NCERT Solutions: Integers

# NCERT Solutions for Class 8 Maths Chapter 1 - Integers

## 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

(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

The document NCERT Solutions for Class 8 Maths Chapter 1 - Integers is a part of the Class 6 Course Mathematics (Maths) Class 6.
All you need of Class 6 at this link: Class 6

## Mathematics (Maths) Class 6

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## FAQs on NCERT Solutions for Class 8 Maths Chapter 1 - Integers

 1. What are integers?
Ans. Integers are a set of whole numbers and their opposites. They include all the numbers like -3, -2, -1, 0, 1, 2, 3, and so on.
 2. What is the difference between positive and negative integers?
Ans. Positive integers are greater than zero, whereas negative integers are less than zero. Positive integers are written without any sign, whereas negative integers are written with a negative sign (-) before the number.
 3. How do we add integers?
Ans. To add integers with the same sign, add their absolute values and keep the common sign. To add integers with different signs, subtract their absolute values and keep the sign of the integer with the greater absolute value.
 4. Can we multiply any two integers and obtain another integer?
Ans. Yes, we can multiply any two integers and obtain another integer. The product of two integers with the same sign is always positive, and the product of two integers with different signs is always negative.
 5. What is the absolute value of an integer?
Ans. The absolute value of an integer is the distance of the integer from zero on the number line. It is always a positive number. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5.

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