# Brilliant’s Composite Mathematics Class 7 Solutions Chapter 2

## 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

Question no – (12)

Solution :

= 23/24 – (-7/8)

= 23/24 + 7/8

= 23 + 21/24

= 44/24

= 11/6

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 :

Updated: June 9, 2023 — 4:06 pm