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Integers

Integers

 

Class –VI Mathematics
(Ex. 6.1)
Question 1.Write opposite 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

Answer:

(a) Decrease in weight

(b) 30 km south

(c) 326 AD

(d) Profit of Rs. 700

(e) 100 m below sea level


NCERT Solutions for Class 6 Maths Exercise 6.1

Question 2.Represent the following numbers as integers with appropriate signs.

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

(b)A submarine is moving at a depth eight thousand meters below the sea level.

(c)A deposit of rupees two hundred.

(d)Withdrawal of rupees seven hundred.

Answer:

(a) (+) 200 meters

(b) (–) 800 meters

(c) (+) 200 Rupees

(d) (–) 700 Rupees


Question 3.Represent the following numbers on number line:

(a) +5

(b) –10

(c) +8

(d) –1

(e) –6

Answer:

(a)

(b) 


NCERT Solutions for Class 6 Maths Exercise 6.1

Question 4.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 values.

Answer:

(a) F

(b) Negative

(c) B = (+) 4; E = (–) 10

(d) E

(e) D, C, B, A, O, H, G, F, E


Question 5.Following is the list of temperatures of five places in India, on a particular day of the year.
PlaceTemperature
Siachin10 C below 0C_______________________
Shimla2C below 0C_______________________
Ahmedabad30C above 0C_______________________
Delhi20C above 0C_______________________
Srinagar5C below 0C_______________________

(a)Write the temperature 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.

(a)Which is the coolest place?

(b)Write the names of the place where temperature are above 10oC.

Answer:

(a)

PlaceTemperature
Siachen(-) 10C
Shimla(–) 2C
Ahmedabad(+) 30C
Delhi(+) 20C
Srinagar(–) 5C

(b)Number line

(c)Siachin

(d)Ahemadabad, Delhi


NCERT Solutions for Class 6 Maths Exercise 6.1

Question 6.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

Answer:

(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


Question 7.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

Answer:

(a) –6, –5, –4, –3, –2, –1

(b) –3, –2, –1, 0, 1, 2, 3

(c) –14, –13, –12, –11, –10, –9

(d) –29, –28, –27, –26, –25, –24


NCERT Solutions for Class 6 Maths Exercise 6.1

Question 8.

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

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

Answer:

(a) –19, –18, –17, –16

(b) –11, –12, –13, –14


Question 9.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.

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

(c)Smallest negative integer is –1.

(d)–26 is larger than –25.

Answer:

(a) True

(b) False

(c) False

(d) False


NCERT Solutions for Class 6 Maths Exercise 6.1

Question 10.Draw a number line and answer the following:

(a)Draw a number line will we reach if we move 4 numbers to the right of –2.

(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?

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

Answer:

(a)

(c) On left side

(d) On right side

 

(Ex. 6.2)
Question 1.Using the number line write the integer which is:

(a) 3 more than 5

(b) 5 more than –5

(c) 6 less than 2

(d) 3 less than –2

Answer:

(a) 8

(b) 0

(c) –4

(d) –5


Question 2.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)

Answer:

(a) 9 + (–6) = 3

(b) 5 + (–11) = –6

(c) (–1) + (–7) = –8

(d) (–5) + 10 = 5

(e)(–1) + (–2) + (–3) = –6

(f)(–2) + 8 + (–4) = 2


NCERT Solutions for Class 6 Maths Exercise 6.2

Question 3.Add without using number line:

(a) 11 + (–7)

(b) (–13) + (+18)

(c) (–10) + (+19)

(d) (–250) + (+150)

(e) (–380) + (–270)

(f) (–217) + (–100)

Answer:

(a) 11 + (–7) = 11 – 7 = 4

(b) (–13) + 18 = 5

(c) (–10) + (+19) = –10 + 19 = 9

(d) (–250) + (+150) = –250 + 150 = –100

(e) (–380) + (–270) = –380 – 270 = –650

(f) (–217) + (–100) = –217 v 100 = –317


Question 4.Find the sum of:

(a) 137 and –354

(b) –52 and 52

(c) –213, 39 and 192

(d) –50, –200 and 300

Answer:

(a) 137 + (–354) = 137 – 354 = –217

(b) (–52) + 52 = 0

(c) (–312) + 39 + 192 = –312 + 231 = –81

(d) (–50) + (–200) + 300 = –50 – 200 + 300 = –250 + 300 = 50


NCERT Solutions for Class 6 Maths Exercise 6.2

Question 5.Find the value of:

(a)(–7) + (–9) + 4 + 16

(b)37 + (–2) + (–65) + (–8)

Answer:

(a) (–7) + (–9) + 4 + 16

= –7 – 9 + 4 + 16

= –16 + 20

= 4

(b) 37 + (–2) + (–65) + (–8)

= 37 – 2 – 65 – 8

= 37 – 75

= –38

(Ex. 6.3)
Question 1.ubtract:

(a) 35 – (20)

(b) 72 – (90)

(c) (–15) – (–18)

(d) (–20) – (13)

(e) 23 – (–12)

(f) (–32) – (–40)

Answer:

(a) 35 – 20 = 15

(b) 72 – 90 = –18

(c) (–15) – (–18) = –15 + 18 = 3

(d) –20 – (13) = –20 – 13 = –33

(e) 23 – (–12) = 23 + 12 = 35

(f) (–32) – (–40) = –32 + 40 = 8


NCERT Solutions for Class 6 Maths Exercise 6.3

Question 2.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)

Answer:

(a) (–3) + (–6) < (–3) – (–6)

(b) (–21) – (–10) > (–31) + (–11)

(c) 45 – (–11) > 57 + (–4)

(d) (–25) – (–42) > (–42) – (–25)


Question 3.Fill in the blanks:

(a)(–8) + __________ = 0

(b)13 + __________ = 0

(c)12 + (–12) = __________

(d)(–4) + __________ = –12

(e)__________ – 15 = –10

Answer:

(a) (–8) + 8 = 0

(b) 13 + (–13) = 0

(c) 12 + (–12) = 0

(d) (–4) + (–8) = –12

(e) 5 – 15 = –10


NCERT Solutions for Class 6 Maths Exercise 6.3

Question 4.Find:

(a)(–7) – 8 – (–25)

(b)(–13) + 32 – 8 – 1

(c)(–7) + (–8) + (–90)

(d)50 – (–40) – (–2)

Answer:

(a) (–7) – 8 – (–25)

= –7 – 8 + 25

= –15 + 25

= 10

(b) (–13) + 32 – 8 – 1

= –13 + 32 – 8 – 1

= 32 – 22

= 10

(c) (–7) + (–8) + (–90)

= –7 – 8 – 90

= –105

(d) 50 – (–40) – (–2)

= 50 + 40 + 2

= 92

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