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**Frank ICSE Mathematics Class 8 Solutions Chapter 1 Rational Numbers**

Welcome to NCTB Solutions. Here with this post we are going to help 8th class students for the Solutions of Frank ICSE Mathematics Class 8 Math Book, Chapter 1, Rational Numbers. Here students can easily find step by step solutions of all the problems for Rational Numbers, Exercise 1.1, 1.2, 1.3 and 1.4 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 latest Syllabus.

**Rational Numbers Exercise 1.1 Solution :**

**Question no – (1)**

**Solution :**

**(a)** -11/16 __ 13/- 16

= – 11/16 > 13/- 16

**(b)** -9/-13 __ 36/52

= -9/-13 = 36/52

**(c)** 5/8 __ – 9/14

= 5/8 > -9/14

**(d)** 7/-13 __ -8/15

= 7/- 13 < – 8/15

**Question no – (2) **

**Solution :**

**(a)** In the given question,

= 3/8, 5/-12, -7/16, -13/18, 11/24

Now in ascending order.

= -13/118, 11/- 24, – 7/16, 5/-12, – 3/8

**(b)** In the question,

= 9/25, 2/5, 14/-75, – 19/10, 8/15

Now, in ascending order,

= -19/10, 14/75, 9/25, 2/5, 8/15

**Question no – (3) **

**Solution :**

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

= 7/8, 11/12, 15/-16, 1/4, 14/-15

Now in descending order,

= 11/12, 7/8, 1/4, 14/-15, 15/-16

**(b)** In the given question,

= -5/6, -3, -13/-4, 17/-6, -11/1, -13/9

Now, in the descending order,

= – 5/6, – 11/12, -13/9, 17/-6, -3

**Question no – (4) **

**Solution :**

**(a) -5/13 + 12/13**

= -5/13 + 12/13

= -5 + 12/13

= 7/13 …(simplified)

**(b) -8/15 + -/15**

= -8/15 + – 7/15

= – 8 – 7/15

= – 15/15

= – 1 …(simplified)

**(c) 21/25 – 16/25 + 7/25**

= 21/25 – 16/25 + 7/25

= 21 – 16 + 7/25

= 12/25 …(simplified)

**(d) 5/12 – 7/36**

= 5/12 – 7/36

= (5 × 3) – 7/36

= 15 – 7/36

= 8/36

= 2/9 …(simplified)

**(e) – 8/17 + – 4/51**

= – 8/17 + – 4/51

= (- 8) × 3 (- 4)/51

= – 24 – 4/51

= – 28/51 …(simplified)

**(f) – 5/16 + 7/24 – 13/48**

= – 5/16 + 7/24 – 13/48

= (- 5) × 3 + (7 × 2) – 13/48

= 15 + 14 – 13/48

= – 14/48

= – 7/24 …(simplified)

**Question no – (5) **

**Solution :**

**(a) – 11/9 × – 81/88**

= – 11/9 × – 81/88

= 9/8 …(Simplified)

**(b) 8/-9 × 16/-7**

= 8/- 9 × 16/-7

= 128/63 …(Simplified)

**(c) 6/7 × – 49/36**

= – 7/6

**(d) – 5/9 × 49/56 × – 72/35**

= 1

**(e) – 13/9 ÷ 26/27**

= – 3/2

**(f) – 25/7 ÷ 15/14**

= – 25/7 × 14/15

= – 10/3 …(Simplified)

**Question no – (6) **

**Solution :**

**(a)** All whole numbers are rational numbers → **True**

**(b)** All rational numbers are integers. → **False**

**(c)** The rational number -8/5 is in standard from. → **True**

**(d)** Integers satisfy the closure property for subtraction. → **True**

**Question no – (7) **

**Solution :**

**(a) -165/187 =** ___/-** 34**

= – 165/187

= – 15/17

= 30/- 34

**(b) 248/- 280 =** ____**/105**

= 248/- 280

= – 31/35

= – 93/105

**(c) 275/- 330 = – 10/**____

= 275/- 330

= – 5/6

= – 10/12

**(d) -192/256 = 9/**____

= – 192/256

= – 3/4

= 9/-12

**Rational Numbers Exercise 1.2 Solution :**

**Question no – (1) **

**Solution :**

**(a)** 11/15, – 11/15

= Yes, they are additive inverse of each other.

**(b)** – 18/21, 17/21

= Yes, they are additive inverse of each other.

**(c)** 8/-9, 8/9 /17

= Yes, they are additive inverse of each other.

**(d)** – 25/- 52, 25/52

= No, they are not additive inverse of each other.

**Question no – (2) **

**Solution :**

**(a)** 12/17, -17/-12

= Yes, they are reciprocals.

**(b)** -13/27, 27/13

= No, they are not reciprocals.

**(c)** 1/9, 9/-1

= No, they are not reciprocals.

**(d)** -1 3/5, 5/8

= No, they are not reciprocals.

**Question no – (3)**

**Solution :**

The multiplicative inverse of -3/5 × – 8/11 is -55/24

**Question no – (4) **

**Solution :**

**(a)** 5/8 × [3/4 + 7/11] = [5/8 × 3/4] + [5/8 × 7/11]

= Distributive property over addition

**(b)** (- 11/15 × 5/6) × 3 = 11/15 × (5/6 × 3)

= Associative property

**(c)** 12/- 23 × – 23/12 = 11

= Multiplicative identity

**(d)** – 9/17 × 1 = 1 × -9/17 = – 9/17

= Multiplicative identity

**(e)** 6/7 × – 8/9 = – 8/9 × 6/7

= Commutative property

**Question no – (5) **

**Solution :**

**(a) -7/12 + 13/15**

= (-7 × 5) + (13 × 4)/60

= -35 + 52/60

= -7/60 …(Simplified)

**(b) -5/8 + 8/9 + – 11/12**

= (5 × 9) + (8 × 8) + (- 11 × 6)/72

= -40 + 64 – 66/72

= -42/72

= -7/12 …(Simplified)

**(c) (-8/15 + – 13/20) × – 5/6**

= {(-8 × 4) + (-13 × 3)}/60} × – 5/6

= (32 – 39/60) × – 5/6

= – 71/60 × – 5/6

= 71/72 …(Simplified)

**(d) 3 3/5 × -15/16 × 13/20**

= 18/5 × -15/16 × 13/20

= – 351/160 …(Simplified)

**Question no – (6) **

**Solution :**

**(a) 1/8 + – 5/12 + – 3/16**

= 6 + (- 5 × 4) + (- 3 × 3)/46

= – 23/48

**(b) 11/12 + – 1/3 + – 3/4 + 7/6**

= 11 – 4 – 9 + 14/12

= 12/12

= 1

**(c) 5/12 × – 3/8 × – 4/15**

= 1/24

**(d) – 6/7 × 8/- 25 × 35/- 18**

= – 6/7 × 8/- 25 × 35/- 18

= – 8/15

**(e) – 8/15 × – 25/16 ÷ 35/10**

= 5/6 × 10/35

= 5/21

**(f) 7/10 × – 15/14 ÷ 9/8**

= – 3/4 × 8/9

= – 2/3

**Rational Numbers Exercise 1.3 Solution :**

**Question no – (1)**

**Solution :**

**(a)** A – 4/8, B = 7/8, C = 9/8, D = 12/8

**(b)** A = – 4/5, B = – 1/5, C = 2/5, D = 4/5, E = 7/5

**(c)** A = – 9/7, B = – 5/7, C = – 2/7, D = 3/7, ER = 6/7, F = 9/7

**(d)** A = -9/11, B = – 6/11, C = – 3/11, D = 2/11, E = 5/11, F = 7/11, G = 12/11

**Question no – (2) **

**Solution :**

In the given question,

Given rational numbers are – **(a)** 4/5 **(b)** -2/3 **(c)** -2 3/5 **(d)** 3 1/3

**Now on the number line :**

**Question no – (3) **

**Solution :**

In the question give numbers are

= -3/4, 1/4, 7/4

**Now on the number line : **

**Question no – (4)**

**Solution :**

Five rational numbers between -1 and +1 using the method of arithmetic mean are –

= q1 = 1/2 = (- 1 + 1) = 1/2 (0) = 0

= q2 = 1/2 (0+ 1) = 1/2 (1) = 1/2

= q3 = 1/2 (1/2 + 0) = 1/2 (1/2) = 1/4

**∴** Numbers are 0, 1/4, 1/2

**Question no – (5)**

**Solution :**

= q1 = 1/2 (2 + 3) = 1/2 950 = 5/2

= q2 = 1/2 (2 + 5/2) = 1/2 (9/2) = 9/4

= q3 = 1/2 (2 + 9/4) = 1/2 917/4) = 17/8

= q4 = 1/2 (2 + 17/80 = 1/2 (33/8) = 33/16

= q5 = 1/2 (2 + 33/16) = 1/2 (65/16) = 65/32

**∴** Numbers are = 65/32, 33/16, 17/8, 9/4, 5/2

**Question no – (6)**

**Solution :**

**(a)** = q1 = 1/2 (1/2 + 2/3) = 1/2 (7/6) = 7/12

= q2 = 1/2 (1/2 + 7/12) = 1/2 913/12) = 13/224

= q3 = 1/2 (1/2 + 13/24) = 1/2 (25/24) = 25/48

**(b)** = – 3/4 = – 3 × 50/4 × 50 = – 150/200,

= – 4/5 = – 4 × 40/5 × 40 = – 160/200

**∴ **Numbers = – 151/200, – 152/200, – 153/200

**(c)** = 2/7 = 2 × 2/7 × 2 = 4/14

= 2 = 2 × 14/1 × 14 = 28/14

**∴** Numbers = 5/14, 8/14, 20/14

**(d)** = – 3 = – 3 × 5/1 × 5 = – 15/5, – 7/5

**∴** Numbers are = – 8/5, – 9/5, – 10/5

**Rational Numbers Exercise 1.4 Solution :**

**Question no – (1)**

**Solution :**

According to the question,

The product two rational numbers is = -8/9.

One of them is = 10/3

The other number = ?

Now, The other number,

= – 8/9 ÷ 10/3

= – 8/9 × 3/10

= – 4/15

Therefore, the other number will be – 4/15

**Question no – (2)**

**Solution :**

= (2/9 + 4/9) = 14 + 36/63 = 50/63

= (2/9 – 4/7) = 14 – 36/63 = -22/62

= 50/63 × – 63/22

= – 25/11

**Question no – (3)**

**Solution :**

In the question given,

= -9/14 and 11/8

**∴** Required number,

= (- 9/14 – 11/18)

= – 81 – 77/+ 126

= 158/126

Therefore, the required number will be 158/126

**Question no – (4)**

**Solution :**

= 5/9 + – 8/7

= 35 – 72/63

= – 37/63

= 7/8 × 3/8

= 21/40

**∴** – 37/63 × 40/21

= – 1480/1323

**Question no – (5)**

**Solution :**

According to the question,

The sum of two rational numbers is 8/25.

One of them is 3/16,

The other number.

Step by Step solution :

**∴** The other number,

= (8/25 – 3/10)

= 128 – 75/400

= 53/400

Therefore, the other number will be 53/400

**Next Chapter Solution : **

Chapter 2 | Chapter 3 | Chapter 4 | Chapter 5 | Chapter 6 | Chapter 7 |

Chapter 8 | Chapter 9 | Chapter 10 | Chapter 11 | Chapter 12 | Chapter 13 |

Chapter 14 | Chapter 15 | Chapter 16 | Chapter 17 | Chapter 18 | Chapter 19 |