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Frank Learning Maths Class 6 Solutions Chapter 4 Integers
Welcome to NCTB Solution. Here with this post we are going to help 6th class students for the Solutions of Frank Learning Maths Class 6 Book, Chapter 4 Integers. Here students can easily find step by step solutions of all the problems for Integers. Here students will find solutions for Exercise 4.1, 4.2 and 4.3. Exercise wise proper solutions. All the problem are solved with easily understandable methods so that all the students can understand easily. Here in this post all Mathematic solutions are based on the CBSE latest curriculum.
Integers Exercise 4.1 Solution
Question no – (1)
Solution :
(a) Earnings of Rs. 5000
Integer = +5000
(b) Decrease in rainfall by 10 mm
Integer = -10 mm
(c) 45 km North
Integer = +45 km
(d) Going 1 km towards the west
Integer = -1 km
(e) 40c below the freezing point
Integer = -40c
(f) Going 300 m below the ground level into a mine
Integer = -300 m
(g) An aeroplane flying at a height of 1800 m above the sea level
Integer = +1800 m.
Question no – (2)
Solution :
(a) The opposite of -234 is 234
(b) The opposite of 208 is -2085
(c) The opposite of -4096 is 4096
Question no – (3)
Solution :
(a) 5 < 8
(b) -1 < 0
(c) 0 > -6
(d) -40 > -50
(e) -105 > -200
(f) -3000 > -4125
Question no – (4)
Solution :
Range | Integers | Smallest | Greatest | |
(a) | 0 and 8 | 1, 2, 3, 4, 5, 6, 7 | 1 | 7 |
(b) | 0 and -8 | -7, -6, -5, -4, -3, -2, -1 | -7 | -1 |
(c) | -4 and 4 | -3, -2, -1, 0, 1, 2,
3, |
-3 | 3 |
(d) | -10 and -19 | -18, -17, -16, -15, -14, -13, -12, -11 | -18 | -11 |
Question no – (5)
Solution :
(a) Five negative integers just succeeding -2 are -21, -20, -19, -18, -17.
(b) Five negative integers just greater than -96 are -95, -94, -93, -92, -91.
(c) Five negative integers just preceding -32 are -33, -34, -35, -36, -37.
(d) Five negative integers just less than -70 are -71, -72, -73, -74, -75.
Question no – (6)
Solution :
-1 is the greatest negative integer.
For each positive integer, there exists a positive integer which is greater than that.
Therefore, I can’t find the greatest positive integer.
Question no – (7)
Solution :
We need two integers whose sum is 6 and difference is also 6.
We taking 0 and 6 as two integers.
Adding this two integers,
= 0 + 6 = 6
Subtracting this two integers,
= 6 – 0 = 6
Hence, 0 and 6 are the required two integers.
Question no – (8)
Solution :
Five integers which are less than -100 but greater than -150
-101, -102, -103, -104, -105,
Question no – (11)
Solution :
(a) Given integers, -9, -10, -5, 0, 3, 5, -7
Now in ascending order,
= -10, -9, -7, -5, 0, 3, 5
(b) Given integers, -30, -45, -33, -48, -84
Now in ascending order,
= -84, -48, -45, -33, -30
(c) Given integers, -94, -105, -501, -61, -100
Now in ascending order,
= -501, -105, -100, -94, -61
(d) Given integers, -253, -352, -523, -532, -325
Now in ascending order,
= -532, -523, -352, -325, -253
Question no – (12)
Solution :
(a) Given numbers, 4, 9, 0, -9, -4, -6
Now in descending order,
= 9, 4, 0, -4, -6, -9
(b) Given numbers, -15, -20, -18, -1, -7
Now in descending order,
= -1,-7, -15, -18, -20
(c) Given numbers, -68, -86, -73, -37, 0
Now in descending order,
= 0, -37, -68, -73, -86
(d) Given numbers, -157, -517, -715, -175, -751
Now in descending order,
= -157, -175, -517, -715, -751
Question no – (14)
Solution :
(a) The sign which is used for integers less than 0 is (–) or Negative sign.
(b) The integer 5 units to the right of zero on number line is 5
(c) The Predecessor of -1 is -2 or Negative 2
(d) There are total six (6) integers between -5 and 2.
(e) There are Five (5) whole numbers lying between -5 and 5.
(f) There are only One (1) natural numbers between -7 and 2
(g) The successor of the predecessor of -50 is -50
Question no – (16)
Solution :
(a) -8, -6, -4 …
Next three integers = -2, -0, 2
(b) -40, -35, -30, …
Next three integers = -25, -20, -15
(c) -21, -18, -15, …
Next three integers = -12, -9, -6
(d) 16, 13, 10, …
Next three integers = 7, 4, 1
(e) -66, -60, -54, …
Next three integers = -48, -42, -36
(f) -84, -72, -60, …
Next three integers = -48, -36, -24
Question no – (17)
Solution :
(a) 4 more than 5
So, the integer is 9
(b) 3 more than -7
So, the integer is 4
(c) 8 less than 2
So, the integer is -6
(d) 2 less than -3
So, the integer is -2
Question no – (18)
Solution :
(a) Zero is a positive integer
= False, Zero is neither positive nor negative
(b) Smallest negative integer is -1
= False, greatest negative integer is -1
(c) -37 is less than -36
= True
(d) -9 is to the right of -10 on the number line.
= True
(e) -18 is to the left of -16 on the number line.
= True
Try These 4 (i) :
Question no – (1)
Solution :
(a) Opposite of Increase by 50c is Decrease by 50c
(b) Opposite of 20 km North is 20 km south
(c) Opposite of Profit of Rs.1600 is Loss of Rs. 1600
(d) Opposite of 100 m above sea level is 100 m below sea level.
Question no – (2)
Solution :
(a) Earning Rs. 15, 000 as integer,
= +15000
(b) Depth of 85 m as integer,
= -85 m
(c) 9 steps forward as integer,
= +9
(d) Gain of Rs. 700 as integer,
= +700
Question no – (3)
Solution :
(a) Opposite of 19 is -19
(b) Opposite of -25 is 25
(c) Opposite of -204 is 204
(d) Opposite of 1000 is -1000
Question no – (4)
Solution :
(a) The absolute value of 39 is 39
(b) The absolute value of -65 is 65
(c) The absolute value of -208 is 208
(d) The absolute value of 1000 is 1000.
Question no – (5)
Solution :
Three real-life situations in which integers can be used are –
(a) profit – loss :
Profit is denoted by positive integers and loss is denoted by negative integers
(b) Measuring temperature :
Temperature above 00c is denoted by positive integer and temperature below 00c is denoted by negative integer.
(c) Height – Depth :
Height is denoted by positive integer and depth is denoted by negative integer.
Try These 4 (ii) :
Question no – (1)
Solution :
(1) (+9) + (+3)
= 9 + 3
= 12
∴ The sum will be 12
(2) (-10) + (-5)
= -10 -5
= -15
∴ The sum will be -15
(3) (-8) + (-4)
= -8 -4
= -12
∴ The sum will be -12
(4) (+10) + (+5)
= +10 +5
= +15
∴ The sum will be +15
Try These 4 (iii) :
Question no – (1)
Solution :
(a) -4, 2
= -4 +2
= -2
∴ The sum will be -2
(b) -9, 14
= -9 + 14
= +5
∴ The sum will be +5
(c) 18, -10
= 18 – 10
= 8
∴ The sum will be 8
(d) 12, -7
= 12 – 7
= 5
∴ The sum will be 5
Question no – (2)
Solution :
(a) -16, 5
= -16 + 5
= -11
∴ The sum will be -11
(b) -7, 3
= -7 + 3
= -4
∴ The sum will be -4
(c) -8, -11
= -8 -11
= -19
∴ The sum will be -19
(d) 6, 10
= 6 + 10
= 16
∴ The sum will be 16
Try These 4 (iv) :
Question no – (1)
Solution :
(a) 7, -4
= The answer is 3
(b) -9, 5
= The answer is -4
(c) 6, -10
= The answer is -4
(d) 6, -4
= The answer is 2
Question no – (3)
Solution :
(a) The additive inverse of 8 is -8
(b) The additive inverse of -19 is 19
(c) The additive inverse of 15 is -15
(d) The additive inverse of -100 is 100
(e) The additive inverse of -56 is 56
Integers Exercise 4.2 Solution
Question no – (1)
Solution :
(a) 9 + (-7)
= The answer is +2
(b) 4 + (-12)
= The answer is -8
(c) (-2) + (-6)
= The answer is -8
(d) (-7) + 14
= The answer is 7
(e) (-1) + (-2) + (-4)
= The answer is -7
(f) (-3) + 5 + (-2)
= The answer is 0
Question no – (2)
Solution :
(a) -13, 18
= -13 + 18
= 5
∴ The answer will be 5
(b) -45, 24
= -45 + 24
= -21
∴ The answer will be -21
(c) -256, 150
= -256 + 150
= -106
∴ The answer will be -106
(d) -315, -100
= -315 -100
= -415
∴ The answer will be -415
(e) -500, -680
= -500 -680
= -1180
∴ The answer will be -1180
(f) -463, 254
= -463 + 254
= -109
∴ The answer will be -109
(g) -1060, 900
= -1060 +900
= -160
∴ The answer will be -160
Question no – (3)
Solution :
(a) -40, -190, 320
= -40 -190 + 320
= -230 +320
= 90
Therefore, the sum will be 90
(b) -512, 69, 171
= -512 + 69 + 171
= -512 + 240
= -272
Therefore, the sum will be -272
Question no – (4)
Solution :
(a) 54 + (-3) + (-66) + 17
= 54 – 3 – 66 + 17
= 54 + 17 – 3 – 66
= 71 – 69
= 2
∴ The sum will be 2
(b) -8 + (-9) + 7 + 18
= 8 – 9 + 7 + 18
= 8 + 7 + 18 – 9
= 33 – 9
= 24
∴ The sum will be 24
(c) 30 + (-43) + (-63) + 55
= 30 – 43 – 63 + 55
= 30 + 55 – 43 – 63
= 85 – 106
= -21
∴ The sum will be -21
(d) -6 + (-7) + 34 + 26
= -6 -7 + 34 + 26
= 34 + 26 – 6 -7
= 60 – 13
= 47
∴ The sum will be 47
(e) -65 + 87 + (-43) + (-55) + 65
= -65 + 87 – 43 – 55 + 65
= 87 +65 – 65 – 43 – 55
= 87 – 43 – 55
= 87 – 98
= -11
∴ The sum will be -11
Therefore, The smallest answer is -11 and the biggest one is 47
Question no – (5)
Solution :
(a) The sum of an integer and its opposite is Zero.
This statement is True.
(b) The sum of two positive integers is always less than Zero.
This statement is False.
(c) The sum of a negative integer and a positive integer is always Negative.
This statement is False.
(d) The sum of two negative integers is always greater than Zero –
This statement is False.
(e) Additive inverse of an integer is always Negative.
This statement is False.
Question no – (6)
Solution :
(a) -23 + (-5) = (-5) + (-23)
= [Commutative property]
(b) -39 + {(-8) + (-91)} = {-39 + (-8)} + (-9)
= [Associative property]
(c) -781 + 0 = -781
= [Additive identity]
(d) -22 + (-18) = -40
= [Closure property]
(e) (-5) + {(-6) + (-8)} = {(-5) + (-6)} + (-8)
= [Associative property]
(f) -26 + (-7) = -33
= [Closure property]
Question no – (7)
Solution :
As per the given question,
In Srinagar, the temperature was 4°C in the morning.
It dropped by 7 degrees at night
Now, At night, the temperature was,
= (4 – 7)°C
= – 3°C
∴ The next day the temperature was,
= (-3 -2)°C
= -5°C
Therefore, the temperature of that day was -5°C
Question no – (8)
Solution :
According to the question,
(a) 0 + 1 -2 + 3 – 4 + 5 – 6 + 7 – 8 + 9 = 5
(b) 0 + 1 – 2 + 3 + 4 + 5 – 6 – 7 + 8 – 9 = -3
Question no – (9)
Solution :
Five distinct integers whose sum is 5 are (5, -10, +10, -20, +20)
Question no – (10)
Solution :
As per the question,
1+ 2 -3 + 4 + 5 – 6 -7 +8 – 9 = x – 5
Now, according to the question,
= 1 + 2 – 3 + 4 + 5 – 6 – 7 + 8 – 9
= 9
Integers Exercise 4.3 Solution
Question no – (1)
Solution :
(a) 8 – 3
= 5
(b) 36 – 21
= 15
(c) 83 – 90
= -7
(d) -10 – (-18)
= 8
Question no – (2)
Solution :
(a) -16, -15
= -15 + 16
= 1
∴ The answer will be 1
(b) -451, -286
= -286 + 451
= 165
∴ The answer will be 165
(c) 5123, -2154
= -2154 – 5123
= -7277
∴ The answer will be -7277
(d) -1040, -562
= -562 + 1040
= +478
∴ The answer will be +478
Question no – (3)
Solution :
(a) Given number is 200
We know, Predecessor means -1
∴ 200 – 1
= 199
So, the Predecessor of 200 is 199
(b) Given number is -599
∴ (-599) – 1
= -600
Thus, the Predecessor of -599 is -600
(c) Given number is -8000
∴ (-8000) – 1
= -8001
Hence, the Predecessor of -8000 is -8001
(d) Given number is 9999
∴ 9999 – 1
= 9998
Therefore, the Predecessor of 9999 is 9998
Question no – (4)
Solution :
(a) -1001
We know, Successor means + 1
∴ (-1001) + 1
= -1000
So, the Successor of -1001 is -1000
(b) 2900
We know, Successor means +1
∴ 2900 + 1
= 2901
Thus, the Successor of -2900 is 29
(c) -6160
We know, successor means +1
∴ (-6160) + 1
= -6159
Hence, the Successor of -6160 is -6159.
(d) 19999
We know, successor means +1
∴ 19999 + 1
= 20000
Therefore, the successor of 19999 is 20000.
Question no – (5)
Solution :
(a) -10 – 5 – (-35)
= -10 – 5 + 35
= -15 + 35
= 20 ….(Simplified)
(b) -15 + 34 – 14 – 6
= -15 – 14 – 6 + 34
= -35 + 34
= 1 ….(Simplified)
(c) 100 – (-100) – (-100)
= 100 + 100 + 100
= 300 ….(Simplified)
(d) -26 + (-13) + (-52)
= -26 – 13 – 52
= -91 ….(Simplified)
(e) -13 + (-17) – (-22) – (-40)
= -13 – 17 + 22 + 40
= -30 + 62
= +32 ….(Simplified)
(f) 84 + (-99) + 33 – (-28) – 46
= 84 + 33 + 28 – 99 -46
= 145 – 145
= 0 ….(Simplified)
Question no – (6)
Solution :
(a) a and b are closed under subtraction
= -3 – 5 = -8, which is an integer
so a, b are closed under subtraction
(b) a – (b – c) = (a – b) –c
= -3 –{(5) – (-7)} = -3-{5 + 7} = -3 – 12 = -15
= (-3-5) – (-7) = -8 + 7 = 1
= a – (b – c) ≠ (a – b) –c
(c) a – b = b – a
= -3 – 5 = -8 ≠ 8 = 5 – (-3)
(d) b and c are closed under subtraction
= 5 – (-7) = 5 + 7 = 12, which is an integer
So, b and c are closed under subtraction
Question no – (7)
Solution :
As per the question,
In Ladakh, one afternoon, the temperature was 2°C.
Temperature dropped = 5°C at night
∴ At night, the temperature is,
= (2 – 5)0c
= -30°C
Question no – (8)
Solution :
According to the question,
A submarine was situated = 700 m below the sea level.
it ascends = 250 m
∴ The new position will be,
= (700 – 250) m
= 450 m
Thus, the new position of submarine will be 450 m below the sea level.
Question no – (9)
Solution :
Given in the question,
Reeta’s scores in four successive rounds = 35, -5,-10, 20
∴ Her total score will be,
= 35 + (-5) + (-10) + 20
= 325 + 20 – 15
= 55 – 15
= 40
Thus, her total score at the end was 40.
Question no – (10)
Solution :
According to the given question,
At Manali, the temperature Friday = -4°C
It dropped by Saturday = 3°C
Temperature at Manali on Saturday = ?
On Sunday, it rose by = 5°C.
Temperature on this day = ?
∴ On Saturday, the temperature was,
= (-4-3)°C
= -7°C
∴ On Sunday the temperature was,
= (-7 + 5)°C
= -2°C
Question no – (12)
Solution :
(a) -5
= Left
(b) 11
= Right
(c) 0?
= Left
Question no – (13)
Solution :
(a) -5 – 2
= The temperature is -5°C and drops by 2°C
(b) 8 – 3
= The temperature is 8°C and drops by 3°C
(c) -3 + 4
= The temperature is -3°C and rises by 4°C
(d) 3 + 5
= The temperature is 3°C and rises by 5°C
Integers Chapter Check-up Solution :
Question no – (1)
Solution :
(a) 16,-11,-62, 75, -92,-4
Smallest = -92
Largest = 75
(b) -25, -3, +19, 20, -30, 48
Smallest = -30
Largest = 48
(c) +48, -65, 72, -5, -9,-29
Smallest = -65
Largest = 72
Question no – (4)
Solution :
(a) (- 3) + (- 6) < ( – 3) – (- 6)
(b) (- 21) – (- 10) > (- 31) + (- 11)
(c) 45 – (- 11) > 57 + (- 4)
(d) (- 25) – (- 42) > (- 42) – (- 25)
Question no – (5)
Solution :
Her Profit by selling 5 pens is,
= (5 × 4)
= 20 rupees .
Her loss by selling 6 pencils is,
= (6 × 2)
= 12 rupees.
Her overall profit,
= (20 – 12)
= 8 rupees
Question no – (6)
Solution :
As per the given question,
The sum of two integers is = 47.
If one of the integers is = -24,
The other integer is = ?
∴ The other integer is,
= 47 – (- 24)
= 47 + 24
= 71
Therefore, the other integer is 71.
Question no – (7)
Solution :
Column I | Column I |
(i) The additive inverse of + 2 | (b) -2 |
(ii) The greatest negative integer | (e) – 1 |
(iii) The smallest positive integer | (d) 1 |
(iv) The smallest integer greater than every negative integer. | (a) 0 |
(v) Sum of predecessor and successor of +1 | (c) 2 |
Question no – (8)
Solution :
(a) 30 + (- 25) + (- 10)
= 30 – 25 – 10
= 30 – 35
= – 5
(b) (- 20) + (- 5)
= – 20 – 5
= – 25
(c) 70 + (- 20) + ( – 30)
= 70 – 20 – 30
= 70 – 50
= 20
(d) – 50 + (- 60) + 50
= 50 – 50 – 60
= 0 – 60
= – 60
(e) 1 + (- 2) + (- 3) + (- 4)
= 1 – 2 – 3
= – 1 – 9
(f) 0 + (- 5) +(- 2)
= 0 – 5 – 2
= – 7
(g) 0 – (- 6) –(+ 6)
= 0 + 6 – 6
= 0
(h) 0 – 2 – (- 2)
= 0 – 2 + 2
= 0
Question no – (9)
Solution :
As per the question,
The sum of two integers is = 30.
If one of the integers = -42,
The other integer is = ?
Now, Second integer + (- 42) = 30
∴ Second integer,
= 30 – (- 42)
= 30 + 42
= 72
Therefore, the other integer is 72
Question no – (10)
Solution :
According to the question,
= 375 – {(300) + 250}
= 375 – {- 50}
= 375 + 50
= 425
Previous Chapter Solution :