4
(2) (37) + (-2) + (-65) + (-8)
= 37-2-65-8
= 37- 75 =- 38
Exercise – 6.3
1. Find
(1) 35 -(20)
(2) 72 -(90)
(3) (-15) -(-18)
(4) (-20) -(13)
(5) 23 -(-12)
(6) (-32) -(-40)
Solution: (1) 35-20 = 15
(2) 72 -90 = -18
(3) (-15)- (-18) =- 15 + 18 = 3
(4) (-20) -(13) = -20 -13 = -33
(5) 23 -(-12) = 23 + 12 = 35
(6) (-32) -(-40) =-32 + 40 = 8
2. Fill in the blanks with >, < or = sign.
(1) (- 3) + (- 6) _________ (- 3)- (- 6)
(2) (-21) -(-10) ___________ (— 31) + (— 11)
(3) 45 – (- 11)___________ 57 + (-4)
(4) (-25) -(-42)__________ (- 42)- (- 25)
Solution: (1) < : (-3) + (-6) = -3- 6 = -9
(-3) -(-6) –3 + 6 = 3
Since, -9 < 3
(-3) + (-6) < (-3)- (-6)
(2) > : (-21)- (-10) = -21 + 10 = -11
(-31) + (-11) = -31 – 11 = -42
Since, -11 > -42
(-21) -(-10) >(-31) + (-11)
(3) > : 45- (-11) = 45 + 11 = 56
57 + (-4) = 57- 4 = 53
Since, 56 > 53
45 -(-11) >57 + (-4)
(4) > : (-25)- (-42) = -25 + 42 = 17
(-42)- (-25) = -42 + 25 = -17
Since, 17 >-17
(-25)- (-42) > (-42)- (-25)
3. Fill in the blanks
(1) (-8) +_______=0
(2) 13 +_________=0
(3) 12 + (-12) =_____
(4) (-4) +________=-12
(5) _________ -15 = -10
Solution: (1) 8 : (-8) + 8 = 0
(2) -13 : 13 + (-13) = 0
(3) 0:12 + (-12) = 0
(4) -8: (-4) + (-8) =-12
(5) 5: 5- 15 = -10
4. Find
(1) (-7)-8- (-25)
(2) (-13) + 32 -8-1
(3) (- 7) + (- 8) + (- 90)
(4) 50 -(-40) -(-2)
Solution: (1) (-7)- 8- (-25)
=-7-8 + 25
= -15 + 25 = 10
(2) (-13) +32-8-1
= -13 +32-8-1
= 32- 22 = 10
(3) (-7) + (-8) + (-90)
= -7- 8- 90 =- 105
(4) 50 -(-40) -(-2)
= 50 + 40 + 2 = 92
Section-2 NCERT Exemplar
Directions: 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
(1) +
(2) –
(3) x
(4) ÷
Solution: (2): Every integer which is less than 0 has negative sign.
2. The integer ‘5 units to the right of 0 on the number line’ is
(1) +5
(2) -5
(3) +4
(4) -4
Solution: (1): The integer which is 5 units to the right of 0 on the number line is +5.
3. The predecessor of the integer -1 is
(1) 0
(2) 2
(3) -2
(4) 1
Solution: (3): The predecessor of the integer -1 is -2.
4. Number of integers lying between -1 and 1 is
(1) 1
(2) 2
(3) 3
(4) 0
Solution: (1): Only 1 integer lies between -1 and1 i.e., 0
5. Number of whole numbers lying between -5 and 5 is
(1) 10
(2) 3
(3) 4
(4) 5
Solution: (4): There are 5 whole numbers lying between -5 and 5 i.e., 0, 1, 2, 3 and 4.
6. The greatest integer lying between -10 and -15 is
(1) -10
(2) -11
(3) -15
(4) -14
Solution: (2): -11 is the greatest integer lying between -10 and -15
7. The least integer lying between -10 and -15 is
(1) -10
(2) -11
(3) -15
(4) -14
Solution: (4): -14 is the least integer lying between -10 and -15.
8. On the number line, the integer 5 is located
(1) to the left of 0
(2) to the right of 0
(3) to the left of 1
(4) to the left of-2
Solution: (2):
The above number line shows that the integer 5 is located to the right of 0
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?
(1) (-1,10)
(2) (-3,-5)
(3) (-5,-3)
(4) (-6,0)
Solution: (2) :
On observing all the options by using a number line, we get that there is only one pair (-3, -5) in which the first integer is not on the left of the other integer.
10. The integer with negative sign (-) is always less than
(1) 0
(2) -3
(3) -1
(4) -2
Solution: (1): All the negative integers are less than 0.
11. An integer with positive sign (+) is always greater than
(1) 0
(2) 1
(3) 2
(4) 3
Solution: (1): All the positive integers are greater than 0.
12. The successor of the predecessor of -50 is
(1) -48
(2) -49
(3) -50
(4) -51
Solution: (3): The predecessor of -50 is -51 and the successor of -51 is -50.
13. The additive inverse of a negative integer
(1) is always negative
(2) is always positive
(3) is the same integer
(4) zero
Solution: (2): 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°C at A and -1°C at 6. Which of the following statement is true?
(1) A is cooler than B
(2) Bis cooler than A
(3) There is a difference of 2°C in the temperature
(4) The temperature at A is 4°C higher than that at B.
Solution: (1) :- 4°C < -1°C [ – 4 lies on the left of-1 on the number line]
Thus, A is cooler than B.
15. When a negative integer is subtracted from another negative integer, the sign of the result
(1) is always negative
(2) is always positive
(3) is never negative
(4) depends on the numerical value of the integers
Solution: (4): When a negative integer is subtracted from another negative integer, the sign of the result depends on the numerical
value of the integers.
16. The statement “When an integer is added to itself, the sum is greater than the integer” is
(1) always true
(2) never true
(3) true only when the integer is positive
(4) true for non-negative integers
Solution: (3): When an integer is added to itself, the sum is greater than the integer only when the integer is positive.
17. Which of the following shows the maximum rise in temperature?
(1) 0°C to 1 0°C
(2) -4°C to 8°C
(3) -15°C to -8°C
(4) -7°C to 0°C
Solution: (2) : (1) Rise in temperature = (10- 0)°C = 10°C
(2) Rise in temperature = (8- (-4))°C = (8 + 4)°C = 12°C
(3) Rise in temperature = (-8- (-15))°C = (-8 + 15)°C = 7°C
(4) Rise in temperature = (0- (-7))°C = (0 + 7)°C = 7°C
Thus, option (2) has maximum rise in temperature.
Directions: In questions 18 to 39, state whether the given statements are true (T) orfalse (6).
18. The smallest natural number is zero.
Solution: False
Since,1 is the smallest natural number.
19. Zero is not an integer as it is neither positive nor negative.
Solution: False
0 is neither positive nor negative, but it is an integer.
20. The sum of all the integers between -5 and -1 is -6.
Solution: False
-4, -3 and -2 lie between -5 and -1 and their sum is (-4) + (-3) + (-2) =-4-3-2 = -9
21. The successor of the integer 1 is 0.
Solution: False
0 is the predecessor of 1.
22. Every positive integer is larger than every negative integer.
Solution: True
Since positive integers lies on the right side of 0 and negative integers lies on the left side of 0 and the integers lying on the right are
always greater.
23. The sum of any two negative integers is always greater than both the integers.
Solution: False
Since, the sum of any two negative integers is always smaller than both the integers.
24. The sum ofany two negative integers is always smaller than both the integers.
Solution: True
25. The sum of any two positive integers is greater than both the integers.
Solution: True
26. All whole numbers are integers.
Solution: True
Integers are the collection of 0, positive integers and negative integers.
Whole numbers are the collection of 0 and positive integers.
All whole numbers are integers.
27. All integers are whole numbers.
Solution: False
Integers are the collection of 0, positive integers and negative integers.
Whole numbers are the collection of 0 and positive integers.
All integers are not whole numbers.
28. Since 5 >3, therefore -5 > -3.
Solution: False
Since,5 lies on the right of 3 on the number line 5>3
And-3 lies on the right of-5 on the number line, -3 >-5.
29. Zero is less than every positive integer.
Solution: True
Since, zero lies on the left side of every positive integer on the number line. Therefore, zero is less than every positive integer.
30. Zero is larger than every negative integer.
Solution: True
Since, zero lies on the right side of every negative integer on the number line.
Therefore, zero is larger than every negative integer.
31. Zero is neither positive nor negative.
Solution: True
32. On the number line, an integer on the right of a given integer is always larger than the integer.
Solution: True
33. -2 is to the left of-5 on the number line.
Solution: False
Since, -2 lies on the right of-5 on the number line.
34. The smallest integer is 0.
Solution: False
Since, zero is greater than all the negative integers.
0 is not the smallest integer.
35. 6 and -6 are at the same distance from 0 on the number line.
Solution: True
The integer 6 is 6 units to the right of 0 and the integer -6 is 6 units to the left of 0.
Thus, 6 and -6 are at the same distance from 0 on the number line.
36. The difference between an integer and its additive inverse is always even.
Solution: True
Let a be any integer and -a is its additive inverse.
Difference = a- (-a) = a + a = 2a, which is an even number.
37. The sum of an integer and its additive inverse is always zero.
Solution: True
Let a be any integer and -a is its additive inverse.
Sum = a + (-a) =a- a = 0.
38. The sum of two negative integers is a positive
integer.
Solution: False
Since, the sum of two negative integers is always negative.
39. The sum of three different integers can never be zero.
Solution: False
Let -3, 1, 2 are three different integers.
Sum = (-3) +1 + 2 =-3 + 3 = 0
Directions: In questions 40 to 49, fill in the blanks to make the statements true.
40. On the number line, -1 5 is to the zero.
Solution: Left
41. On the number line, 10 is to the of zero.
Solution: Right
42. The additive Inverse of 14 is_.
Solution: -14: Additive inverse of an integer is obtained by changing the sign of the integer.
Additive inverse of 14 is -14.
43. The additive inverse of-1 is
Solution: 1
44. The additive inverse of 0 is
Solution: 0
45. The number of integers lying between -5 and 5 is
Solution: 9: The integers lying between -5 and 5 are -4, -3, -2, -1, 0, 1, 2, 3, 4 i.e., 9 in number
46. (-11) + (-2) + (-1) =____________
Solution: -14: (-11) + (-2) + (-1) =-11- 2-1 = “14
47.___________ + (-11) + 111 = 130
Solution: 30
48. (-80) + 0 + (-90) =____________
Solution: -170: (-80) + 0 + (-90) =-80 + 0- 90 =-170
49. -3456 = -8910
Solution: -5454
Directions: In questions 50 to 58,fill in the blanks using <, = or >.
50. (-11) + (-15)___________ 11+15
Solution: < : (-11) + (-15) = -11-15 = -26
11 + 15 = 26 and -26 < 26
51. (-71) + (+9)___________ (-81) + (-9)
Solution: >: (-71) + (9) = -71 + 9 = -62
(-81) + (-9) = -81- 9 = -90 and -62 > -90
52. 0__________ 1
Solution: <:0<1
53. -60__________ 50
Solution: < : -60 < 50
54. -10__________ -11
Solution: >: —10 > —11
55. -101___________ -102
Solution: >: -101 >-102
56. (-2) + (-5) + (-6)__________ (-3) + (-4) + (-6)
Solution: = : (-2) + (-5) + (-6) = -2- 5- 6 = -13
(-3) + (-4) + (-6) =-3-4- 6 =-13
And -13 =-13
57. 0 __________ -2
Solution: >:0>-2
58. 1+2 + 3________ (-1 ) + (-2) + (-3)
Solution: >: 1 +2+3=6
(-1) + (-2) + (-3) =-l-2-3 =-6
And 6 > -6
59. Match the items of Column I with that of Column II:
Solution:
(i)–>(B), (ii)–> (E), (iii) —> (B), (iv) –> (A),(v) –> (B)
(i) The additive inverse of +2 is -2.
(ii) The greatest negative integer is -1.
(iii) The greatest negative even integer is -2.
(iv) The smallest integer 0 is greater than every negative integer.
(v) Predecessor and successor of -1 are -2 and 0 respectively.
∴ Sum = -2 + 0 = -2
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)
Solution: (1) 30 + (-25) + (-10) = 30 + (-25- 10) = 30 + (-35) = 30- 35 = -5
(2) (-20) + (-5) = -20-5 = -25
(3) 70 + (-20) + (-30) = 70 + (-20- 30) = 70 + (-50) = 70- 50 = 20
(4) -50 + (-60) + 50 = (-50 -60) + 50 = -110 + 50 = -60
(5) 1 + (-2) + (-3) + (-4) =1 +(-2-3-4)=1+ (-9) =1- 9 = -8
(6) 0 + (-5) + (-2) 0 + (-5 -2) « 0 + (-7) = 0- 7 = -7
(7)0- (-6)- (+6) = 0 + 6- 6 = 6- 6 = 0
(8) 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, write the following using integers with the appropriate signs:
(1) 200 m above sea level
(2) 1 00 m below sea level
(3) 10m above sea level
(4) sea level
Solution: (1) 200 m above sea level = + 200
(2) 100 m below sea level =- 100
(3) 10 m above sea level = + 10
(4) Sea level = 0
62. Write the opposite of each of the following :
(1) Decrease in size
(2) Failure
(3) Profit of? 10
(4) 1000 AD
(5) Rise in water level
(6) 60 km south
(7)10m 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? 100 in the Bank account
(11) 20°C rise in temperature.
Solution: (1) Increase in size.
(2) Success.
(3) Loss of? 10
(4) 1000 BC
(5) Fall in water level.
(6) 60 km north.
(7)10 m below the danger mark of river Ganga.
(8) 20 m above the danger mark of the river Brahmaputra.
(9) Losing by a margin of 2000 votes.
(10)Withdrawing ? 100 from the Bank account.
(11) 20°C fall in temperature.
63. Temperature of a place at 12:00 noon was +5°C. Temperature increased by 3°C in first hour and decreased by 1°C in the second hour. What was the temperature at 2:00 pm?
Solution:
Given
Temperature of a place at 12:00 noon was +5°C. Temperature increased by 3°C in first hour and decreased by 1°C in the second hour.
Temperature at 12 : 00 noon = + 5°C
Temperature at 1 : 00 p.m. = 5°C + 3°C = 8°C
And temperature at 2 : 00 p.m. = 8°C- 1°C = 7°C
64. Write the digits 0, 1,2, 3, 9 in this order and insert ‘+’ or between them to get the result 3.
Solution: The digits can be written as 0-1-2-3-4-5-6+7+8+9=3
65. Write the integer which is its own additive inverse.
Solution: 0 is the integer which is its own additive inverse
66. Write six distinct integers whose sum is 7.
Solution: 1 + 2 + 3 + 6 + (-2) + (-3) = 7
The six distinct integers are 1, 2, 3, 6, -2 and -3.
67. Write the integer which is 4 more than its additive inverse.
Solution: Let x be the required integer.
According to question,
x = 4 + (-x), where (-x) is the additive inverse of x.
=> x = 4-x => x + x = 4
=> 2x = 4 => x = 2
The required integer is 2.
68. Write the integer which is 2 less than its additive inverse.
Solution: Let the required integer be x.
According to question,
x = (-x)- 2, where -x is the additive inverse of x.
x=-x-2 => x + x = -2
2x = -2 => x = —1
69. Write two integers whose sum is less than both the integers.
Solution: We can take any two negative integers, i.e., -2 and -4.
Sum = -2 + (-4) = -2- 4 = -6, which is less than both -2 and -4.
70. Write two distinct integers whose sum is equal to one of the integers.
Solution: Two distinct integers whose sum is equal to one of the integer, then one must be 0 in them.
Let us take 0 and 4.
Sum = 0 + 4 =4.
71. Using number line, how do you compare
(1) two negative integers?
(2) two positive integers?
(3) one positive and one negative integer?
Solution: Since, the integer lying on right is greater than the integer lying on left.
In all of the given cases (1), (2) and (3), we can compare by using the number line by observing which one of the given integers lie
on tine right or left.
72. Observe the following : 1 +2-3+4+5-6-7+8-9=-5 Change one’-‘sign as’+’sign to get the sum 9.
Solution: On observing the given expression, l + 2- 3 + 4 +5-6- 7 +8- 9 = -5, we noticed that (-7) should be replaced by (+7) to get a result of 9.
Thus, 1+2-3+4+5-6+7+8-9
= (l+2 + 4 + 5 + 7 + 8)-(3 + 6 + 9)
= 27-18 = 9
73. Arrange the following integers in the ascending order: -2, 1,0, -3, 4, -5
Solution: Ascending order of given integers is, -5, -3, -2, 0,1, 4
74. Arrange the following integers in the descending order: -3, 0, -1,-4, -6
Solution: Descending order of given integers is, 0, -1, -3, -4, -6
75. Write two integers whose sum is 6 and difference is also 6.
Solution: We have, 6 + 0 = 6,
6-0 = 6
The required two integers are 6 and 0.
76. Write five integers which are less than -100 but greater than -1 50.
Solution: The required five integers which are less than -100 but greater than -150 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.
Solution: There are many pairs of integers which are at the same distance from 2 i.e., (1,3), (0,4), (-1, 5) and (-2, 6)
78. The sum of two integers is 30. If one of the integers is -42, then find the other.
Solution:
Given
The sum of two integers is 30. If one of the integers is -42
Let the required integer be x.
According to question,
x + (-42) = 30
=>x -42 = 30
=> x = 30 + 42 = 72
79. Sum of two integers is -80. If one of the integers is -90, then find the other.
Solution:
Given
Sum of two integers is -80. If one of the integers is -90
Let the required integer be x.
According to question,
x + (-90) = -80
=> x- 90 =- 80 => x = -80 + 90 = 10
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?
Solution: (1) If we are at 8 on the number line, then to reach the integer -5, we must move towards the left on the number line.
(2) If we are at 8 on the number line, then to reach the integer 11, we must move towards the right on the number line.
(3) If we are at 8 on the number line, then to reach the integer 0, we must move towards the left on the number line.
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
Solution: (1) We want to know an integer 4 more than -5.
So, we start from -5 and proceed 4 steps to the right, then we obtain -1 as shown below.
Hence, 4 more than -5 is -1.
(2) We want to know an integer 3 less than 2.
So, we start from 2 and proceed 3 steps to the left, then we obtain -1 as shown below.
Hence, 3 less than 2 is -1.
(3) We want to know an integer 2 less than-2.
So, we start from -2 and proceed 2 steps to the left, then we obtain -4 as shown below.
Hence, 2 less than -2 is -4
82. Find the value of 49 -(-40) -(-3) + 69
Solution: We have,
49- (-40)- (-3) + 69
= 49 + 40 + 3 + 69 = 161
The value of 49 -(-40) -(-3) + 69= 161
83. Subtract -5308 from the sum [(-2100) + (-2001)1]
Solution: We have, [(-2100) + (-2001)]
= [-2100-2001]
= -4101
Required difference = —4101- (-5308)
= -4101 + 5308 = 1207