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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)**

**Next Chapter Solution : **

👉 Chapter 3 👈