Page 120
Exercise 6.1
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
Answer:
(a) Increase in weight – Decrease in weight
(b) 30 km north – 30 km south
(c) 326 BC – 326 AD
(d) Loss of Rs 700 – Gain of Rs 700
(e) 100 m above sea level – 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.
Answer:
(a) An aeroplane is flying at a height two thousand metre above the ground : +2000
(b) A submarine is moving at a depth, eight hundred metre below the sea level : -800
(c) A deposit of rupees two hundred : +200
(d) Withdrawal of rupees seven hundred : -700
Q3. Represent the following numbers on a number line :
(a) +5 (b) -10 (c) +8
(d) -1 (e) -6
Answer:
(a) +5
(b) -10
(c) +8
(d) -1
(e) -6
Q4. Adjacent figure is a vertical number line, representing integers.
Observe it and locate the following points:
(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.
Answer:
(a) Point F is -8.
(b) Point G is -6, a negative integer.
(c) Point B is 4 and Point E is -10.
(d) The point E has the value -10 which is the least value on this number line.
(e) All the points in decreasing order of value are E < F < G < H < A < B < C < D.
Q5. Following is the list of temperatures of five places in India on a particular day of the year.
|
Place
|
Temperature
|
|
Siachin
|
10°C below 0°C
|
|
Shimla
|
2°C below 0°C
|
|
Ahmedabad
|
30°C above 0°C
|
|
Delhi
|
20°C above 0°C
|
|
Srinagar
|
5°C below 0°C
|
(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.
Answer:
(a)
|
Place
|
Temperature
|
Temperature in integer form
|
|
Siachin
|
10°C below 0°C
|
-10
|
|
Shimla
|
2°C below 0°C
|
-2
|
|
Ahmedabad
|
30°C above 0°C
|
+30
|
|
Delhi
|
20°C above 0°C
|
+20
|
|
Srinagar
|
5°C below 0°C
|
-5
|
(b)
(c) The coolest place is Siachin.
(d) Ahmedabad and Delhi are the places where 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 (b) – 3, – 8 (c) 0, – 1
(d) – 11, 10 (e) – 6, 6 (f) 1, – 100
Answer:
On the number line the number on the right is greater than the number on the left and the numbers increase as we move to the right and decrease as we move to the left.
(a) 2, 9 : 9 > 2, so 9 will be on right of number 2.
(b) – 3, – 8 : -3 > -8, so -3 will be on right of -8.
(c) 0, – 1 : 0 > -1, so 0 will be on right of -1.
(d) -11, 10 : 10 > -11, so 10 will be on right of -11.
(e) -6, 6 : 6 > -6, so 6 will be on right of -6.
(f) 1, -100 : 1 > -100, so 1 will be on right of -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
Answer:
(i) All the integers between 0 and -7 are -6, -5, -4, -3, -2 and -1.
(ii)All the integers between -4 and 4 are -3, -2, -1, 0, 1, 2 and 3.
(iii) All the integers between -8 and -15 are -14, -13, -12, -11, -10 and -9.
(iv) All the integers between -30 and -23 are -29, -28, -27, -26, -25 and -24.
Q8. (a) Write four negative integers greater than -20.
(b) Write four negative integers less than -10.
Answer:
(a) Four negative integers greater than -20 are -19, -18, -17 and -16.
(b) Four negative integers less than -10 are -11, -12, -13 and -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.
(b) -100 is to the right of -50 on a number line.
(c) Smallest negative integer is -1.
(d) -26 is greater than -25.
Answer:
On the number line the number on the right is greater than the number on the left and the numbers increase as we move to the right and decrease as we move to the left.
(a) True, -8 > -10 so -8 is to the right of -10 on a number line.
(b) False, -50 > -100 so -50 will be to the right of -100 on a number line.
(c) False, -1 is the largest negative integer.
(d) False, -26 < -25.
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.
(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) When 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?
Page 128
Exercise 6.2
Q1. 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) 3 more than 5
On the number line, we will move 3 steps to the right from 5 thus reaching 8. Therefore, we get
5 + 3 = 8
(b) 5 more than –5
On the number line, we will move 5 steps to the right from -5 thus reaching 0. Therefore, we get
5 + (-5) = 5 – 5 = 0
(c) 6 less than 2
On the number line, we will move 6 steps to the left from 2 thus reaching -4. Therefore, we get
2 - 6 = 2 – 6 = -4
(d) 3 less than –2
On the number line, we will move 3 steps to the left from -2 thus reaching -5. Therefore, we get
-2 - 3 = -5
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)
Answer:
(a) 9 + (-6)
On the number line, we will move 6 steps to the left from 9 thus reaching 3. Therefore, we get
9 - 6 = 3
(b) 5 + (-11)
On the number line, we will move 11 steps to the left from 5 thus reaching -6. Therefore, we get
5 - 11 = -6
(c) (-1) + (-7)
On the number line, we will move 7 steps to the left from -1 thus reaching -8. Therefore, we get
-1 - 7 = -8
(d) (-5) + 10
On the number line, we will move 10 steps to the right from -5 thus reaching 5. Therefore, we get
-5 + 10 = 5
(e) (-1) + (-2) + (-3)
On the number line, we first move 2 steps to the left from -1 thus reaching -3 and then we move 3 steps to the left of -3 and reach -6. Therefore, we get
(-1) + (-2) + (-3) = -1 - 2 - 3 = -6
Q3. 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)
= -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 - 100 = -317
Q4. Find the sum of :
(a) 137 and – 354 (b) – 52 and 52
(c) – 312, 39 and 192 (d) – 50, – 200 and 300
Answer:
When a positive integer is added to an integer, the resulting integer becomes greater than the given integer.
When a negative integer is added to an integer, the resulting integer becomes less than the given integer.
(a) 137 and -354
= (+137) + (-354)
= 137 - 354 = -217
(b) -52 and 52
= (+52) + (-52)
= 52 – 52 = 0
(c) – 312, 39 and 192
= (-312) + (+39) + (+192)
= -312 + 39 + 192
= -312 + 231 = -81
(d) -50, -200 and 300
= (-50) + (-200) + (+300)
= -50 – 200 + 300
= -250 + 300 or 300 – 250
= +50
Q5. Find the sum :
(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
Page 131
Exercise 6.3
Q1. Find
(a) 35 - (20)
(b) 72 - (90)
(c) (-15) - (-18)
(d) (-20) - (13)
(e) 23 - (-12)
(f) (-32) - (-40)
Answer:
To subtract an integer from another integer it is enough to add the additive inverse of the integer that is being subtracted, to the other integer.
(a) 35 - (+20)
= 35 - 20 = 15
(b) 72 - (+90)
= 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
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)
Answer:
(a) (-3) + (-6) ______ (-3) - (-6)
(-3) + (-6) = -3 – 6 = -9
(-3) – (-6) = -3 + 6 = +3
Hence, (-3) + (-6) < (-3) - (-6)
(b) (-21) - (-10) _____ (-31) + (-11)
(-21) - (-10) = -21 + 10 = -11
(-31) + (-11) = -31 - 11 = -42
Hence, (-21) - (-10) > (-31) + (-11)
(c) 45 - (-11) ______ 57 + (-4)
(+45) - (-11) = 45 + 11 = +56
(+57) + (-4) = 57 - 4 = +53
Hence, 45 - (-11) > 57 + (-4)
(d) (-25) - (-42) _____ (-42) - (-25)
(-25) - (-42) = -25 + 42 = +17
(-42) - (-25) = -42 + 25 = -17
Hence, (-25) - (-42) > (-42) - (-25)
Q3. Fill in the blanks.
(a) (-8) + _____ = 0
(b) 13 + _____ = 0
(c) 12 + (-12) = ____
(d) (-4) + ____ = -12
(e) ____ - 15 = -10
Answer:
Numbers that are additive inverse of each other when added to each other give the sum zero, for example 2 and -2; 25 and -25.
(a) (-8) + _____ = 0
Additive inverse of -8 is +8
So, (-8) + (+8) = 0
(b) 13 + _____ = 0
Additive inverse of +13 is -13
So, (+13) + (-13) = 0
(c) 12 + (-12) = ____
12 and -12 are additive inverse of each other so their sum will be zero.
So, (+12) + (-12) = 0
(d) (-4) + ____ = -12
Suppose the missing number is x
(-4) + x = -12
x = -12 + 4
x = -8
So, (-4) + (-8) = -12
(e) ____ - 15 = -10
Suppose the missing number is x
x - 15 = -10
x = -10 + 15
x = +5
So, (+5) - (+15) = -10
Q4. 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
= -22 + 32
= +10
(c) (-7) + (-8) + (-90)
= -7 - 8 - 90
= -105
(d) 50 - (-40) - (-2)
= 50 + 40 + 2
= +92