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Brilliant’s Composite Mathematics Class 6 Solutions Chapter 5 Integers
Welcome to NCTB Solutions. Here with this post we are going to help 6th class students for the Solutions of Brilliant’s Composite Mathematics Class 6 Math Book, Chapter 5, Integers. Here students can easily find step by step solutions of all the problems for Integers, Exercise 5.1, 5.2, 5.3, 5.4, 5.5, 5.6 and 5.7 Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily.
Integers Exercise 5.1 Solution
Question no – (1)
Solution :
(i) Deposit of money in a Bank.
(ii) Losing a game.
(iii) going fast
(iv) Increase in death rate.
(v) Decrease in birth rate.
Question no – (2)
Solution :
(i) Given, 5 °C below zero
= – 5 °C
(ii) Given, 9 °C above zero,
= 9 °C
(iii) Given, 15 °C below freezing point
= 15 °C
(iv) Given, 5 km above sea level
= 5 km
(v) Given, A deposits of Rs 2500
= 2500
(vi) Given, A withdrawal of Rs. 1500
= – 1500
(vii) Given, A loss of Rs. 2500
= – 25000
(viii) Given, A gain of Rs. 350
= 350
Question no – (3)
Solution :
(i) Given, -2, 2
= -2 is on the left of the number line.
(ii) Given,4, 7
= 4 is on the left of the number line.
(iii) Given,-9, -11
= – 11 is on the left of the number line.
(iv) Given, -3, 5
= -3 is on the left of the number line.
Question no – (3)
Solution :
(i) Given, 5, 17
= 17 is on the right of the number line.
(ii) Given, -3, -9
= -3 is on the right of the number line.
(iii) Given, -1, 0
= 0 is on the right of the number line.
(iv) Given, 27, -37
= 27 is on the right of the number line.
Question no – (5)
Solution :
(i) Given, 3 more than 5
Using number line :
= 3 + 5
= 8
(ii) Given, 7 less than 4
Using number line :
= 4 – 7
= -3
(iii) Given, 4 more than -6.
Using number line :
= -2 – 7
= -9
(iv) Given, 7 less than -2
Using number line :
= – 2 – 7
= – 9
Question no – (6)
Solution :
Given numbers,
(i) -7 ; (ii) 2
(iii) -3; (iv) 9
(v) 6; (vi) -5
Now on number line,
Question no – (7)
Solution :
(i) Given, 2 and -3
= 2 is larger
(ii) Given, 0 and -3
= 0 is larger
(iii) Given, -7 and -4
= -4 is larger
(iv) Given, -5 and -3
= -3 is larger
(v) Given, -199 and -299
= -199 is larger
(vi) Given, -217 and -503
= -217 is larger
(vii) Given, 5 and -5
= 5 is larger
(viii) Given, -19 and -21
= -19 is larger
Question no – (8)
Solution :
(i) Given, 0 and -1
= -1 is smaller
(ii) Given, -1 and -3
= -3 is smaller
(iii) Given, 7 and -8
= -8 is smaller
(iv) Given, -27 and -37
= -37 is smaller
(v) Given, -15 and 5
= -15 is smaller
(vi) Given, -217 and -503
= -503 is smaller
(vii) Given, 5 and -5
=-5 is smaller
(viii) Given, -19 and -21
= -21 is smaller.
Question no – (9)
Solution :
(i) All integers between -7 and 2 are -6, -5, -4, -2, -3, -1, 0, 1
(ii) All integers between -9 and -3 are -8, -7, -6, -5, -4
(iii) All integers between -5 and 5 are -4, -3, -2, -1, 0, 1, 122, 3, 4
(iv) All integers between -6 and 2 are -5, -4, -3, -2, -1, 0, 1
Question no – (10)
Solution :
(i) Given, 0 * -5
= 0 > -5
(ii) Given, -5 * -15
= -5 > -15
(iii) Given, -9, -7
= -9 < -7
(iv) Given, -3, * 5
= -3 < 5
(v) Given, -158 * -253
= -158 > -253
(vi) Given, -313 * -313
= -313 < -213
(vii) Given, -81 * 18
= -81 < 18
(viii) Given, -27 * -12
= -27 > -127
Question no – (11)
Solution :
(i) The absolute value of 0 is 0
(ii) The absolute value of -70 is 70
(iii) The absolute value of 17 is 17
(iv) The absolute value of -295 is 295
(v) The absolute value of (x – 3) if x is less than 3
= (x – 3) = x – 3
(vi) The absolute value of (x – 3) if x is less than 3
= – (x – 3)
Question no – (12)
Solution :
(i) Given integers, -5, -9, 0, 13, 5, 6
Now, in Increasing order -9, -5, 0, 5, 6, 13
(ii) Given integers, 151, -15, -251, -91, 13, 91
Now, in Increasing order = -251, -91, -15, 13, 91, 151
(iii) Given integers, -81, -9, 109, -99, 0, 151
Now, in Increasing order = -99, -81, -9, 0 , 109, 157
(iv) Given integers, 0, -15, -35, -7, 77, -371
Now, in Increasing order = -371, -35, 15, – 7, 0, 77
Question no – (13)
Solution :
(i) Given, -96, 176, 39, 269, 279
In decreasing order = 279 39 -96, -176 -269
(ii) Given, -108, -208, 196, -176, 9, 0
In decreasing order = 196, 9, 0, -108, -176, -208
(iii) Given, -55, -555, -5, 0, 95, 25,
In decreasing order = 95, 25, 0, -5, -55, -555
(iv) Given, -469, 239, -156. 3, -73, -108
In decreasing order = 239, 3, -73, -108, -156, -469
(v) Given, -41, 9, -10, 0, 1, 10, -25
In decreasing order = 10, 9, 1, 0, -10, -25, -41
(vi) Given, 0, -5, -2, 7, -7, 3, 5
In decreasing order = 7, 5, 3, 0, -2, -5, -7
Question no – (14)
Solution :
(i) |- 23|
= 23
∴ The value is 23
(ii) |0|
= 0
∴ The value is 0
(iii) |173 – 19|;
= 154
∴ The value is 154
(iv) – |27| – |- 27|
= – 27 – 27
= – 54
∴ The value is – 54
(v) |561| – | – 161|
= 561 – 161
= 400
(vi) – |56 – 101|
= – |- 45|
= – 45
∴ The value is 400
(vi) |- 20| + |- 25|
= 20 + 25
= 45
∴ The value is 45
(viii) |51| + |- 31|
= 51 + 31
= 82
∴ The value is 82
Question no – (15)
Solution :
Four negative integers greater than -8 are -7, -6, -5, and -4
Question no – (16)
Solution :
Six negative integers less than -15 are -14, -17, -18, -19, -20, and -21.
Question no – (17)
Solution :
(i) Zero is not an integer → False
(ii) Zero is the smallest integer → True
(iii) The opposite of zero is zero → True
(iv) – 15 is greater than – 10 → False
(v) Zero is larger than every negative integer → True
(vi) A positive integer is greater than its opposite → True
(vii) The absolute value of an integer is always greater than the integer → False
(viii) The value of 0 | is 0 → True
(ix) Every negative integer is less than every natural number → True
(x) – 3° C is warmer than -2° C → False
(xi) – 361 is greater than 0 → False
Integers Exercise 5.2 Solution
Question no – (1)
Solution :
Given numbers are,
(i) -4 + 7 ; (ii) 5 + (-7)
(iii) -2 + (-8) ;(iv) -2 + 5 +(-6)
(v) (-1) + 4 + (-4)
Now, on a number line,
Question no – (2)
Solution :
(i) Given, 10 + (-60);
= – 50
(ii) Given, 70 + (-39);
= – 68
(iii) Given, (-47) + (-59):
= 31
(iv) Given, (-68) + 0:
= – 106
(v) Given, (-31) + 31 ;
= 0
(vi) Given, (179) + (-951).
= – 1130
Question no – (3)
Solution :
(i) Given, -345, 222
= (-345) + 222
= -123
(ii) Given, 2657, – 31
= 2657 + (- 31)
= 2626
(iii) Given, 1000, – 99
= 1000 + (99)
= 1
(iv) Given,- 6897, 0 ;
= – 6897 + 0
= – 6879
(v) Given, 3003, – 999 ;
= 3003 + (999)
= 2004
(vi) Given, – 547, 2639, 657
= (- 547) + 2639 + 657
= 2749
(vii) Given, -872, – 571, – 694;
= -872 + (- 571) + (- 694)
= -2137
(viii) Given, 1979, – 1879, – 1368
= 1979 + (- 1879) + (- 1368)
= 1268
(ix) Given, -5329, 6448, 2371
= -5329 + 6448 + 2371
= 3490
(x) Given, -9999, 1003, 7707, – 797
= (-9999) + 1003 + 7707 + (- 797)
= -2086
Question no – (4)
Solution :
(i) 200 + (- 66) + (- 134)
= 0
So, the sum is 0
(ii) 1262 + (- 366) + (- 962) + 566:
= 500
Thus, the sum is 500
(iii) 473 + (- 245) + (- 473) + 145 + 4005:
= 3905
Hence, the sum is 3905
(iv) 113 + (- 547) + (- 547) + (- 547) + 1850.
= 322
Hence, the sum is 322
(v) 473 + (- 245) + (- 473) + 145 + 4005:
= 3905
Hence, the sum is 3905
(vi) 113 + (- 547) + (- 547) + (- 547) + 1850.
= 322
Hence, the sum is 322
Question no – (5)
Solution :
(i) Given, (- 306, 198)
– 306
198
———————–
= 108
(ii) Given, (- 1298 – 368)
– 12 98
– 368
———————–
= – 1666
(iii) Given, (479 – 163)
479
– 163
———————–
= 316
Question no – (7)
Solution :
(i) Additive inverse of -13 is 13
(ii) The additive inverse of 59 is -59
(iii) The additive inverse of -267 is 267
(iv) The additive inverse of 978 is -978
Question no – (8)
Solution :
(i) Given number, -47
Now,
= – 47 + 1
= – 46
∴ The successor of -47 is – 46
(ii) Given number, -978
= – 978 + 1
= – 977
∴ The successor of -978 is – 977
(iii) Given number, -92
= – 92 – 1
= – 93
∴ The predecessor of -92 is -93
(iv) Given number, -42
= – (- 42)
= 42
∴ The negative of -42 is 42
Question no – (9)
Solution :
(i) a – b = a + b + (-1)
Now,= 3 * 4;
= 3 + 4 + (- 1)
= 7 + (- 1)
= 6
Thus, the value will be 6
(ii) a – b = a + b + (-1),
Now, 4 * (- 6)
= 4 + (- 6) + (- 1)
= – 2 – 1
= – 3
Hence, the value will be – 3
(iii) a – b = a + b + (-1)
Now, (-9) * 13
= – 9 + (3 + (- 1)
= + 3
Thus, the value will be +3
(iv) a – b = a + b + (-1)
Now, (- 127) + (- 37)
= 1 (- 127) + (- 37) + (- 1)
= – 165
Thus, the value will be -165
Question no – (10)
Solution :
Given, (- 1 + 0) = – 1
= (0 + 1) = 1
= (- 1 + 1) = 0
= 1 – (- 1) = 2
= – 1 – (- 1)
= – 2
Yes, because sum of integer is an integer.
Question no – (11)
Solution :
As per the question,
A car was driven 75 km due north of Delhi
Then 95 km due South
Now, (95 – 75)
= 20 km south
Hence, the car 20 km south from the Delhi.
Question no – (12)
Solution :
(i) The sum of an integer and its opposite is zero → True
(ii) The sum of an integer and 0 is zero → False
(iii) The sum of a negative integer and a positive integer is always a negative integer → False
(iv) The sum of two negative integers is positive → False
(v) O is a positive integer → False
(vi) The successor of – 276ls – 277 → False
(vii) On a number line – 25 and 25 are at the same distance from 0 → True
(viii) The sum of three different integers can never be zero → False
Integers Exercise 5.3 Solution
Question no – (1)
Solution :
(i) Given, 7, 13
= (13 – 7)
= 6
(ii) Given, 20, – 15
= – 15 – 20
= 35
(iii) Given, 32, – 674
= – 64 – 32
= – 96
(iv) Given, – 164, – 271`
= – 271 – (- 164)
= – 217 + 164
= – 107
(v) Given, 1001, – 999;
= – 999 – 1000
= – 2000
(vi) Given, 8760, 0;
= 0 – 8760
= – 8760
(vii) 9734, – 2796
= – 2796 – 9734
= – 12530
(viii) – 6745, 2679;
= 2679 – (- 6745)
= 2679 + 6745
(ix) -5467, 7983;
= 7983 – (- 5467)
= 7983 + 5467
= 13450
(x) 11456, – 976
= – 976 – 11456
= – 12432
Question no – (2)
Solution :
First, 8 – (- 6)
= 8 + 6
= 14
Now, -6 – 8
= – 14
∴ No the two results is not same.
Question no – (3)
Solution :
As per the given question,
Subtract the sum of 96 and -163 from 230
Now, according to the question,
= 230 – 1(- 163 + 96)
= 230 – (- 67)
= 230 + 67
= 297
Question no – (4)
Solution :
-670 – (-273 – 575) …(according to the question)
= -6 – (- 848)
= -670 + 848
= 178
Question no – (5)
Solution :
∴ (66 – 77) – 88 …(according to the question)
= – 11 – 88
= – 99
Question no – (6)
Solution :
Now, according to the question,
= [- 7 – 1 – 67] + (- 56)
= (+ 67 – 7) =- 56
= + 60 – 56
= 4
Question no – (7)
Solution :
(i) Given, [37 – (-8)] * [11 – (-30)]
= 37+ 8
= 45
= 11 + 30
= 43
∴ 45 > 43
∴ [37 – (-8) > [11- (-30)]
(ii) [- 13 (-17)] * [-22 – (-40)]
= -13 + 17
= 4
= -22 + 40
= 18
∴ 4 < 18
∴ [-13 -(-17)] < [-22-(-40)]
(iii) [(-20) – (+20)] * [20 – (-20)]
= -20-20
= -40
= 20+20
= 40
∴ -40 < 40
∴ [(-20 – (20)] < [20 – (-20 )]
Question no – (8)
Solution :
(i) -7 + __ = 0
= -7 + 7
= 0
(ii) 79 + __ = 0
= 79 + ( -79 )
= 0
(iii) __ + 27 = 0
= ( -27 ) +27
= 0
(iv) __ + 215 = -64
= x = -64 + 215
= 151
∴ 151 -215 = -64
Question no – (9)
Solution :
As per the given question,
The sum of two integers is = 68.
One of them is = -42.
The other one = ?
∴ Required number,
= 68 – (-42)
= 68 + 42
= 10
Hence, the other number will be 10
Question no – (10)
Solution :
According to the question,
The sum of two integer is = -396.
One of them is = 64
The other one is = ?
∴ Required number,
= -396 – (64)
= -460
Therefore, the other number will be -460
Question no – (11)
Solution :
p is predecessor of q,
∴ p = q – 1
∴ p – q
= q – 1 – q
= -1
Therefore, the value of p – q will be -1.
Question no – (12)
Solution :
(i) 219 is a odd number in this series there left 2
For 219th term.
∴ 219th term = 2
(ii) 130 is a even number.
∴ 130th term = 0
Question no – (14)
Solution :
(i) Given, -15 – (-17)
= – 15 + 17
= 13
Hence, the value is 13
(ii) Given, -6 – 8 – (-27)
= -14 + 27
= 13
Thus, the value is 13
(iii) Given, (2 – 3) + (3- 2)
= – 1 + 1
= 0
Therefore, the value is 0
(iv) Given, -15 + 67 – 19 + 8 – 1
= 52 – 11 -1
= 52 – 12
= 40
Therefore, the value is 40
(v) Given, 55 (-46) – (-2)
= 55- 46 + 2
= 55 – 44
= 11
Therefore, the value is 11
(vi) Given, 28 – [(-3) + 17]
= 28 + 14
= 14
Therefore, the value is 14
Question no – (15)
Solution :
Given, a △ b = a – b + (-2)
(i) 3 △ 4
= 3 -4 + (-2)
= – 1 + 2
= – 3
Thus the value is -3
(ii) 17 △ (-7)
= 17 – (-7) + (-2)
= 17 + 7 – 2
= 24 – 2
= 22
Thus the value is 22
(iii) (-6) △ (-5)
= -6 – (-5) + (-2)
= – 6 + 5 – 2
= – 1 – 2
= -3
Thus the value is -3
Question no – (16)
Solution :
(i) The difference of two integers is always an integer → True.
(ii) -15 > -8-(-9) (given)
= -15 > -8 – (-9)
= -15 > -8+9
= -15 > 1
Thus, the statement is False
(iii) Given, (-9) – 6 = (-6) – (-9)
= (-9) – 6 = – 6 – (-9)
= -9 – 6 = – 6 + 9
= -15
= 3
Hence, the statement is False.
(iv) Given, 3 + (-3) + 3 + (-3) + 3 = 0
= 3+(-3) +3+(-3) + 3 = 0
∴ 3 = 0
Thus, the statement is False.
(v) Given, -9 – 15 + 30 – 37 – (-30) + 7 is 80
= -9 – 15 + 30 + 37 – (-30) + 7
= -24 + 30 + 37 + 30 + 7
= -24 + 60 + 44
= 60 + 20
= 80
Thus, the statement is True.
(vi) The negative of a negative integer is a positive integer → True.
(vii) If a and b are two integers such that a > b, then (a – b) is always a positive integer → True.
(x) -17 + (-5) + 22 < 17 + (-5) – 22
= -17 -5 + 22 , 17 -5 – 22
= -22 + 22 < 17 – 27
= 0 < -10
Thus, the statement is False.
Integers Exercise 5.4 Solution
Question no – (1)
Solution :
(i) Given, 7 x (-10)
= -70
(ii) Given, (- 3) x 9
= -27
(iii) Given, (- 8) x (- 9)
= 72
(iv) Given, 0 x (-220)
= 0
(v) Given, (- 2) x (- 3) x 9
= 54
(vi) Given, (-3) x (-4) x 5
= 60
Question no – (2)
Solution :
(i) Given, 18 x (-15) x (-4)
= 18 x 16
= 1080
(ii) Given, (- 55) x 45 x (- 10)
= (-2475 ) x ( 49)
= 24750
(iii) Given, (- 10) x (- 10) x (- 10)
= (100) x (-10)
= -1000
(iv) Given, (- 7) x (- 7) x (- 7) x (- 7)
= (49) x (49)
= 240
(v) Given, ( -1)x (- 2) x (- 3) x (- 4) x (- 5)
= (2) x (-3) x ( 20)
= -6×20
= -120
(vi) Given, (- 3) x (- 1 ) x ( – 9) x(- 10 )
= (3) × (90)
= 270
(vii) Given, (-746) × (- 7)
= 5225
(viii) Given, (-138) × (-243) × (0)
= 0
Question no – (3)
Solution :
(i) Given, 15 [-7 + 19] = (15 × (-7)) + (15 × 19)
LHS, 15 × (-7+19 )
= 15 × 12
= 180
RHS, ( 15 × (-7) ) + ( 15 × 19 )
= -105 + 285
= 180
∴ LHA = RHS (Verified)
(ii) Given, 23 × [19 – 12] = (23 × 19) – (23 × 12)
LHS, 23 × [ 19-12]
= 23 × 7
= 161
RHS, (23 × 19) – (23 × 12)
= 437 – 236
= 161
∴ LHS = RHS (Verified)
(iii) Given, 45 × [5 + (-11) ] = (45 × 5) + [45 × (-11)]
LHS, 45 × [ 5 + ( -11)
= 45 × ( -6)
= 270
RHS, (45 × 5) + [45 × (-11)]
= 225 + (-495 )
= -270
∴ LHS = RHS (Verified)
Question no – (4)
Solution :
(i) Given, (-7) × 6 + (-7) × 4
∴ (-7) × 6 + (-7) × 4
= (-7) (6 + 4)
= -7 × 10
= – 70…(Simplified)
(ii) Given, 15 × (- 11) + 5 × (-11)
∴ 15 × (-11) + 5 × (-11)
= 5 × (- 33) + 5 × (-11)
= 5 [- 33 + (-11)]
= 5 × (-44)
= – 220…(Simplified)
(iii) Given, 120 × (-15) + 120 × 5
∴ 120 × (- 15) + 120 × 5
= 120 [ -15+5]
= 120 × ( -10)
= – 1200…(Simplified)
(iv) Given, 215 × 53 – 15 × 53
∴ 215 × 53 – 15 × 53
= [215 – 15] × 53
= 10600…(Simplified)
Question no – (5)
Solution :
| x | 5 | 4 | 0 | -5 | -4 |
| 5 | 25 | 20 | 0 | -25 | -20 |
| 4 | 20 | 16 | 0 | -20 | -16 |
| 0 | 0 | 0 | 0 | 0 | 0 |
| -5 | -25 | -20 | 0 | 25 | 20 |
| -4 | -20 | -16 | 0 | 20 | 16 |
Question no – (6)
Solution :
(i) Given, 39
= 39 × (-1)
= -39
(ii) Given, -115
= (-115 ) × (- 1)
= 115
(iii) Given, 0
= 0 × (- 1)
= 0
(iv) Given, -23
= (- 23) × (- 1)
= 23
Question no – (7)
Solution :
(i) If we multiply together 6 negative integer and 2 positive integers then the sign of the product will be Positive (+)
(ii) If we multiply together 19 negative integers and 7 positive integers then the sign of the product will be Negative (-)
Question no – (8)
Solution :
(i) The product of three negative integers is a negative integer → True.
(ii) The product of a negative integer and a positive integer may be zero → False.
(iii) The product of two negative integers is a positive integer → True.
(iv) Of the two integers if one is negative, then the product must be negative → True.
(v) For all non-zero integers a and b, the product a × b is always greater than either a or b → False.
(vi) There does not exist an integer b such that for a > 1, a × b = b × a = b → False.
Question no – (9)
Solution :
(i) Given, (8 + 9) × 10 and 8 + 9 × 10
First, (8 + 9) × 10
= (8 × 9 ) × 10
= 72 × 10
= 720
Now, = 8 + 9 × 10
= 8 + 90
= 98
Therefore, 8 + 9 × 10 < (8 × 9) × 10
(ii) Given, (8 – 9) × 10 and 8 – 9 × 10
First, (8 – 9) × 10
= (-9 ) × 10
= (-1 ) × 10
=- 10
Now, 8 – 9 × 10
= 8 – 90
= -82
Therefore, (8 – 9) × 10 > 8 – 9 × 10
(iii) Given, [(-2) – (5)] × (-6) and (-2) – 5 × (-6)
First, [( -2 ) – ( 5 )] × 6
= (- 7) × (-6)
= 42
Now (-2 ) – 5 × (-6 )
= – 2 + 3 0
= 28
Therefore, [ (-2) – (- 5) ] × (- 6) > (- 2) – 5 × (- 6)
Integers Exercise 5.6 Solution
Question no – (3)
Solution :
(ii) 100
∴ (100)2
= (100) × (100)
= 10000
Hence, the square of 100 is 10000
(iii) -70
∴ (-70)2
= (-70) × (- 70)
= 4900
Thus. the square of -70 is 4900
(iv) 150
∴ (150)2
= 150 × 150
= 22500
Hence, the square of 150 is 22500
(v) 1000
∴ (1000)2
= 1000 × 1000
= 1000000
Thus, the square of 1000 is 1000000
Question no – (4)
Solution :
(i) (10)2;
= 10 × 10
= 100
∴ The value is 100
(ii) (25)2
= 25 × 25
= 625
∴ The value is 625
(iii) 1100
= 1
∴ The value is 1
(iv) (- 1)25
= – 1
∴ The value is -1
(v) (- 2)8
= – 2 × – 2 × -2 × – 2 × -2 × -2 × – 2 × -2
= 256
∴ The value is 256
(vi) (- 7)3
= – 7 × – 7 × – 7 ×
= – 343
∴ The value is – 343
(vii) (- 3)6
= – 3 × – 3 × – 3 × – 3 × – 3 × – 3
= – 729
∴ The value is – 729
(viii) (- 2)6
= – 2 × – 2 × – 2 × – 2 × – 2 × – 2
= 64
∴ The value is 64
(ix) (31)2
= 31 × 31
= 961
∴ The value is 961
(x) (14)2
= 14 × 14
= 19
∴ The value is 19
Question no – (5)
Solution :
First ten natural numbers square :
| 12 = 1 | 62 = 36 |
| 22 = 4 | 72 = 64 |
| 32 = 9 | 82 = 64 |
| 42 = 16 | 92 = 81 |
| 52 = 25 | 102 = 100 |
Note that the unit digits are 1, 4, 5, 6, 9, 0
Question no – (6)
Solution :
Cube of 1st 10 natural numbers are
| 13 = 1 | 63 = 216 |
| 23 = 8 | 73 = 343 |
| 33 = 27 | 83 = 512 |
| 33 = 64 | 93 = 729 |
| 53 = 125 | 103 = 1000 |
Question no – (7)
Solution :
(i) 7
∴ 73
= 7 × 7 × 7
= 343
Thus, the cube of 7 is 343
(ii) 9
∴ 93
= 9 × 9 × 9
= 729
Thus, the cube of 9 is 729
(iii) 5
∴ 53
= 5 × 5 × 5
= 125
Thus, the cube of 5 is 125
(iv) Given number, 100
∴ 1003
= 100 × 100 × 100
= 1000000
Thus, the cube of 100 is 1000000
(v) -13
∴ (-13)3
= (-13) × (-13) × (-13)
= -2197
Thus, the cube of -13 is –2197
(x) 1000
∴ (1000)3
= 1000 × 1000 × 1000
= 1000000000
Thus, the Cube of 1000 is 1000000000
Question no – (8)
Solution :
(i) (- 2)4 × (- 2)2 = (- 2)7
L.H.S, (- 2)4 × (- 2)3
= (- 2)4 + 3
= (- 2)7 = R.H.S (Verified)
(ii) (3)5 × (3)4 = 39
∴ L.H.S, 35 × 34
= 35+4
= 39
= R.H.S…(Verified)
(iii) 102 × 103 = 105
∴ L.H.S, 102 × 103
= 102+3
= 105
∴ LHS = R.H.S (Verified)
(iv) (- 4)5 ÷ (- 4)2 = (- 4)3
∴ L.H.S, (-4)5 ÷(- 4)2
= (- 4)5/(-4)2 = (-4)5-2
= (- 4)3
∴ L.H.S = R.H.S (Verified)
(vi) 23 × (- 3)2 × 8 = 26 × (- 3)2
∴ L.H.S, 23 × (- 3)2 × 8
= 23 × 23 × (- 3)2
= 26 × (- 3)2
∴ LHS = R.H.S (Verified)
Question no – (9)
Solution :
(i) Square of every integer positive → True
(ii) Cube of every integer is positive → False
(iii) Square of a negative integer is negative → False
(iv) Cube of a negative integer is positive → False
(v) 46 ÷ 45 = 4
= 46 ÷ 45
= 46/45 = 46-5
= 41
= 4
= True
(vi) 34 is equal to 43
= 34 = 81
= 43 = 64
= 34 ≠ 43 [False]
Integers Exercise 5.7 Solution
Question no – (1)
Solution :
(i) 18 – (2 × 5) + 4
= 18 – 10 + 4
= 12
∴ The value is 12
(ii) 12 – (5 – 3) + 2
= 12 – 2 + 2
= 12
∴ The value is 12
(iii) 15 – (15 – 6 ÷ 3)
= 15 – 915 – 2)
= 15 – 13
= 2
∴ The value is 2
(iv) 12 – (3 × 5) + 3
= 3 + 3
= 0
∴ The value is 0
(v) (- 40) × (- 1) + (- 28) ÷ 7
= 40 + (- 4)
= 36
∴ The value is 36
(vi) 17 + (- 3) × (- 5) – 6
= 17 + 15 – 6
= 17 + 9
= 26
∴ The value is 26
Question no – (2)
Solution :
(i) Given, Three is multiplied by the sum of two and four
∴ Mathematical expression = 3 × (2 + 4)
(iii) Given, Twelve divided by the sum of one and three
In mathematical expression = 12 ÷ (1 + 3)
(iv) Given, Six subtracted from the sum of eight and two.
Now in mathematical expression = (8 + 2) – 6
Question no – (3)
Solution :
(i) 7 – {6 – 12 ÷ (5 + 9 × 2 – 19)}
Now, 7 – {6 – 12 ÷ (5 + 9 × 2 – 19)}
= 7 {6 – 12 ÷ (5 + 18 – 19)}]
= 7 {6 – 12 ÷ 4}
= 7 {6 – 3}
= 7 – 3
= 4…(Simplified)
(ii) 121 ÷ [17 – {15 – 3 (7 – 4)}]
Now, 121 ÷ [17 – {15 – 3 (7 – 4)}]
= 121 ÷ [17 – {15 – 3 × 3}]
= 121 ÷ [17 – {15 – 9}]
= 121 ÷ [17 – 6]
= 121 ÷ 11
= 11…(Simplified)
(iii) 3 [18 – {7 – (3 – 2)}
Now, 3 [18 – {7 – (3 – 2)}
= 3 × [18 – {7 – (3 – 2)}]
= 3 × [18 – {7 – 1]]
= 3 [18 – 6]
= 3 × 12
= 36…(Simplified)
(iv) [0.7 – [1.3 – 5.2 – (8.1 – 7.2 – 3.5)}
Now, [0.7 – [1.3 – 5.2 – (8.1 – 7.2 – 3.5)}
= 0.7 – [1.3 – 5.2 – (- 2.6)}]
= 0.7 – [1.3 – 5.2 + 2.6]
= 0.7 – (- 14)
= 0.7 + 1.4
= 21…(Simplified)
(v) 81 × [59 – {7 × 8 + (13 – 2 × 5)}]
Now, 81 × [59 – {7 × 8 + (13 – 2 × 5)}]
= 81 [59 – {7 × 8 + 913 – 10)}]
= 81 [59 – 7 × 8 + 3)}]
= 81 [59 – {56 + 3}]
= 81 × [59 – 59]
= 81 × 0
= 0…(Simplified)
(vi) 41 + [13 – {15 – (13 – 4 – 1)}]
Now, 41 + [13 – {15 – (13 – 4 – 1)}]
= 41 + [13 – {15 – 10}]
= 41 + [13 – 5]
= 41 + 8
= 49…(Simplified)
(vii) 45 ÷ 8 – (- 7) + 21 ÷ (- 3)
Now, 45 ÷ 8 – (- 7) + 21 ÷ (- 3)
= 45 ÷ 15 + 21 ÷ (- 3)
= 3 – 7
= -4…(Simplified)
(viii) 3 [18 + {3 + 4 (4 – 2)}]
Now, 3 [18 + {3 + 4 (4 – 2)}]
= 3 × [18 + {3 + 4 × 2}]
= 3 × [18 + {3 + 8}]
= 3 × [18 + 11]
= 3 × 29
= 87…(Simplified)
(ix) (-1) {(-5) + (-25)} × (-7) – (8 – 10) (-4)
Now, (- 1) {( – 5) + (- 25)} × (- 7) – (8 – 10) (- 4)
= – 1 {(30)} × (- 7) + 4 × (- 2)
= 30 × (- 7) – 8
= -210 – 8
= – 218…(Simplified)
(x) 2 – [2 – {2 (2 – 2 – 2)}]
Now, 2 – [2 – {2 (2 – 2 – 2)}]
= 2 – [2 – {2 – (2 – 0}]
= 2 – [2 – {2 – 2}]
= 2 – [2 – 0]
= 2 – 2
= 0…(Simplified)
Next Chapter Solution :
👉 Chapter 6 👈