Exercise 6.1 

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Q1. Write opposites of the following :

(a) Increase in weight

(b) 30 km north

(c) 326 BC

(d) Loss of Rs 700

(e) 100 m above sea level

Solution: Q1. 

(a) Increase in weight 

Answer : Decrease in weight

(b) 30 km North 

Answer : 30 km Sounth

(c) 326 BC 

Answer : 326 AD 

(d) Loss of Rs 700 

Answer : Profit of Rs 700.

(e) 100 m above sea level

Answer : 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.
(b) A submarine is moving at a depth, eight hundred metre below the sea level.
(c) A deposit of rupees two hundred.
(d) Withdrawal of rupees seven hundred.

Solution Q2. 

(a) An aeroplane is flying at a height two thousand metre above the
ground.

Answer : + 2000 m 

(b) A submarine is moving at a depth, eight hundred metre below the sea level.

Answer : - 800 m 

(c) A deposit of rupees two hundred.

Answer : + Rs 200

(d) Withdrawal of rupees seven hundred.

Answer : - Rs 700 

Q3. Represent the following numbers on a number line :

(a) + 5

(b) – 10

(c) + 8

(d) – 1

(e) – 6

Solution Q3: 

(a) + 5 

Answer :  

(b) – 10 

Answer : 

(c) + 8

Answer : 

(d) – 1 

Answer : 

(e) – 6

Answer : 

Q4. 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.

Solution Q4. 

 

 

 

 

 

 

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.
(b) Following is the number line representing the temperature in degree Celsius.

Plot the name of the city against its temperature.
(c) Which is the coolest place?
(d) Write the names of the places where temperatures are above 10°C.

Solution Q5: 

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

Answer: 

(b) Following is the number line representing the temperature in degree Celsius.

Plot the name of the city against its temperature.

(c) Which is the coolest place?

Answer : The coolest place is Siachin 

(d) Write the names of the places where temperatures are above 10°C.

Answer : Delhi and Ahmedabad. 

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

(a) 2, 9

(b) – 3, – 8

(c) 0, – 1

(d) – 11, 10

(e) – 6, 6

(f) 1, – 100

Solution Q6: 

(a) 9 is right to 2

(b) –3 is right to –8

(c) 0 is right to –1

(d) 10 is right to –11

(e) 6 is right to –6

(f) 1 is right to –100

Q7. Write all the integers between the given pairs (write them in the increasing order.)
(a) 0 and – 7

(b) – 4 and 4

(c) – 8 and – 15

(d) – 30 and – 23

Solution Q7: 

(a) 0 and – 7 

Answer : –6, –5, –4, –3, –2, –1 

(b) – 4 and 4

Answer :  –3, –2, –1, 0, 1, 2, 3 

(c) – 8 and – 15 

Answer :  –14, –13, –12, –11, –10, –9 

(d) – 30 and – 23

Answer : –29, –28, –27, –26, –25, –24

Q8. (a) Write four negative integers greater than – 20.

Solution : –19, –18, –17, –16

(b) Write four negative integers less than – 10.

Solution :  –11, –12, –13, –14

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.

Solution : True (T)

(b) – 100 is to the right of – 50 on a number line.

Solution : False (F)

(c) Smallest negative integer is – 1.

Solution: False (F)

(d) – 26 is greater than – 25.

Solution: False (F)

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.

Solution : 

(b) Which number will we reach if we move 5 numbers to the left of 1.

(c) If we are at – 8 on the number line, in which direction should we move to reach – 13?

Solution: We should move to left side. 

(d) If we are at – 6 on the number line, in which direction should we move to reach – 1?

Solution: We should move to right side. 

Exercise 6.2 

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Q1. Using the number line write the integer which is :

(a) 3 more than 5

Solution: 

(b) 5 more than –5

Solution : 

(c) 6 less than 2

Solution : 

(d) 3 less than –2

Solution : 

Q2. Use number line and add the following integers :
(a) 9 + (– 6)
(b) 5 + (– 11)
(c) (– 1) + (– 7)
(d) (– 5) + 10
(e) (– 1) + (– 2) + (– 3)
(f) (– 2) + 8 + (– 4)

Solution Q2: 

(a) 9 + (– 6)

Solution: 

(b) 5 + (– 11)

Solution : 

(c) (– 1) + (– 7)

Solution : 

(d) (– 5) + 10

Solution : 

(e) (– 1) + (– 2) + (– 3)

Solution : 

(f) (– 2) + 8 + (– 4)

Solution : 

Q3. Add without using number line :

(a) 11 + (– 7)

(b) (– 13) + (+ 18)

(c) (– 10) + (+ 19)

(d) (– 250) + (+ 150)

(e) (– 380) + (– 270)

(f) (– 217) + (– 100)

Q4. Find the sum of :

(a) 137 and – 354

(b) – 52 and 52

(c) – 312, 39 and 192

(d) – 50, – 200 and 300

Solution: 

(a) 137 and – 354 

  137 + (-354)

= 137 - 354

= – 217 Answer

Solution: 

(b) – 52 and 52

= (- 52) + 52 

= 0 Answer

Solution: 

(c) – 312, 39 and 192 

   (– 312) + 39 + 192 

= - 312 + 231

= - 81 Answer

Solution: 

(d) – 50, – 200 and 300

   (– 50) + (– 200) + 300

= (- 250) + 300

= 50 Answer

Q5. Find the sum :
(a) (– 7) + (– 9) + 4 + 16
(b) (37) + (– 2) + (– 65) + (– 8)

Solution: 

(a) (– 7) + (– 9) + 4 + 16

= (- 16) + 20 

= 4 Answer

Solution : 
(b) (37) + (– 2) + (– 65) + (– 8)

= (37) + (- 75) 

= 37 - 57 

= – 38 Answer

Exercise 6.3

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Q1. Find
(a) 35 – (20)

(b) 72 – (90)
(c) (– 15) – (– 18)

(d) (–20) – (13)
(e) 23 – (– 12)

(f) (–32) – (– 40)

Solution: 

(a) 35 – (20)

= 15 Answer

(b) 72 – (90)

= - 18 Answer
(c) (– 15) – (– 18)

= - 15 + 18 

= 3 Answer

(d) (–20) – (13)

= - 20 - 13

= - 33 Answer

(e) 23 – (– 12)

= 23 + 12

= 35 Answer

(f) (–32) – (– 40)

= - 32 + 40 

= 8 Answer 

Q2. Fill in the blanks with >, < or = sign.
(a) (– 3) + (– 6) ______ (– 3) – (– 6)
(b) (– 21) – (– 10) _____ (– 31) + (– 11)
(c) 45 – (– 11) ______ 57 + (– 4)
(d) (– 25) – (– 42) _____ (– 42) – (– 25)

Solution: 

(a) (– 3) + (– 6) ______ (– 3) – (– 6)

= - 9 __________ - 3 + 6

= - 9 < 3 Answer
(b) (– 21) – (– 10) _____ (– 31) + (– 11)

= - 21 + 10 ________ - 31 - 11

= - 11 > - 42 Answer

(c) 45 – (– 11) ______ 57 + (– 4)

= 45 + 11 _____ 57 - 4 

= 56 > 53 Answer

(d) (– 25) – (– 42) _____ (– 42) – (– 25)

= - 25 + 42 ______ - 42 + 25 

= 17 > - 17 Answer

Q3. Fill in the blanks.
(a) (– 8) + _____ = 0
(b) 13 + _____ = 0
(c) 12 + (– 12) = ____
(d) (– 4) + ____ = – 12
(e) ____ – 15 = – 10

Solution : 

(a) (– 8) + _____ = 0

= - 8 + 8 = 0 

(a) 8 Answer

(b) 13 + _____ = 0

= 13 + (- 13) = 0 

(b) - 13 Answer

(c) 12 + (– 12) = ____

= 12 + (-12) = 0 

(c) 0 Answer
(d) (– 4) + ____ = – 12

= - 4 + (-8) = - 12

(d) - 8 Answer

(e) ____ – 15 = – 10

= 5 - 15 = - 10

(e) 5 Answer

Q4. Find
(a) (– 7) – 8 – (– 25)
(b) (– 13) + 32 – 8 – 1
(c) (– 7) + (– 8) + (– 90)
(d) 50 – (– 40) – (– 2)

Solution : 

(a) (– 7) – 8 – (– 25) 

= - 7 - 8 + 25 

= - 15 + 25 

= 10 Answer

(b) (– 13) + 32 – 8 – 1 

= - 13 + 32 - 9 

= 32 - 22

= 10 Answer

(c) (– 7) + (– 8) + (– 90) 

= - 7 - 8 - 90 

= - 105 Answer

(d) 50 – (– 40) – (– 2) 

= 50 + 40 + 2 

= 92 Answer