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Brilliant’s Composite Mathematics Class 7 Solutions Chapter 2 Operations On Rational Numbers
Welcome to NCTB Solutions. Here with this post we are going to help 7th class students for the Solutions of Brilliant’s Composite Mathematics Class 7 Math Book, Chapter 2, Operations On Rational Numbers. Here students can easily find step by step solutions of all the problems for Operations On Rational Numbers, Exercise 2.1, 2.2, 2.3, 2.4 and 2.5 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.
Operations On Rational Numbers Exercise 2.1 Solution
Question no – (1)
Solution :
Given, 4/5, -17/5
= 2/9 + 8/-17
= 34 – 16/135
= 18/153
Question no – (2)
Solution :
Given, 8/-11, -9/11
= 8/-11 + -9/11
= -8 – 9/11
= – 17/11
Question no – (3)
Solution :
Given, 2/9, 8/-17
= 2/9 + 8/-17
= 34 – 16/135
= 18/153
Question no – (4)
Solution :
Given, 5/13, 4/15
= 5/13 + 4/15
= 75 + 52/195
= 127/195
Question no – (5)
Solution :
Given, -2/3 + 4/5
= 10 + 12/15
= 2/15…(Simplified)
Question no – (6)
Solution :
Given, 3/7 + -4/5
= 15 – 28/35
= -13/35…(Simplified)
Question no – (7)
Solution :
Given, 5/4 + 4/7
= 35 + 16/28
= 51/28…(Simplified)
Question no – (8)
Solution :
Given, 3/26 + 10/-39
= 9 – 20/78
= -11/78…(Simplified)
Verify that x + y + x if
Question no – (9)
Solution :
Given, x = 5/9, y = 7/12
L.H.S, x + y
= 5/9+7/12
= 20+21/36
= 41/36
R.H.S, y + x
= 7/12+5/9
= 21+20/36
= 41/36
∴ L.H.S = R.H.S [Prove]
Question no – (10)
Solution :
Given, x = -8/15, y = 11/12
L.H.S, x + y
= -8/15+11/12
= -32+55/60
= 13/60
R.H.S, y + x
= 11/12 + -8/15
= 55–32/60
= 13/60
∴ L.H.S = R.H.S [Prove]
Question no – (11)
Solution :
Given, x = -3/4, y = 4/7, z = 3/10
L.H.S, (x + y)+ Z
= (-3/4 + 4/7)+ 3/10
= (-21+16/28)+ 3/10
= -5/28+3/10
= -25+42/140
= 17/140
R.H.S, x (x + z)
= -3/4 (4/7 + 3/10)
= -3/4 (40+21/70)
= -3/4 (61/70)
= -183/280
∴ L.H.S ≠ R.H.S [Prove]
Question no – (12)
Solution :
Given, x = -4/5, y = 6/7, z = 7/10
L.H.S, (X + Y) + Z
= (-4/5+6/7)+7/10
= (-28 + 30/35)+7/10
= 2/35+7/10
= 4 +49/70
= 53/70
R.H.S, x (y + z)
= -4/5 (6/7 + 7/10)
= -4/5 (60 + 49/70)
= -4/5 × 109/70
= -436/350
∴ L.H.S = R.H.S [Prove]
Question no – (13)
Solution :
Given, 3/8 + 1/2 + -2/5 + 7/8 + -3/2 + 4/5
= (1/3 + 1/2 + 7/8 + 4/5) – (2/5 + 3/2)
= (80 + 120 + 30 + 48/240) – (4 + 15/10)
= 278/240 – 19/10
= 278 – 456/240
= -178/240
= – 13/20
Question no – (14)
Solution :
Given, 4/7 + -11/15 + -8/9 + -3/7 + 14/15 + 5/9
= (4/7 – 3/7) – (8/9 – 5/9)
= (4-3/7) – (8-5/9)
= 1/7 – 3/9
= 9-21/63
= 12/63
= 4/21
Question no – (15)
Solution :
(a) -6/13 + 5/8 = 5/8 = __
= or, x = -6/13
(b) 4/11 + 8/-17 = 8/-17+ __
= or, x = 4/11
(c) 2/9 + __ = -17/19 + 2/9
= or, x = -17/19
(d) 6/11 + -9/13 __ + 6/11
= or, x = -9/13
(e) (-3/7 + 5/11) + -2/57 = -3/7 + (__ + -2/57)
= or, -3/7 + 5/11 + -2/57
= – 3/7 + x + -2/57
or, x = 5/11
(f) (5/6 + -7/15) + 18/37 = 5/6 + (-/15 + __)
= or, 5/6 + -7/15+18/37 = 5/6 + -7/15+x
= or, x = 18/37
Question no – (16)
Solution :
= -2/3 + (6/5 + 8/3) = (-2/3 + 6/5) + 8/3
= Associate
Question no – (17)
Solution :
= (2/7 + -3/2) + 11/13 = 2/7 + (-3/2+11/13)
= Associate
Question no – (18)
Solution :
= 5/19 + -7/12 =-7/12 + 5/19
= Commutative
Question no – (19)
Solution :
= 13/19 + 15/-17 = 15/-17 + 13/19
= Commutative
Operations On Rational Numbers Exercise 2.2 Solution
Question no – (1)
Solution :
Given numbers, 15/23, -7/23
= -7/23 -15/23
= -7 -15/23
= -22/23
Question no – (2)
Solution :
Given numbers, 8/15, 7/20
= 7/20 – 8/15
= 21 – 32/60
= -11/60
Question no – (3)
Solution :
Given numbers, 13/27, 19/30
= 19/30 – 13/27
= 171 – 130/270
= 41/270
Question no – (4)
Solution :
Given numbers, 11/12, -14/15
= 1 – 14/15 – 11/12
= -56 – 55/56
= -111/60
Question no – (5)
Solution :
Given numbers, -5/8, -3/7
= -3/7 – 5/8
= -24 + 35/56
= 11/56
Question no – (6)
Solution :
Given numbers, 7/20, -4/5
= -4/5 – 7/20
= -61 – 7/20
= -23/20
Question no – (7)
Solution :
(a) 13/15 – 7/20
= 52-21/60
= 31/60
(b) 7/20 – 13/15
= 21-52/60
= -31/60
No, two result are not same.
Question no – (9)
Solution :
Other number,
= -1/12 – 5/6
= -1 – 10/12
= -11/12
Therefore, the other number will be -11/12
Question no – (10)
Solution :
Other number,
= 12/15 – 5/12
= 48 – 20/60
= 28/60
= 7/12
Hence, the the other number will be 7/12
Question no – (11)
Solution :
Required number,
= -5/11 – 5/9
= -45 – 55/99
= -100/99
Thus, -100/99 should be added.
Question no – (12)
Solution :
= 23/24 – (-7/8)
= 23/24 + 7/8
= 23 + 21/24
= 44/24
= 11/6
Therefore, 11/6 should be added.
Question no – (13)
Solution :
-5/17 – 7/34 = -1/2
= -10 -7/34
= -17/34
= -1/2
Question no – (14)
Solution :
-7/15 + 22/15 = 1
or, 7/15 + 1=x
or, x = 7 + 15/15
= 22/15
Question no – (15)
Solution :
-4/9 – 7/18
= -8 – 7/18
= -15/18
Question no – (16)
Solution :
62/92 + 7/23 = 3/4
= x + 7/23 = 3/4
or, x = 3/4 – 7/23
= 69-7/92
= 62/92
Question no – (17)
Solution :
Given, 3/5 + -7/10 > 1/2
L.H.S, 3/5 + -7/10
= 3/5 – 7/10
= 6 – 7/10
= -1/10
Hence, the statement is False
Question no – (18)
Solution :
Given, -4/7 – -7/5 > 2/3
L.H.S, -4/7 – -7/5
= -4/7 + 7/5
= -20 + 49/35
= 29/35
∴ 29/35 > 2/3
Thus, the statement is True.
Question no – (19)
Solution :
The negative of a rational number always exists – True
Question no – (20)
Solution :
The negative of a negative rational number is always a positive rational number
The statement is True.
Question no – (21)
Solution :
|2/3 + -4/5| = |2/3| + |4/5|
This statement is – False.
Question no – (22)
Solution :
For every rational number x, we have x – 0 = 0 – x = x
This statement is False
Operations On Rational Numbers Exercise 2.3 Solution
Question no – (1)
Solution :
Given, 4/9, -8/13
= 4/9 × -8/13
= -32/127
Question no – (2)
Solution :
Given, 11/13, -2/9
= 11/13 × -2/9
= -22/127
Question no – (3)
Solution :
Given, -7/4, 6/5
= 7/4 × 6/5
= -22/10
Question no – (4)
Solution :
Given, -11/24, 0
= -11/24 × 0
= 0
Question no – (5)
Solution :
Given, x = 6/5, y = -9/8
L.H.S, x × y
= – 6/5 × -9/8
= -27/20
R.H.S, x × y
= -9/8 × 6/5
= -27/20
∴ L.H.S = R.H.S
Question no – (6)
Solution :
Given, x = 11/15, y= 9/-16
L.H.S, x × y
= 11/15 × 9/-16
= 33/-80
R.H.S, y × x
= 9/-16 × 11/15
= 33/-80
∴ L.H.S = R.H.S
Question no – (7)
Solution :
Given, x = -3/4, y = 7/11
L.H.S, x × y
= -3/4 × 7/11
= -21/44
R.H.S, y × x
= 7/11 × -3/4
= -21/44
∴ L.H.S = R.H.S
Question no – (8)
Solution :
Given, x = 7/4, y = 2/5
L.H.S, x × y
= 7/4 × 2/5
= 7/10
R.H.S, y × x
= 2/5 × 7/4
= 7/10
∴ L.H.S = R.H.S
Question no – (9)
Solution :
Given, x = -3/4, y = -8/5
L.H.S, x × y
= -3/4 × -8/5
= 6/5
R.H.S, y × x
= -3/4 × -8/5
= 6/5
∴ L.H.S = R.H.S
Question no – (10)
Solution :
Given, x= 9/5, y = -11/8
L.H.S, x × y
= 9/5 × -11/8
= -99/40
R.H.S, y × x
= -11/8 × 9/5
= -99/40
∴ L.H.S = R.H.S
Question no – (11)
Solution :
Given, x = 2/3, y = 6/5, z 9/2
L.H.S, x × (y × z)
= 2/3 × (6/5 × 9/2)
= 2/3 × 3/5 × 9
= 18/5
R.H.S, (x × y) × z
= (2/3 × 6/5) × 9/2
= 2 × 2/5 × 9/2
= 18/5
∴ L.H.S = R.H.S
Question no – (12)
Solution :
Given, x = -3/5, y = 10/13, z = -11/12
L.H.S, x × (y × z)
= -3/5 × (10/13 × -11/12)
= -3/5 × 5/13 × -11/6
= 11/26
R.H.S, (x × y) × z
= (-3/5 × 10/13) × -11/12
= -3 × 2/13 × -11/12
= 11/26
∴ L.H.S = R.H.S
Question no – (13)
Solution :
Given, x = -4/5, y = -7/11, z = 15/14
L.H.S, x × (y × z)
= -4/5 × (-7/11 × 15/14)
= -4/8 × -7/11 × 15/14
= 6/11
R.H.S, (x × y) × z
= (-4/5 × – 7/11) × 15/14
= -4/5 × – 7/11 × 15/14
= 6/11
∴ L.H.S = R.H.S
Question no – (14)
Solution :
Given, x = -13/15, y = 15/16, z = 10/36
L.H.S, x × (y × z)
= -13/15 × 15/16 × 10/36
= -45/288
R.H.S, (x × y) × z
= -13/ 15 × 15/10 × 10/36
= -45/288
∴ L.H.S = R.H.S
Question no – (15)
Solution :
Given, x = -4/3, y= 1/2, z = -7/5
L.H.S, x × [y + z]
= -4/3 × [1/2 + -7/5]
= -4/3 × -[5-14/10]
= -4/3 × -9/10
= 6/5
R.H.S, (x × y) + (x × z)
= (-4/3×1/2) + (1/2 × -7/5)
= -2/3 – 7/10
= -20 – 21/30
= -41/30
∴ L.H.S ≠ R.H.S
Question no – (16)
Solution :
Given, x = 2/3, y = 6/5, z = 9/2
L.H.S, 2/3 × (6/5 × 9/2)
= 2/3 × ) (12 + 54/10)
= 2/3 × 66/10
= 11/15
R.H.S, (x × y) + (y × z)
= (2/3 × 6/5) + (6/5 × 9/2)
= 4/5 + 27/10
= 8 + 27/10
= 35/10 = 7/5
∴ L.H.S ≠ R.H.S
Question no – (17)
Solution :
Given, x = 7/10, y = 3/4, z = 9/5
L.H.S, x × (y + z)
= 7/10 × (3/4 + 9/5)
= 7/10 × 51/20
= 357/200
R.H.S, (x × y) + (y × z)
= (7/10 × 3/4) + (3/4 × 9/5)
= 21/40 + 27/20
= 21 + 54/40
= 75/40
∴ L.H.S ≠ R.H.S
Question no – (18)
Solution :
Given, X = 8/15, Y = -7/26, Z = -11/39
L.H.S, x × (y + z)
= 8/15 × (-7/26 + -11/39)
= 8/15 × (-21/22/78)
= 48/15 × -43/78
= -172/585
R.H.S, (x × y) (y × z)
= (8/5 × -7/26) + (-7/26 × -11/39)
= -28/45 – 77/1014
∴ L.H.S ≠ R.H.S
Question no – (19)
Solution :
(a) Product of two positive rational numbers is always Positive.
(b) Product of two negative rational numbers is always Positive.
(c) Product of a positive rational number and a negative rational number in always Negative.
(d) Product of a non-zero rational number and zero rational number is always 1
(e) Product of non-zero rational numbers and its multiplicative inverse is always 1
Question no – (20)
Solution :
= 3/13 × -8/11 × -8/11 × 3/13
= Commutative property of multiplication
Question no – (21)
Solution :
= 2/3 × (3/2) = 1
= Multiplicative inverse of non-Zero element exists
Question no – (22)
Solution :
= 5/11 × 1 = 5/11
= Multiplicative identity of element exists, Multiplicative property of zero
Question no – (23)
Solution :
= (1/3 × 3/7) × 4/11 = 1/3 × (3/7 × 4/11)
= Associative property of Multiplication
Question no – (24)
Solution :
3/7 × [4/9 + 8/17] = (3/7 × 4/9) + (3/7 × 8/17)
= Distributive property of Multiplicative over additive
Question no – (25)
Solution :
= 4/5 × 7/11 × 12/25 × 0 = 0
= Property of zero
Operations On Rational Numbers Exercise 2.4 Solution
Question no – (1)
Solution :
Given, 3/19
Reciprocal = 19/3
Question no – (2)
Solution :
Given, 4/-15
Reciprocal = -15/4
Question no – (3)
Solution :
Given, -28/45
Reciprocal = -45/28
Question no – (4)
Solution :
Given, 49/60
Reciprocal = 60/49
Question no – (5)
Solution :
Given, 5/9 × 3/-7
Reciprocal = 5/9 × 3/-7
= 15/21
= -21/15
Question no – (6)
Solution :
Given, 20/39 × 15/28
Reciprocal = 75/91
Question no – (7)
Solution :
Given, 11/15 ÷ 33/20
Reciprocal = 11/15 × 20/33
= 4/9
= 9/4
Question no – (8)
Solution :
Given, 11 × 23/24
Reciprocal = 24/253
Question no – (11)
Solution :
Given, 3/4, -9/8
= 3/4 × 8/-9
= – 2/3
Question no – (12)
Solution :
Given, 7/3, 11/3
= 7/3 × 3/11
= 7/11
Question no – (13)
Solution :
Given, -9/10, -3/5
= -9/10 × 5/-8
= 3/2
Question no – (14)
Solution :
Given, 2/3, -5/7
= 2/3 × – 7/11
Question no – (15)
Solution :
Other number,
= 7/4 ÷ 7/9
= -7/4 × 9/7
= -9/4
Therefore, the other number will be -9/4
Question no – (16)
Solution :
Other number,
= -14/27 ÷ 7/9
= -14/27 × 9/7
= -2/3
Therefore, the other number will be -2/3
Question no – (17)
Solution :
Other number,
= -16/51 ÷ -4/15
= -16/17 × 15/-4
= 20/17
Hence, the other number will be 20/17
Question no – (18)
Solution :
(a) If x is reciprocal of y, then the reciprocal of y is x
(b) The rational number zero is Not the reciprocal of any number
(c) The reciprocal of a positive rational numbers is Positive.
(d) The product of a non-zero rational number and its reciprocal is always 1.
Operations On Rational Numbers Exercise 2.5 Solution
Question no – (1)
Solution :
1st, 3/4 = 3 × 11/4 × 11
= 33/44
2nd, -6/11
= -6 × 4/11 × 4
= -24/44
Thus, rational numbers are 33/44, -24/44
Question no – (2)
Solution :
1st, -4/5 = -4 × 9/5 × 9 = -36/45
2nd, 8/9 = 8 × 5/9 × 5 = 40/45
Hence, the rational numbers are, -36/45, -35/45, -1/45, -0, 1/45, -40/45
Question no – (4)
Solution :
First, |x + y|
= x + y
= -3/14 + 5/21
= -9 + 10/42
= 1/42
∴ |x + y| = |x | + |y|
Now, |x| + |y|
= x + y
= -3/14 + 5/21
= -9 + 10/42
= 1/42
Question no – (5)
Solution :
First, |x + y|
= -4/5 + 5/7
= -28 + 25/35
= 3/35
∴ |x + y| = | x | + | y |
Now, |x| + |y|
= x + y
= – 4/5 + 5/7
= -28 + 25/35
= 3/35
Question no – (6)
Solution :
First, |x – y|
= 4/15 – 7/12
= 12 – 35/60 = 23/60
Now, |x| – |y|
= 4/15 – 7/12
= 12 – 35/60
= 23/60
∴ |x – y| = |x| – |y|…(Verified)
Question no – (7)
Solution :
First, 9/16 – -7/15
= 135 + 112/240
= 247/240
Now, | x | – | y |
= 9/16 – -7/15
= 135+112/240
= 247/240
∴ | x – y | = | x | – | y |…(Verified)
Question no – (8)
Solution :
= |x × y|
= 5/6 × -7/8
= -35/48
|x|×|y|
= 5/6 × -7/8
= -35/48
∴ |x × y| = | x | × | y |…(Verified)
Question no – (9)
Solution :
= |x × y|
= 8/9 × 3/4
= 2/3
|x|×|y|
= 8/9 × 3/4
= 2/3
∴ |x × y| = | x | × | y |…(Verified)
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