Class โ 6 CH-6 INTEGERS
MATHS NCERT SOLUTIONS
Exercise 6.1
Question 1 :
Write opposite of the following:
(a) Increase in weight
(b) 30 km north
(c) 326 BC
(d) Loss of โน700
(e) 100 m above sea level
Solution 1:
(a) Decrease in weight
(b) 30 km south
(c) 326 AD
(d) Profit of โน700
(e) 100 m below sea level
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.
Solution 2:
(a) (+) 200 meters
(b) (โ) 800 meters
(c) (+) 200 Rupees
(d) (โ) 700 Rupees
Question 3:
Represent the following numbers on number line:
(a) +5
(b) โ10
(c) +8
(d) โ1
(e) โ6
Solution 3:
Question 4:
Adjacent figure is a vertical number line, representing integers. Observe it and locate the following
points:
points:
(a) If point D is +8 then which point is โ8?
(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.
Solution 4:
(a) F
(b) Negative
(c) B = (+) 4; E = (โ) 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.
Place Temperature
Siachin 10ยฐC below 0ยฐC ____________________
Shimla 2ยฐC below 0ยฐC ____________________
Ahmedabad 30ยฐC above 0ยฐC ____________________
Delhi 20ยฐC above 0ยฐC ____________________
Srinagar 5ยฐC below 0ยฐC ____________________
(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.
(c) Which is the coolest place?
(d) Write the names of the place where temperature are above 10ยฐC.
Solution 5:
Place Temperature
(a) Siachin (โ) 10ยฐC
Shimla (โ) 2ยฐC
Ahmedabad (+) 30ยฐC
Delhi (+) 20ยฐC
Srinagar (โ) 5ยฐC
(c) Siachin is the coolest place.
(d) Ahemadabad and Delhi
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) โ3, โ8
(c) 0, โ1
(d) โ11, 10
(e) โ6, 6
(f) 1, โ100
Solution 6:
(a) 9 is right to 2
(b) โ3 is right to โ8
(c) 0 is right to โ1
(d) 10 is right to โ11
(e) 6 is right to โ6
(f) 1 is right to โ100
Question 7:
Write all the integers between the given pairs (write them in the increasing order):
(a) 0 and โ7
(b) โ4 and 4
(c) โ8 and โ15
(d) โ30 and โ23
Solution 7:
(a) โ6, โ5, โ4, โ3, โ2, โ1
(b) โ3, โ2, โ1, 0, 1, 2, 3
(c) โ14, โ13, โ12, โ11, โ10, โ9
(d) โ29, โ28, โ27, โ26, โ25, โ24
Question 8:
(a) Write four negative integers greater than โ20.
(b) Write four negative integers less than โ10.
Solution 8:
(a) โ19, โ18, โ17, โ16
(b) โ11, โ12, โ13, โ14
Question 9:
For the following statements write True (T) or False (F). If the statement is false, correct the statement:
(a) โ8 is to the right of โ10 on a number line.
(b) โ100 is the right of โ50 on a number line.
(c) Smallest negative integer is โ1.
(d) โ26 is larger than โ25.
Solution 9:
(a) True
(b) False
(c) False
(d) False
Question 10:
Draw a number line and Solution the following:
(a) Draw a number line will we reach if we move 4 numbers to the right of โ2.
(b) Which number will we reach if we move 5 numbers to the left of 1.
(c) If we are at โ8 on the number line, in which direction should we move to reach โ13?
(d) If we are at โ6 on the number line, in which direction should we move to reach โ1?
Solution 10:
(c) On left side
(d) On right side
โ
Exercise 6.2
Question 1:
Using the number line write the integer which is:
(a) 3 more than 5
(b) 5 more than โ5
(c) 6 less than 2
(d) 3 less than โ2
Solution 1:
(a) 8
(b) 0
(c) โ4
(d) โ5
Question 2:
Use number line and add the following integers:
(a) 9 + (โ6)
(b) 5 + (โ11)
(c) (โ1) + (โ7)
(d) (โ5) + 10
(e) (โ1) + (โ2) + (โ3)
(f) (โ2) + 8 + (โ4)
Solution 2:
(a) 9 + (โ6) = 3
(b) 5 + (โ11) = โ6
(c) (โ1) + (โ7) = โ8
(d) (โ5) + 10 = 5
(e) (โ1) + (โ2) + (โ3) = โ6
(f) (โ2) + 8 + (โ4) = 2
Question 3:
Add without using number line:
(a) 11 + (โ7)
(b) (โ13) + (+18)
(c) (โ10) + (+19)
(d) (โ250) + (+150)
(e) (โ380) + (โ270)
(f) (โ217) + (โ100)
Solution 3:
(a) 11 + (โ7) = 11 โ 7 = 4
(b) (โ13) + 18 = 5
(c) (โ10) + (+19) = โ10 + 19 = 9
(d) (โ250) + (+150) = โ250 + 150 = โ100
(e) (โ380) + (โ270) = โ380 โ 270 = โ650
(f) (โ217) + (โ100) = โ217 - 100 = โ317
Question 4:
Find the sum of:
(a) 137 and โ354
(b) โ52 and 52
(c) โ213, 39 and 192
(d) โ50, โ200 and 300
Solution 4:
(a) 137 + (โ354) = 137 โ 354 = โ217
(b) (โ52) + 52 = 0
(c) (โ312) + 39 + 192 = โ312 + 231 = โ81
(d) (โ50) + (โ200) + 300 = โ50 โ 200 + 300 = โ250 + 300 = 50
Question 5:
Find the value of:
(a) (โ7) + (โ9) + 4 + 16 (b) 37 + (โ2) + (โ65) + (โ8)
Solution 5:
(a) (โ7) + (โ9) + 4 + 16
= โ7 โ 9 + 4 + 16
= โ16 + 20
= 4
(b) 37 + (โ2) + (โ65) + (โ8)
= 37 โ 2 โ 65 โ 8
= 37 โ 75
= โ38
Exercise 6.3
Question 1:
Subtract:
(a) 35 โ (20)
(b) 72 โ (90)
(c) (โ15) โ (โ18)
(d) (โ20) โ (13)
(e) 23 โ (โ12)
(f) (โ32) โ (โ40)
Solution 1:
(a) 35 โ 20 = 15
(b) 72 โ 90 = โ18
(c) (โ15) โ (โ18) = โ15 + 18 = 3
(d) โ20 โ (13) = โ20 โ 13 = โ33
(e) 23 โ (โ12) = 23 + 12 = 35
(f) (โ32) โ (โ40) = โ32 + 40 = 8
Question 2:
Fill in the blanks with >, < or = sign:
(a) (โ3) + (โ6) _______________ (โ3) โ (โ6)
(b) (โ21) โ (โ10) _______________ (โ31) + (โ11)
(c) 45 โ (โ11) _______________ 57 + (โ4) (d) (โ25) โ (โ42) _______________ (โ42) โ (โ25)
Solution 2:
(a) (โ3) + (โ6) <(โ3) โ (โ6)
(b) (โ21) โ (โ10) > (โ31) + (โ11)
(c) 45 โ (โ11) > 57 + (โ4)
(d) (โ25) โ (โ42) > (โ42) โ (โ25)
Question 3:
Fill in the blanks:
(a) (โ8) + __________ = 0
(b) 13 + __________ = 0
(c) 12 + (โ12) = __________
(d) (โ4) + __________ = โ12
(e) __________ โ 15 = โ10
Solution 3:
(a) (โ8) + 8 = 0
(b) 13 + (โ13) = 0
(c) 12 + (โ12) = 0
(d) (โ4) + (โ8) = โ12
(e) 5 โ 15 = โ10
Question 4:
Find:
(a) (โ7) โ 8 โ (โ25)
(b) (โ13) + 32 โ 8 โ 1
(c) (โ7) + (โ8) + (โ90)
(d) 50 โ (โ40) โ (โ2)
Solution 4:
(a) (โ7) โ 8 โ (โ25)
= โ7 โ 8 + 25
= โ15 + 25
= 10
(b) (โ13) + 32 โ 8 โ 1
= โ13 + 32 โ 8 โ 1
= 32 โ 22
= 10
(c) (โ7) + (โ8) + (โ90)
= โ7 โ 8 โ 90
= โ105
(d) 50 โ (โ40) โ (โ2)
= 50 + 40 + 2
= 92
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