**Class 8 ICSE Maths Solutions Chapter 1 Rational Numbers (Selina Concise)**

Welcome to NCTB Solutions. Here with this post we are going to help 8th class students for the Solutions of Selina Class 8 ICSE Math Book, Chapter 1, Rational Numbers. Here students can easily find step by step solutions of all the problems for Rational Numbers, Exercise 1A, 1B, 1C, 1D and 1E 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. Here in this post students will get chapter 1 solutions. Here in this post all the solutions are based on ICSE latest Syllabus.

**Rational Numbers Exercise 1(A) Solution :**

**Question no – (1) **

**Solution : **

**(i) – 5/8 and 3/8**

= – 5 + 3/8

= – 2/8

= – 1/4

This is a rational number.

**(ii) -8/13 and – 4/13**

= – 8/13 + – 4/13

= – 8/13 – 4/13

= – 8 – 4/13

= – 12/13

**∴** It is a rational number.

**(iii)** Given, 6/11 and – 9/11

= 6/11 + – 9/11

= 6/11 – 9/11

= 6 – 9/11

= – 3/11

Its also a rational number.

**(iv) 5/- 26 and 8/39**

= 5/- 26 + 8/39

= – 15 + 16/78

= 1/78

**∴** Its is also a rational number.

**(v) 5/- 6 and 2/3**

= 5/- 6 + 2/3

= – 5 + 4/6

= – 1/6

**(vi) – 2/ and 2/5**

= – 2 + 2/5

= – 10 + 2/5

= – 8/5

**(vii) 9/- 4 and – 3/8**

= 9/- 4 + – 3/8

= 9/- 4 – 3/8

= – 18 – 3/8

= – 21/8

**(viii) 7/- 18 and 8/27**

= – 21 + 16/54

= – 5/54

**Question no – (2) **

**Solution : **

**(i) 5/9 + -7/6**

= 5/9 – 7/6

= 10 – 21/18

= -11/18

**(ii) 4 + 3/-5**

= 4 – 3/5

= 20 – 3/5

= 17/5

**(iii) 1/-15 + 5/-12**

= 1/-15 – 5/12

= – 4 – 25/60

= – 29/60

**(iv) 5/9 + 3/-4**

= 5/9 – 3/4

= 20 – 27/36

= -7/36

**(v) – 8/9 + -5/12**

= – 8/9 – 5/12

= – 32 – 15/36

= – 47/36

**(vi) 0 + -2/7**

= 0 – 2/7

= 0 – 2/7

= – 2/7

**(vii) 5/-11 + 0**

= -5/11

**(viii) 2 + -3/5**

= 2 – 3/5

= 10 – 3/5

= 7/5

**(ix) 4/-9 + 1**

= -4/9 + 1

= -4 + 9/9

= 5/9

**Question no – (3) **

**Solution : **

**(i) 3/7 + -4/9 + -11/7 + 7/9**

= 3/7 – 4/9 – 11/7 + 7/9

= 27 – 28 – 99 + 49/63

= – 51/63

= – 17/21

**(ii) 2/3 + -4/5 + 1/3 + 2/5**

= 2/3 – 4/5 + 1/3 + 2/5

= 10 – 12 + 5 + 6/15

= – 2 + 5 + 6/15

= 9/15

= 3/5

**(iii) 4/7 + 0 + -8/9 + -13/7 + 17/9**

= 4/7 – 8/9 – 13/7 + 17/9

= 36 – 56 – 117 + 119/63

= – 18/63

= – 2/7

**(iv) 3/8 + -5/12 + 3/7 + 3/12 + -5/8 + -2/7**

= 3/8 – 5/12 + 3/7 + 3/12 – 5/8 – 2/7

= 63 – 70 + 72 + 42 – 105 – 48/168

= -46/168

= – 23/84

**Question no – (4) **

**Solution : **

**(i)** Given, -8/7 and 5/14

**∴** -8/7 + 5/14

= -16 + 5/14

= -11/14

And, 5/14 + -8/7

= 5/14 – 8/7

= 5 – 16/14

= -11/14

**∴** -8/7 + 5/14 = 5/14 + – 8/7

**(ii) 5/9 and 5/-12**

**∴** 5/9 + 5/-12

= 5/9 – 5/12

= 20 – 15/36

= 5/36

And, 5/-12 + 5/9

= -15 + 20/36

= 5/36

**∴** 5/9 + 5/-12 = 5/-12 + 5/9

**(iii) -4/5 and -13/-15**

**∴** -4/5 + 13/15

= -12 + 13/15

= 1/15

And, -13/-15 + -4/5

= 13/15 – 4/5

= 13 – 12/15

= 1/15

**∴** -4/5 + -13/-15 = – 13/-15 + -4/5

**(iv) 2/-5 and 11/-15**

**∴** 2/-5 + 11/-15

= 2/-5 – 11/15

= -6 – 11/15

= -17/15

And, 11/- 15 + 2/-5

= 11/-5 – 2/5

= -11 – 6/15

= -17/15

**∴** 2/-5 + 11/-15 = 11/-15 + 2/-5

**(v) 3 and -2/7**

**∴** 3 + -2/7

= 3 – 2/7

= 21 – 2/7

= 19/7

And, -2/7 + 3

= -2 + 21/7

= 19/7

**∴** 3 + -2/7 = -2/7 + 3

**(vi) -2 and 3/-5**

**∴** -2 + 3/-5

= -2 – 3/5

= -10 – 3/5

= -13/5

And, 3/-5 + (-2)

= 3/ – 5 – 2

= – 3 – 10/5

= – 13/5

**∴** – 2 = 3/- 5 = 3/-5 + (-2)

**Question no – (5) **

**Solution : **

**(i)** In the given question, 1/2, 2/3 and -1/6

∴ 1/2 + (4 – 1/6)

= 1/2 + 3/6

= 3 + 3/6

= 6/6

= 1

And, (1/2 + 2/3) + – 1/6

= (3 + 4/6) – 1/6

= 7/6 – 1/6

= 7 – 1/6

= 6/6

= 1

**Question no – (6) **

**Solution : **

**(i)** The additive inverse of -3/8 is 3/8

**(ii)** The additive inverse of 4/-9 is 4/9

**(iii)** The additive inverse (negative) of -7/5 is 7/5

**(iii)** The additive inverse (negative) of -4/-13 is 4/13

**(iv)** The additive inverse (negative) of 0 is 0

**(v)** The additive inverse (negative) of -2 is 2

**(vi)** The additive inverse (negative) of 1 is 1

**(vii)** The additive inverse (negative) of -1/3 is 1/3

**(viii)** The additive inverse (negative) of -3/1 is 3/1

**Question no – (7) **

**Solution : **

**(i)** Additive inverse of -5/-12 =__ -5/12__

**(ii)** -5/-12 + its additive inverse

= – 5/- 12 + (- 5/12)

= 0

So, -5/-12 + its additive inverse **0**

**(iii)** If a/b is additive inverse of – c/d, then – c/d is additive inverse of__ a/b__

And so, a/b + (-c)/d = (-c)/d + a/b = __0__

**Question no – (8) **

**Solution : **

**(i)** 7/9 = 7 + 5/9 + 5

= **False**

**(ii)** 7/9 = 7 – 5/9 – 5

= **False**

**(iii)** 7/9 = 7 × 5/9 × 5

= **True**

**(iv)** 7/9 = 7 ÷ 5/9÷ 5

= **True**

**(v)** – 5/- 12 is a negative rational number

= **False**

**(vi)** -13/25 is smaller than – 25/13

= **False**

**Rational Numbers Exercise 1(B) Solution :**

**Question no – (1) **

**Solution : **

**(i) 2/3 – 4/5**

= 10 – 12/15

= -2/15

**(ii) -4/9 – 2/-3**

= -4/9 + 2/3

= -4 + 6/9

= 2/9

**(iii) -1 – 4/9**

= -9 – 4/9

= -13/9

**(iv) -2/7 – 3/-14**

= -2/7 + 13/14

= -4 + 3/14

= -1/14

**(v) -5/18 – (-2/9)**

= -5/18 + 2/9

= -5 + 4/18

= -1/18

**(vi) 5/21 – (-13/42)**

= 5/21 + 13/42

= 10 + 13/42

= 23/42

**Question no – (2) **

**Solution : **

**(i) 5/8 from -3/8**

**∴** -3/8 – 5/8

= -3 – 5/8

= -8/8

= -1

**(ii) -8/11 from 4/11**

**∴** 4/11 – 8/11

= 4/11 + 8/11

= 4 + 8/11

= 12/11

**(iii) 4/9 from – 5/9**

**∴** -5/9 – 4/9

= -5 – 4/9

= -9/9

= -1

**(iv) 1/4 from -3/8**

**∴** -3/8 – 1/4

= -3 – 2/8

= -5/8

**(v) -5/8 from -13/16**

**∴** -13/16 – 5/8

= -13/16 + 5/8

= -13 + 16/16

= -3/16

**(vi) -9/22 from 5/33**

**∴** 5/33 – (-9/22)

= 5/33 + 9/22

= 10 + 27/66

= 37/66

**Question no – (3) **

**Solution : **

As per the question,

Sum of two rational numbers = 9/20

One number = 2/5,

Other number = ?

**∴** Other rational numbers,

= (9/20 – 2/5)

= 9 – 8/20

= 1/20

Therefore, other rational number will be 1/20.

**Question no – (4) **

**Solution : **

As per the question we know,

Sum of two rational numbers = -2/3

One number = -8/15

Other number = ?

**∴** Other rational number,

= (-2/3 – -8/15)

= -2/3 + 8/15

= -10 + 8/15

= -2/15

Hence, other rational number will be -2/15.

**Question no – (5) **

**Solution : **

According to the question,

Sum of two rational numbers = -6

One number = -8/5

Other number = ?

**∴** Other rational number,

= (- 6) – (-8/5)

= (- 6 + 8/5)

= – 30 + 8/5

= – 22/5

Therefore, other rational number will be -22/5.

**Question no – (6) **

**Solution : **

Number should be added,

= (5/9 – (-7/8)

= (5/9 + 7/8)

= (40 + 63/720)

= 103/72

= 1 31/72

Hence, 1 31/72 should be added to get 5/9.

**Question no – (7) **

**Solution : **

Number should be added,

= (-2/3 – (-5/9)

= (-2/3 + 5/9)

= – 6 + 5/9)

= -1/9

Therefore, -1/9 should be added to get -2/3.

**Question no – (8) **

**Solution : **

Number should be subtracted,

= (-5/6 – 4/9)

= -15 – 8/18

= -23/18

= -1 5/18

Therefore, -1 5/18 should be subtracted from -5/6 to get 4/9.

**Question no – (9) **

**Solution : **

**(i) Number should be subtracted,**

= (-2 – 3/8)

= -16 – 3/8

= -19/8

Thus, -19/8 should be subtracted from -2 to get 3/8.

**(ii) Number should be added,**

= (3/8 – (- 2)

= 3/8 + 2

= 3 + 16/8

= 19/8

Therefore, 19/8 should be added to -2 to get 3/8.

**Question no – (10) **

**Solution : **

**(i) 3/7 + -4/9 – -11/7 – 7/9**

= 3/7 – 4/9 + 11/7 – 7/9

= 27 – 28 + 99 – 49/63

= 49/63

= 7/9

**(ii) 2/3 + -4/5 – 1/3 – 2/5**

= 2/3 – 4/5 – 1/3 – 2/5

= 10 – 12 – 5 – 6/15

= – 13/15

**(iii) 4/7 – -8/9 – -13/7 + 17/9**

= 4/7 + 8/9 + 13/7 + 17/9

= 36 + 56 + 117 + 119/63

= 328/63

= 5 13/63

**Rational Numbers Exercise 1(C) Solution :**

**Question no – (1) **

**Solution : **

**(i) -14/5 × -6/7**

= 12/5

= 2 2/5

**(ii) 7/6 × -18/91**

= – 3/13

**(iii) -125/72 × 9/-5**

= 25/8

= 3 1/8

**(iv) -11/9 × -51/-44**

= – 51/36

= – 17/12

**(v) -16/5 × 20/8**

= – 8

**(2) Multiply **

**Solution : **

**(i) 5/6 and 8/9**

**∴** 5/6 × 8/9

= 20/27

**(ii) 2/7 and -14/9**

**∴** 2/7 × – 14/9

= – 4/9

**(iii) -7/10 and 4**

**∴** -7/10 × 4

= -7/2

**(iv) 36/-7 and -9/28**

**∴** 36/-7 × -9/28

= -81/49

= 1 32/49

**(v) -7/10 and -8/15**

**∴** -7/10 × -8/15

= + 28/75

**(vi) 3/-2 and -7/3**

**∴** 3/-2 × -7/3

= 7/2

**Question no – (3) **

**Solution : **

**(i) (2/-3 × 5/4) + (5/9 × 3/-10)**

= 5/-6 – 1/6

= -5 – 1/6

= -1

**(ii) (2 × 1/4) – (-18/7 × -7/15)**

= (1/2 – 18/15)

= 15 – 36/30

= -7/30

**(iii) (-5 × 2/15) – (-6 × 2/9)**

= -2/3 + 4/3

= -2 + 4/3

= 2/3

**(iv) (8/5 × -3/2) + (-3/10 × 9/16)**

= -12/5 – 27/160

= -384 – 27/160

= -411/160

**Question no – (4)**

**Solution : **

**(i)** **7/-5**

= -7/5 × 1

= -7/5

**(ii) -3/-4**

= -3/-4 × 1

= -3/ -4

= 3/4

**(iii) 0**

= 0 × 1

= 0

**(iv) -8/13**

= -8/13 × 1

= -8/13

**(v) -6/-7**

= -6/-7 × 1

= -6/-7

= 6/7

**Question no – (5) **

**Solution : **

**(i) -1/5 and 2/9**

= -1/5 × 2/9

= -2/45

And, 2/9 × -1/5

= -2/45

**(ii) 5/-3 and 13/-11**

= 5/-3 × 13/-11

= 65/33

And, 13/-11 × 5/-3

= 65/33

**(iii) 3 and -8/9**

= 3 × -8/9

= -24/9

And, -8/9 × 3

= -24/9

**Question no – (6) **

**Solution : **

**(i) 5**

= 1/5

**(ii) -3**

= -1/3

**(iii) 5/11**

= 11/5

= 2 1/5

**(iv) -7/-8**

= 7/8

= 8/7

**(v) -8/-7**

= 8/7

= 7/8

**(vi) 15/-17**

= -17/15

= -1 2/15

**Question no – (7) **

**Solution : **

**(i) 3/5 × 2/3**

= 2/5

= 5/2

So, the reciprocal is 5/2.

**(ii) -8/3 × 13/-7**

= – 104/ – 21

= 21/104

Hence, the reciprocal is 21/104

**(iii) -3/5 × -1/13**

= + 3/65

= 65/3

= 21 2/3

Therefore, the reciprocal is 21 2/3

**Question no – (8) **

**Solution : **

As per the question the values of,

x = 4/5,

y = – -2/3

z = – 4

**(i) Here, (x + y) × z + y × z**

= (4/5 + -2/3) × -4 = 4/5 × -4 + -2/3 × -4

= 12 – 10/15 × -4

= -16/5 + 8/3

= -48 + 40/15

= -8/15

= -8/15

**(ii) Now, (x + y) × z + y × z**

= (2/1 + 4/5) × 3/-10

= 2 × 3/-10 – 4/5 × 3/-10

= 10 + 4/4 × 3/-10

= 3/-5 + 6/-25

= -15 – 6/25

= 14/5 × 3/-10 = -21/25

= -21/25 = -21/25 **…(Proved)**

**Question no – (9)**

**Solution : **

According to the question the values of

x = 4/5,

y = -7/4

z = 3

Now,

**(i) x × (y – z) = x × y – x × z**

= 4/5 ( -7/4 – 3) = 4/5 × – 7/4 – 4/5 × 3

= 4/5 × (-7 – 12/4) = – 7/5 – 12/5

= 4/5 × – 19/4 = -19/5

-19/5 = -19/5…(Proved)

**(ii) x × (y – z) = x × y – x × z**

= 3/4 ×(8/9 – (-5)) = 3/4 × 8/9 – 3/4 × (-5)

= 3/4 (8/9 + 5) = 2/3 + 15/4

= 3/4 (8 + 45/9) = 8 + 45/12

= 3/4 × 53/9 = 53/12

= 53/12 = 53/12…(Proved)

**Question no – (10) **

**Solution : **

**(i)** 3/5 × – 8/9 = – 8/9 × 3/5

= Commutative property.

**(ii)** – 3/4 × (5/7 × – 8/15) = (- 3/4 × 5/7) × – 8/15

= Associative property

**(iii)** 4/5 × (3/- 8 + – 4/7) = 4/5 × 3/- 8 + 4/5 × – 4/7

= Distributive property.

**(iv)** – 7/5 × 5/ – 7 = 1

= Inverse existence.

**(v)** 8/ – 9 × 1 = 1 × 8/- 9 = 8/- 9

= Existence of identity.

**Question no – (11) **

**Solution : **

**(i)** The product of two positive rational numbers is always __Positive.__

**(ii)** The product of two negative rational numbers is always __Positive.__

**(iii)** If two rational numbers have opposite signs then their product is always __Negative.__

**(iv)** The reciprocal of a positive rational number is ** Positive** and the reciprocal of a negative rational number is

__Negative.__**(v)** Rational number 0 has ** No** reciprocal.

**(vi)** The product of a rational number and its reciprocal is __1.__

**(vii)** The numbers ** 1 and -1 **are their own reciprocals.

**(viii)** If m is reciprocal of n, then the reciprocal of n is __‘m’.__

**Rational Numbers Exercise 1(D) Solution :**

**Question no – (1) **

**Solution : **

**(i) 1 ÷ 1/3**

= 1 × 3

= 3

**(ii) 3 ÷ 3/5**

= 3 × 5/3

= 5

**(iii) -5/12 ÷ 1/16**

= – 5/12 × 16

= – 20/3

**(iv) -21/16 ÷ (-7/8)**

= – 21/16 × 8/-7

= 3/2

**(v) 0 ÷ (-4/7)**

= 0 × (-7/4)

= 0

**(vi) 8/-5 ÷ 24/25**

= 8/- 5 × 25/24

= – 5/3

**(vii) -3/4 ÷ (-9)**

= -3/4 × 1/- 9

= 1/12

**(viii) 3/4 ÷ (-5/12)**

= 3/4 × – 12/5

= -9/5

**(ix) -5 ÷ (-10/11)**

= -5 × – 11/10

= 11/2

**(x) -7/11 ÷ (-3/44)**

= -7/11 × 44/-3

= 28/3

= 9 1/3

**Question no – (2)**

**Solution : **

**(i)** Given, 3 by 1/3

= 3 ÷ 1/3

= 3 × 3

= 9

**(ii) -2 by (-1/2)**

= -2 ÷ (-1/2)

= -2 × (-2)

= 4

**(iii) 0 by 7/-9**

= 0 ÷ (7/-9)

= 0 × (-9/70

= 0

**(iv) -5/8 by 1/4**

= -5/8 ÷ 1/4

= -5/8 × 4

= -5/2

**(v) -3/4 by -9/16**

= -3/4 ÷ – 9/16

= -3/4 × 16/- 9

= 4/3

= 1 1/3

**Question no – (3) **

**Solution : **

As per the question,

Product of two rational numbers = -2.

One number = 4/7

Other number = ?

**∴** The other number,

= -2 ÷ 4/7

= -2 × 7/4

= -7/2

Therefore, the other number will be -7/2.

**Question no – (4) **

**Solution : **

According to the given question,

Product of two rational numbers = -4/9

One number = -2/27

Other number = ?

**∴** The other number,

= -4/9 ÷ (-2/27)

= -4/9 × 27/-2

= 64

Therefore, the other number will be 6.

**Question no – (5) **

**Solution : **

**(i)** Given in the question,

m = 5/3,

n = ?

Here, m × n = -25/9

= 5/3 × n = -25/9

= n = -25/9 × 5/3

= -5/3

Hence, n is -5/3

**(ii)** Given in the question,

n = -10/9,

m = ?

Here, m × -10/9 = -25/9

= m = -25/9 × 9/-10

= -5/2

Therefore, m is -5/2

**Question no – (6) **

**Solution : **

The required number,

= – 9/16 ÷ (-3/4)

= – 9/16 × (-4/3)

= 3/4

Thus, 3/4 must be multiplied.

**Question no – (7) **

**Solution : **

The required number,

= 16 ÷ (- 8/13)

= 16 × 13/- 8

= -26

Hence, -26 should be multiplied to get 16.

**Question no – (8) **

**Solution : **

As per the question we know,

3 1/2 litres milk costs = Rs 49,

One litres of milk cost = ?

First, 3 1/2 litres = 7/2 litres

**∴** Now the cost of 1 litres milk,

= 49 ÷ 7/2

= 49 × 2/7

= 14 Rs.

Therefore, the cost of one litres of milk will be Rs. 14.

**Question no – (9) **

**Solution : **

According to the given question,

Cost of 3 2/5 metre of cloth = Rs. 88 1/2

cost of 1 metre of cloth = ?

First, 3 2/5 m = 17/5 m.

**∴** Now the cost of 1 m cloth,

= 177/2 ÷ 17/5

= 177/2 × 5/17

= 885/34

= 26 1/34 Rs.

Therefore, the cost of 1 metre of cloth will be Rs. 26 1/34.

**Question no – (10) **

**Solution : **

[3/7 + (-5/14)] ÷ -1/2…(according to the question)

= (3/7 – 5/14) ÷ -1/2

= 6 – 5/14 ÷ -1/2

= 1/14 × -2

= -1/7

**Question no – (11)**

**Solution : **

**(i)** As per the question the value of,

m = 2/3

n = 3/2

(m + n) ÷ (m – n)

**∴** (2/3 + 3/2) ÷ (2/3 -3/2)

= 4 + 9/6 ÷ 4 – 9/6

= 19/6 ÷ -5/6

= 13/6 × 6/-5

= 13/-5

**(ii)** As per the question the value of,

m = 3/4

n = 4/3

(m + n) ÷ (m – n)

**∴** (3/4 + 4/3) ÷ (3/4 – 4/3)

= 9 + 16/12 ÷ 9 -16/12

= 25/12 × -12/7

= -25/7

**(iii)** As per the question the value of,

m = 4/5

n = -3/10

(m + n) ÷ (m – n)

**∴** (4/5 + -3/10) ÷ (4/5 – -3/10)

= 4/5 – 3/10) ÷ (4/5 + 3/10)

= 8 – 3/10 ÷ 8 + 3/10

= 5/10 × 10/11

= 5/11

**Question no – (12) **

**Solution :**

Given in the question,

Product of two rational numbers = -5

One numbers = -7/15

Other number = ?

Let, number x,

**∴** – 7/15 × x = -5

= x = – 5 × 15/-7

= 75/7

Therefore, other number will be 75/7

**Question no – (13) **

**Solution : **

1st, Sum of (5/8 + – 11/12)

= 5/8 – 11/12

= 15 – 22/24

= – 7/24

**2nd, Difference,**

= (3/7 – 5/14)

= 6 – 5/14

= 1/14

**3rd Divide,**

= – 7/24 ÷ 1/14

= – 7/24 × 14

= – 49/12

= – 4 1/12…(answer)

**Rational Numbers Exercise 1(E) Solution :**

**Question no – (1)**

**Solution : **

Given numbers are, 3/4, 7/4, -3/4 and -7/4

**Now, on number line,**

**Question no – (3)**

**Solution : **

**(i) The rational number between 7 and 8**

= 7 + 8/2

= 15/2

= 7.5

**(ii) The rational number between 3.5 and 5**

= 3.5 + 5/2

= 8.5/2

= 4.25

**(iii) The rational number between 2 and 3.2**

= 2 + 3.2/2

= 5.2/2

= 2.6

**(iv) The rational number between 4.2 and 3.6**

= 4.2 + 3.6/2

= 7.8/2

= 3.9

**(v) The rational number between 1/2 and 2**

= 1/2 + 2/2

= 1 + 4/2/2

= 5/2 × 1/2

= 1.25

**Question no – (4) **

**Solution : **

**(i) 6 and 7**

**∴ **6, 6 + 7/2

= 13/2

= 6 : 5

**∴** 6, 6.5, 7

= 6, 6 + 6.5/2 , 7

= 6, 6.25, 6.5, 7

**∴** The numbers are 6.25 and 6.5

**(ii) 4.8 and 6**

Now, 4.8, 4.8 + 6/2, 6

= 4.8, 5.4, 6

= 4.8, 5.1, 5.4, 6

**∴** The numbers is, 5.1 and 5.4

**(iii) 2.7 and 6.3**

**∴** 2.7, 2.7 + 6.3/2, 6.3

= 2.7, 4.5, 6.3

= 2.7, 4.5, 4.5 + 6.3/2, 6.3

= 2.7, 4.5, 5.4, 6.3

**∴** The numbers are, 4.5 and 5.4

**Question no – (5) **

**Solution : **

**(i)** Given numbers, 3 and 4

= 3, 5+4/2, 4

= 3, 3.5, 4

= 3, 3+3.5/2, 3.5, 4

= 3, 3.25, 3.5, 4

= 3, 3.25, 9.5, 3.75, 4

= 3, 3.25, 3.5, 3.75, 4

**∴** Required numbers are, 3.25, 3.5 and 3.75

**(ii)** Given numbers,10 and 12

**∴** 10, 10+12/2, 12

= 10, 11, 12

= 10, 10+11/2, 11, 12

= 10, 10.5, 11, 11 + 12/2, 12

= 10, 10.5, 11, 11.5, 12

**∴** Required numbers are 10.5, 11 and 11.5

**Question no – (6) **

**Solution :**

Lcm of 5, 3, =15

= 3/5 = 3 × 3/5 × 3

= 9/15

= 2/3 = 2 × 5/3 × 5

= 10/15

Now, 5 + 1 = 6

**∴** 9/15 = 9 × 6/15 × 6 = 54/90

10/15 = 10 × 6/15 × 6 = 60/90.

**∴** The numbers between 3/5 and 2/3 are 55/90, 56/90, 57/90, 58/90, 59/90

**Question no – (7) **

**Solution : **

L.C.M of, 6, 9 = 18

5/6 = 5 × 3/6 × 3

= 15/18

8/9 = 8 × 2/9 × 2

= 16/18

Now, 6 + 1 = 7

15/18 = 15 × 7/18 × 7 = 105/126

16/18 = 16 × 7/18 × 7 = 112/126

**∴** Required numbers are 106/126, 107/126, 108/126, 109/126, and 110/126.

**Question no – (8) **

**Solution : **

For find 7 rational numbers, we multiply by 8/8

2 = 2 × 8/8 = 16/8

And, 3 = 3 × 8/8 = 24/8.

**∴** 7 rational numbers are 17/8, 18/8, 19/8, 20/8, 21/8, 22/8, and 23/8

**Next Chapter Solution : **

👉 Chapter 2 👈