NCERT Solutions for Class 6 Maths - Integers

NCERT SOLUTIONS

Exercise 6.1

Q1. Write opposites of the following:
(a) Increase in weight
Ans: The opposite of increase in weight is decrease in weight.

(b) 30 km North
Ans: The opposite of 30 km North is 30 km South.

(c) 80 m East
Ans: The opposite of 80 m East is 80 m West.

(d) Loss of Rs 700
Ans: The opposite of loss of Rs 700 is gain of Rs 700.

(e) 100 m above sea level
Ans: The opposite of 100 m above sea level is 100 m below sea level.

Q2. Represent the following numbers as integers with appropriate signs.

(a) An aeroplane is flying at a height two thousand metre above the ground.
Ans: (+) 2000 meters

(b) A submarine is moving at a depth, eight hundred metre below the sea level.
Ans: (-) 800 meters

(c) A deposit of rupees two hundred.
Ans: (+) 200 Rupees

(d) Withdrawal of rupees seven hundred.
Ans: (-) 700 Rupees

Q3. Represent the following numbers on a number line:

(a) + 5
Ans: 

(b) -10
Ans:  

(c) + 8
Ans: 

(d) -1
Ans: 

(e) -6
Ans:  

Q4. The adjacent figure is a vertical number line, representing integers. Observe it and locate the following points:
(a) If point D is + 8, then which point is -8?
(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.
Ans: (a) If point D is +8, then point F is -8
(b) Point G is a negative integer
(c) Point B is 4 and point E is – 10
(d) The least value on this number line is point E as it represents – 10
(e) The points in decreasing order of value are D, C, B, A, O, H, G, F, E

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

(a) Write the temperatures of these places in the form of integers in the blank column.
Ans: 

(b) Following is the number line representing the temperature in degree Celsius.
Plot the name of the city against its temperature.
Ans: Number line

(c) Which is the coolest place?
Ans: Siachin is the coolest place.

(d) Write the names of the places where temperatures are above 10°C.
Ans: Ahmedabad and Delhi are the places where the temperatures are above 10°C.

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

(a) 2, 9
Ans: 9 lies to the right on the number line (9 > 2)

(b) -3, -8 
Ans: –3 lies to the right on the number line (- 3 > – 8)

(c) 0, -1
Ans: 0 lies to the right on the number line (0 > -1)

(d) -11, 10
Ans: 10 lies to the right on the number line (10 > -11)

(e) -6, 6
Ans: 6 lies to the right on the number line (6 > -6)

(f) 1, -100
Ans: 1 lies to the right on the number line (1 > -100)

Q7. Write all the integers between the given pairs (write them in increasing order.)
(a) 0 and -7 
Ans: -6, -5, -4, -3, -2, -1 are the integers between 0 and -7

(b) -4 and 4
Ans: -3, -2, -1, 0, 1, 2, 3 are the integers between -4 and 4

(c) -8 and -15
Ans: -14, -13, -12, -11, -10, -9 are the integers between -8 and -15

(d) -30 and -23
Ans: -29, -28, -27, -26, -25, -24 are the integers between -30 and -23

Q8. Answer the following questions.
(a) Write four negative integers greater than -20.
Ans: -19, -18, -17, -16 are the integers greater then -20

(b) Write four negative integers less than -10.
Ans: -11, -12, -13, -14 are the integers less than -10

Q9. For the following statements, write True (T) or False (F). If the statement is false, correct the statement.
(a) -8 is to the right of -10 on a number line.
Ans: True as (-8 > -10)

(b) -100 is to the right of -50 on a number line.
Ans: False as (-50 is greater than -100). 

Correct Statement: -100 lies to the left of -50 on the number line. OR -50 lies to the right of -100 on a number line. 

(c) Smallest negative integer is -1
Ans: False. 

Correct Statement: Greatest negative integer is -1.

(d) -26 is greater than -25.
Ans: False.

Correct Statement: -26 is smaller than -25 OR -25 is greater than -26.  

Q10. Draw a number line and answer the following:
(a) Which number will we reach if we move 4 numbers to the right of -2.
Ans: If we move 4 numbers to the right of -2, we will reach at 2.

(b) Which number will we reach if we move 5 numbers to the left of 1.
Ans: If we move 5 numbers to the left of 1, we will reach at -4.

(c) If we are at -8 on the number line, in which direction should we move to reach -13?
Ans: As -13 lies to the left of -8 on the number line, we should move towards the left direction.

(d) If we are at -6 on the number line, in which direction should we move to reach -1?
Ans: As -1 lies to the right of -6 on the number line, we should move towards the right direction.

Exercise 6.2

Q1. Using the number line write the integer which is:
(a) 3 more than 5
Ans: 8 

(b) 5 more than -5
Ans: 0

(c) 6 less than 2
Ans: -4

(d) 3 less than -2
Ans: -5

Q2. Use number line and add the following integers:
(a) 9 + (-6)
Ans: 9 + (-6) = 3 

(b) 5 + (-11)
Ans: 5 + (-11) = -6

(c) (-1) + (-7)
Ans: (-1) + (-7) = -8

(d) (-5) + 10
Ans: (-5) + 10 = 5 

(e) (-1) + (-2) + (-3)
Ans: (-1) + (-2) + (-3) = -6

(f) (-2) + 8 + (-4)
Ans: (-2) + 8 +(-4) = 2 

Q3. Add without using number line:
(a) 11 + (-7)
Ans: 11 + (-7) = 11 - 7 = 4

(b) (-13) + (+18)
Ans: (-13) + 18 = -13 +18 = 5

(c) (-10) + (+19)
Ans: (-10) + (+19) = -10 + 19 = 9

(d) (-250) + (+ 150)
Ans: (-250) + (+150) = -250 + 150 = -100

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

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

Q4. Find the sum of:
(a) 137 and -354
Ans: 137 and -354
(137) + (-354) = (137) + (-137) + (-217)
= 0 + (-217)  [(137) + (-137) = 0]
= (-217)
= -217

(b) -52 and 52
Ans: -52 and 52
(-52) + (+52) = 0 [(-a) + (+a) = 0]

(c) -312, 39 and 192
Ans: -312, 39 and 192
(-312) + (+39) + (+192)
= (-231) + (-81) + (+39) + (+192)
= (-231) + (-81) + (+231)
= (-231) + (+231) + (-81)
= 0 + (-81) [(-a) + (+a) = 0]
= -81

(d) -50, -200 and 300
Ans: -50, -200 and 300
(-50) + (-200) + (+300)
= (-50) + (-200) + (+200) + (+100)
= (-50) + 0 + (+100) [(-a) + (+a) = 0]
= (-50) + (+100) = (-50) + (+50) + (+50)
= 0 + (+50) [(-a) + (+a) = 0]
= 50

Q5. Find the sum:
(a) (-7) + (-9) + 4 + 16
Ans: (-7) + (-9) + 4 + 16
= -7 - 9 + 4 + 16
= -16 + 20
= 4

(b) (37) + (-2) + (-65) + (-8)
Ans: 37 + (-2) + (-65) + (-8)
= 37 - 2 - 65 - 8
= 37 - 75
= -38

Exercise 6.3

Q1. Subtract: 
(a) 35 - (20)
Ans: 35 - 20 = 15

(b) 72 - (90)
Ans: 72 - 90 = -18

(c) (-15) - (-18)
Ans: (-15) - (-18)
= -15 + 18
= 3

(d) (-20) - (13)
Ans: -20 - (13)
= -20 - 13
= -33

(e) 23 - (-12)
Ans: 23 - (-12)
= 23 + 12
= 35

(f) (-32) - (-40)
Ans: (-32) - (-40)
= -32 + 40
= 8

Q2. Fill in the blanks with >, < or = sign: 
(a) (-3) + (-6) _______________ (-3) - (-6)
Ans: (-3) + (-6) = -9
(-3) – (-6) = -3 + 6 = 3
-9 < 3
Therefore (-3) + (-6) < (-3) – (-6)

(b) (-21) - (-10) _______________ (-31) + (-11)
Ans: -21 – (-10)
= -21 + 10 = -11 -31 + (-11) = -42
-11 > -42
Therefore (-21) – (-10) > (-31) + (-11) 

(c) 45 - (-11) _______________ 57 + (-4)
Ans: 45 – (-11) = 45 + 11 = 56
57 + (-4) = 57 – 4 = 53
56 > 53
Therefore 45 – (-11) > 57 + (-4)

(d) (-25) - (-42) _______________ (-42) - (-25)
Ans: (-25) – (-42) = -25 + 42
= 17 -42 – (-25) = -42 + 25 = -17
17 > -17
Therefore (-25) – (-42) > (-42) – (-25)

Q3. Fill in the blanks: 
(a) (-8) + __________ = 0
Ans: (-8) + 8 = 0

(b) 13 + __________ = 0 
Ans: 13 + (-13) = 0

(c) 12 + (-12) = __________ 
Ans: 12 + (-12) = 0

(d) (-4) + __________ = -12 
Ans: (-4) + (-8) = -12 

(e) __________ - 15 = -10
Ans: 5 - 15 = -10  

Q4. Find: 

(a) (-7) - 8 - (-25)
Ans: = (-7) - 8 - (-25) = -7 - 8 + 25
= -15 + 25
= 10

(b) (-13) + 32 - 8 - 1
Ans: = (-13) + 32 - 8 - 1 = -13 + 32 - 8 - 1
= 32 - 22
= 10

(c) (-7) + (-8) + (-90)
Ans: = (-7) + (-8) + (-90) = -7 - 8 - 90
= -105

(d) 50 - (-40) - (-2)
Ans: = 50 - (-40) - (-2) = 50 + 40 + 2
= 92