Table of contents | |
NCERT SOLUTIONS | |
Exercise 6.1 | |
Exercise 6.2 | |
Exercise 6.3 |
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.
Directions
(c) 80 m East
Ans: The opposite of 80 m East is 80 m West.
Directions
(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
(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.
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
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
94 videos|347 docs|54 tests
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1. What are integers? |
2. What is the difference between positive and negative integers? |
3. How do we add integers? |
4. Can we multiply any two integers and obtain another integer? |
5. What is the absolute value of an integer? |
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