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**Maths Wiz 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 Maths Wiz 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 1A, 1B, 1C, 1D, 1E and 1F 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 1A Solution :**

**Question no – (1) **

**Solution : **

**(a) 2/9 **

**∴** Four rational numbers equivalent to

= 2/9

= 4/18

= 8/36

= 6/27

**(b) – 3/5**

**∴** Four rational numbers equivalent to

= – 3/5

= – 6/10

= – 9/15

= – 12/20

**(c) 7/- 11**

**∴** Four rational numbers equivalent to

= 7/- 11

= 14/- 22

= 21/- 33

= 28/- 44

**(d) – 6/– 13**

**∴** Four rational numbers equivalent to

= – 6/- 13

= 12/26

= – 12/- 26

= – 18/- 39

**Question no – (2) **

**Solution : **

**15/20** in standard form

= 3/4

**64/72** in standard form

= 8/9

**– 54/-63** in standard form

= 6/7

**88/-99** in standard form

= 8/- 9

–**87/156** in standard form

= – 29/52

**Question no – (3) **

**Solution : **

**17/24**

= |17/24|

= 17/24

**∴** The absolute value of 17/24 is **17/24**

**– 6/35**

= |-6/35|

= 6/35

**∴** The absolute value of -6/35 is **6/35**

**– 11/- 17**

= |-11/-17|

= 11/17

**∴** The absolute value of -11/- 17 is **11/17**

**0**

= 101

= 0

**∴** The absolute value of 0 is **0**

**28/- 45**

= |-28/45|

= 0

**∴ **The absolute value of 28/- 45 is **0**

**Question no – (5) **

**Solution : **

**(a)** – 1 ___ – 1/2

= – 1 < – 1/2

**(b)** 1 _____ – 2

= 1 > – 2

**(c)** 0 ____ – 3

= 0 > – 3

**(d)** – 5 ______ – 4

= – 5 < – 4

**(e)** 3 3/4 _____ 1 2/5

= 3 3/4 > 1 2/5

**(f)** – 4 ______ 4 2/3

= – 4 < 4 2/3

**(g)** – 3 4/5 ______ – 4

= – 3 4/5 > – 4

**(h)** – 1/2 ______ – 1 5/6

= – 1/2 > – 1 5/6

**Question no – (6) **

**Solution : **

**(a)** 15/19, – 15/- 19

= Equivalent

**(b)** 28/- 49, – 4/7

= Equivalent

**(c)** 16/17, 26/27

= Not Equivalent

**(d)** 27/99, 51/187

= Not Equivalent

**(e)** 16/20, 4/-5

= Not Equivalent

**Question no – (7) **

**Solution : **

**(a)** – 8/15 ______ – 7/30

= – 8/15 < – 7/30

**(b)** – 1/5 _____ – 1/4

= – 1/5 > – 1/4

**(c)** 3/10 ______ 5/12

= 3/10 < 5/12

**(d)** 5/6 _____ 15/18

= 5/6 = 15/18

**(e)** 1/- 25 _____ 1/50

= 1 – 25 < 1/50

**(f)** 17/40 _____ 0.519

= 17/40 < 0.519

**(g)** – 8.9 _____ – 8 1/4

= – 8.9 < – 8 1/4

**(h)** – 1/8 ____ 4/- 32

= – 1/8 = 4/- 32

**(i)** 18/- 19 ____ – 10/11

= 18/- 19 < – 10/11

**(j)** – 16 _______ 17/- 21

= – 16/25 > 17/- 21

**(k)** – 5/3 ____ 40/27

= – 5/3 < 40/27

**(l)** 15/- 16 _____ – 9/10

= – 15/16 < – 9/10

**Question no – (8) **

**Solution : **

**(a)** Given numbers, – 1/4, 1/2, 7/8, 15/16, – 9/40

Now in ascending order,

= – 0.25, 0.5, 0.875, 0.93, – 0.225

**∴** – 0.25 < 0.225 < 0.5 < 0.873 < 0.93

**(b)** Given numbers, 5/7, – 7/25, 9/- 4, – 6/5, 8/11

= 0.71, – 0.28, – 2.25 – 1.2, 0,72

**∴** – 2.25 < – 1.2 < 0.28 < 0.71 < 0.72

**Question no – (9) **

**Solution : **

**(a)** Given numbers, -1 5/8, 1 11/12, – 1 11/16, 17/9, – 1 5/6

= – 1.625, 1.91, – 1.68, 1.88, – 1.83

∴ 1.91 > 1.88 > – 1.625 > 1.68 > 1.83

**(b)** Given numbers, -7/16, – 1/4, 1/8, 9/32, 18/25

= – 0.43, 0.25 > 0.125 > 1.28 > 0.72

∴ 0.72 > 0.28 > 0.125 > 0.25 > 0.43

**Rational Numbers Exercise 1B Solution :**

**Question no – (1) **

**Solution : **

**(a) 7/20 + 11/20**

= 7/20 + 11/20

= 7 + 11/20

= 18/20

= 9/10

**(b) 1/12 + 7/12**

= 1/12 + 7/12

= 1 + 7/12

= 8/12

= 4/6

= 2/3

**(c) 3/10 – 7/10**

= 3 – 7/10

= – 4/10

= -2/5

**(d) – 5 2/7 – 3 3/7**

= – 37/7 – 24/7

= – 37-24 / 7

= – 63/7

= -8 5/7

**(e) 112/13 + – 229/13**

= 112/13 + – 229/13

= 112-229/13

= 117/13

= -9

**(f) – 243/58 + 719/58 + 273/- 58**

= – 243/58 + 719/58 + 273/- 58

= + 243 – 719 – 273/58

= – 749/58

= – 203/58

= 3 1/2

**(g) – 8 4/5 – 3/5**

= – 8 4/5 – 3/5

= – 44/5 – 3/5

= – 44 – 3/5

= – 47/5

= -9 2/5

**Question no – (2) **

**Solution : **

**(a) 5/7 + – 3/8**

= 5/7 + – 3/8

= 40 – 21/56

= 19/56

**(b) 7/18 – 5/6**

= 7/18 – 5/6

= 14-30/36

= -16/36

= -4/9

**(c) 3/8 – 5/32**

= 3/8 – 5/32

= 12 – 5/32

= 7/32

**(d) 7/- 9 + 1/- 6**

= 7/-9 + 1/-6

= – 14 – 3/18

= – 17/18

**(e) 5 4/5 + (- 3 2/7)**

= 5 4/5 + (- 3 2/7)

= 29/5 – 23/7

= 203 – 105/35

= 98/35

= 2 18/35

**(f) 9 – 11 4/7**

= 9 – 11 4/7

= 9 – 81/7

= 63 – 81/7

= – 18/7

= – 2 4/7

**(g) – 8 4/11 – (- 9)**

= – 8 4/11 – (-9)

= – 92/11 + 9

= – 92 + 99/11

= 7/11

**Question no – (3) **

**Solution : **

Given, 3/4 – 5/7 + 9/14

= 21 – 20 + 18/28

= 19/28 …(Simplified)

**Question no – (4) **

**Solution : **

Given, 5 7/9 – 1 1/10 – 7 11/15

= 52/9 – 11/10 – 116/15

= 520 – 99 – 696/90

= – 275/90 **…(Simplified)**

**Rational Numbers Exercise 1C Solution :**

**Question no – (1) **

**Solution : **

**(a) – 3/4 × (- 8/9)**

= 3/4 × 8/9

= 2/3

**(b) 7/20 × (- 5/14)**

= – 7/20 × 5/14

= – 1/8

**(c) – 24/49 × 35/36**

= – 24/49 × 35/36

= – 10/21

**(d) 17/30 × 45/51**

= 17/30 × 45/51

= 3/6

**Question no – (2) **

**Solution : **

**(a) 6 × 1 2/3**

= 6 × 5/3

= 10

**(b) – 18 × (- 4 5/9)**

= 18 × 41/9

= 82

**(c) 2 1/9 × – 7/38**

= 20/9 × 7/38

= – 70/171

**Question no – (3) **

**Solution : **

Given, 25/4 × (- 8/9) × (- 3 9/11) × (22/- 35)

= (25/4) × (- 8/9) × (- 3 9/11) × (22/- 35)

= – 25/4 × 8/9 × 42/11 × 22/35

= – 120/9

**Question no – (4) **

**Solution :**

**(a) 44/65 ÷ 11/13**

= 44/65 × 11/13

= 4/5

**(b) – 8/17 ÷ 24/-51**

= – 8/17 × 51/24

= + 1

**(c) – 2/25 ÷ 4/35**

= – 2/25 ÷ 4/35

= – 2/25 × 35/4

= – 3/5

**(d) 115 ÷ -23/5**

= 115 × 5/- 23

= – 25

**Question no – (5) **

**Solution : **

**(a) – 1 11/14 ÷ (- 1 7/18)**

= -25/14 × -18/25

= 9/7

**(b) 6 1/3 ÷ (- 2 5/6)**

= 19/3 × 6/17

= 38/17

**(c) – 5 1/4 ÷ 7**

= – 21/4 × 1/7

= – 3/4

**(d) 1 1/12 ÷ 2 5/17**

= 13/12 × 17/39

= 17/36

**Question no – (6) **

**Solution : **

Given, (4/9 ÷ 4/7) × 1 2/7

= 4/9 × 7/4 × 9/7

= 1 …(Simplified)

**Question no – (7) **

**Solution : **

Given, [5 1/2 × (- 1 5/6)] ÷ 2 3/4

= – 11/2 × 11/5 × 4/11

= 22/5 …(Simplified)

**Question no – (8) **

**Solution : **

Given, (- 8/5 ÷ 12) × (- 5/6 ÷ (- 2)

= – 8/5 × 1/12 × (- 5/6 × 1/2)

= – 2/15 × 5/6 × 1/2

= – 1/8 …(Simplified)

**Rational Numbers Exercise 1D Solution :**

**Question no – (1) **

**Solution : **

**(a)** – 7/8 × 11/15 = 11/15 × – 7/8

Property Used : = **Multiplication of associative**

**(b)** 6/7 × 7/6 = 1

Property Used : = **Property of** one

**(c)** – 1/8 + 1/8 = 0

Property Used : = **Addition**

**(d)** – 21/29 + 6/19 = 6/19 + (- 21/29)

Property Used : = **Commutativity property**

**(e)** – 23/70 × 1 = – 23/70

Property Used : = **Property** of **one**

**(f)** 5/8 (1/2 – 1/3) = 5/8 × 1/2 × – 5/8 × 1/3

Property Used : = **Distributivity Property**

**(g)** (1/2 × 1/3) × 1/5 = 1/2 × (1/3 × 1/5)

Property Used : = **Distributivity Properly**

**(h)** (1/2 × 1/3) × 1/5 = 1/2 × (1/3 × 1/5)

Property Used : = **Distributivity property**

**Question no – (2) **

**Solution : **

**(a)** 17/135 × 15/- 51 = 15/- 51 × 17/135

Property Used = **Commutativity Property**

**(b)** 1/9 (18/5 + – 3/20) = 1/9 × 18/5 + 1/9 × (- 3/20)

Property Used = **Distributivity Property**

**(c)** (- 1/2 + 3/7) + (- 4/3) = – 1/2 + [3/7 + (- 4/3)]

Property Used = **Associativity Property**

**(d)** (5/3 × – 4/5) × 3/5 = 5/3 × [(- 4/5) × 3/5]

Property Used = **Closure Property**

**(e)** – 19/20 × 1 = 1 × (- 19/20) = – 19/20

Property Used = **Proper of one**

**(f)** – 17/24 × 24/- 17 = 1

Property Used = **Property of one**

**(g)** – 2/3 + 0 = 0 + (- 2/3) = 2/3

Property Used = **Property of zero**

**(h)** 1/7 + 0 = 0 + 1/7 = 1/7

Property Used = **Property of zero**

**Question no – (3) **

**Solution : **

As per the question,

a = 4/7,

b = – 5/2

c = 4/3,

We have to prove, a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c,

**∴**** a ÷ (b ÷ c)**

= 4/7 ÷ (- 5/2 ÷ 4/3)

= 4/7 ÷ (- 5/2 × 3/4)

= 4/7 × 8/15

= 32/105

**∴**** (a ÷ b) ÷ c**

= (4/7 ÷ (- 5/2)) ÷ 4/3

= (- 4/7 × 2/5) ÷ 4/3

= 8/35 × 3/4

= – 6/35

Therefore, a ÷ (b ÷ c) **≠** (a ÷ b) ÷ c **…(Proved)**

**Question no – (4) **

**Solution : **

As per give question, (8/15 × (-7/18)) + (8/15 × – 11/18)

= (8/15 × (-7/18)) + (8/15 × – 11/18)

= 8/15 ( – 7/18 – 11/18)

= 8/15 (- 7 – 11/18)

= 8/15 × – 18/18

= – 8/15

**Question no – (5) **

**Solution : **

**(a)** Given number, **5/16**

= The Additive inverse of 5/16 is -5/16

**(b) -15/-16**

= The Additive inverse of -15/-16 is -15/16

**(c)** **-8/19**

= The Additive inverse of -8/19 is +8/19

**(d) 20/-23**

= The Additive inverse of 20/-23 is 20/23

**Question no – (6) **

**Solution : **

**(a) -7**

= -1/7

**∴** Multiplicative inverse of -7 is -1/7

**(b)** 10

= 1/10

**∴** Multiplicative inverse of 10 is 1/10

**(c) 17/41**

= 41/17

**∴** Multiplicative inverse of 17/41 is 41/17

**(d) 28/- 59**

= -23/28

**∴** Multiplicative inverse of 28/- 23 is -23/28

(e) -29/- 36

**∴** Multiplicative inverse of -29/- 36 is -36/-29

**(f) ****(1/3 -1/4) × (- 2)**

= (1/3 -1/4) (- 2)

= 4 -3/12 × (- 2)

= -1/6

= -6

**∴** Multiplicative inverse is -6

**(g) 5/8 ÷ (15/16 × -3/2)**

= -5/8 × 32/5 × 3

= -4/3

**∴** Multiplicative Inverse is -3/4

**(h) 16 ÷ (- 32)**

= -16 × 1/32

= -2

**∴ **Multiplicative inverse is -1/2

**Rational Numbers Exercise 1E Solution :**

**Question no – (1)**

**Solution : **

**(a) 6 and 8**

= 6 + 8/2

= 7

**∴** The rational number between 6 and 8 is** 7**

**(b) -3 and 9**

= -3 + 9/2

= 3

**∴** The one rational number between -3 and 9 is** 3**

**(c) 1/3 and 1/4**

= 1/3 + 1/4 /2

= 7/12/2

= 7/12 × 1/2

= 7/14

= 1/2

**∴** The one rational number between 1/3 and 1/4 is** 1/2**

**(d) – 1/8 and 3/16**

= – 1/8 + 3/16/2

= -2 + 3/16/2

= 1/16 × 1/2

= 1/32

**∴** The one rational number between – 1/8 and 3/16 is** 1/32**

**Question no – (2) **

**Solution : **

**(a) 4 and 7**

= gap = 7 – 4

= 3

**∴** Two rational numbers are 5.3/3 and 5.3/4

= 5, 15/4

**∴** The two rational number between 4 and 7 are **5; 15/4**

**(b) – 1 and 6**

= Gap = 1 – 6

= – 7

Two rational numbers -1 – 7/3

= 7/3 and – 1 – 7/4

= 7/4

**∴** The two rational number between – 1 and 6 are **7/3; 7/4 **

**(c) 1/2 and 7/8**

Gap = 7/8 -1/2

= 7 – 4/8

= 3/8

Rational numbers. -1/2.3/8 × 1/3

= – 1/16 and – 1/2 × 3/8 × 1/4

= – 3/64

**∴** The two rational number between 1/2 and 7/8 are **-1/16, -3/64**

**Question no – (3) **

**Solution : **

**(a) – 7 and – 3**

Gap between number,

= – 7 (-3)

= – 7 + 3

= 4

Rational numbers, – 4/4

= – 1, – 2. 4/4

= – 2, – 3

**∴** The three rational number between -7 and -3 are **-1, -2, -3**

**(b) – 2/7 and 6/7**

Gap between number,

= 6/7 + 2/7

= 8/7

we have 8/7 × 4

= 2/7

Rational numbers, 1. 2/7

= 2/7, 2.2/7

= 4/7, 2 2/7

= 6/7

**∴** The three rational number between -2/7 and 6/7 are** 2/7, 4/7, 6/7 **

**(c) 3/8 and 5/12**

= 5/12 – 3/8

= 10 – 9/24

= 1/24

we have 1/24 × 4

= 1

Rational numbers, 1/96, 2.1/24 × 4

= 1/48, 3 × 1/24 × 4

= 1/32

**∴** The three rational number between 3/8 and 5/12 are** 1, 1/48, 1/32**

**Question no – (4) **

**Solution :**

**(a) – 3 and – 8**

Gap between numbers,

= – 3 (- 8)

= – 3 + 8

= 5

We have = 5/6

The rational numbers numbers are,

3 × 5/6 . 1/2 = – 15/12,

-3. 5/18 = 15/18,

-3.5/24 = – 15/24

-3 × 5/30 = – 15/30

**∴** The five rational number between -3 and -8 are **5/6, -15/12, 15/18, 15/24, and -15/30**

**Rational Numbers Exercise 1E Solution :**

**Question no – (1) **

**Solution : **

As per the question,

A group of friends hike = 5 3/4 km,

Stops for lunch and hike = 3 1/5 km.

**∴**** They total hike, **

= 5 3/4 + 3 1/5

= 23/4 + 16/5

= 115 + 64/20

= 179/20 km

Hence, they hike 179/20 km.

**Question no – (2) **

**Solution : **

According to the question,

Ms Joshi walks her dog each day = 4/5 km

Total distance Ms Joshi walks her dog in 6 days = ?

**∴**** Total distance by Joshi**

= 6 × 4/5

= 24/5 km

Therefore, distance Ms Joshi walks her dog in 6 days will be 24/5 km.

**Question no – (3) **

**Solution : **

As per the given question,

Priya completes painting each day = 1/20

She complete in 5 days = ?

**∴ Priya complete her painting in 5 days**

= 1/20 × 5

= 1/4

Hence, in 5 days Priya complete 1/4 of her painting.

**Question no – (4) **

**Solution :**

**Oxygen Left in tank,**

= 219 2/3 – 32 1/3

= 659 – 97/3

= 562/3

**Unused space in tank,**

= 245 3/8 – 562/3

= 245 × 9 – 4496/24

= 5889 – 4496/24

= 1393/24L

Therefore, 1393/24L space in the tank is unused.

**Question no – (5) **

**Solution :**

Water tank Thickness = 25/32 …(as per the question)

**∴**** Outer circle diameter, **

= + 25/32 + 25/32

= 50/32

**∴**** Inner circle diameter, **

= 3.5 – 50/32

= 1120 – 500/320

= 620/320

= 31/16

Hence, the inside diameter of the pipe will be 31/16

**Question no – (6) **

**Solution :**

First, Perimeter of rectangle,

= 2 (12 – 1/2 + 5 1/5)

= 2 (25/2 + 26/5)

= 2 × 125 + 52/10

= 177/5

Now, Area of rectangle,

= 12 1/2 × 5 1/5

= 25/2 × 25/5

= 65 m^{2}

**∴ **Area of a square,

= 1 × 1

= 1m^{2}

So, if there is 4 square, then 4 m^{2} area.

Hence, Unused land,

= 65 – 4

= 61 m^{2}

**Question no – (7) **

**Solution : **

Let, the boy has = x Rs

Then he spend = 3/5x

Remained each,

= x – 3/5x

= 2x/5

then again he spend,

= 2x/5 × 1/4, x/10

Remaining Money,

= 2x/5 – x/10

= 4x – 1x/10

then 3x/10 = 15

= x = 150/3

**∴** x = 50

Therefore, at first he had 50 rupees.

**Rational Numbers Exercise 1F Solution :**

**Question no – (1) **

**Solution : **

As per the question,

A group of friends hike = 5 3/4 km,

Stops for lunch and hike = 3 1/5 km.

**∴** They total hike,

= 5 3/4 + 3 1/5

= 23/4 + 16/5

= 115 + 64/20

= 179/20 km

Hence, they hike 179/20 km.

**Question no – (2) **

**Solution : **

According to the question,

Ms Joshi walks her dog each day = 4/5 km

Total distance Ms Joshi walks her dog in 6 days = ?

**∴** Total distance by Joshi

= 6 × 4/5

= 24/5 km

Therefore, distance Ms. Joshi walks her dog in 6 days will be 24/5 km.

**Question no – (3) **

**Solution : **

As per the given question,

Priya completes painting each day = 1/20

She complete in 5 days = ?

**∴** Priya complete her painting in 5 days

= 1/20 × 5

= 1/4

Hence, in 5 days Priya complete 1/4 of her painting.

**Question no – (4) **

**Solution :**

Oxygen Left in tank,

= 219 2/3 – 32 1/3

= 659 – 97/3

= 562/3

Unused space in tank,

= 245 3/8 – 562/3

= 245 × 9 – 4496/24

= 5889 – 4496/24

= 1393/24L

Therefore, 1393/24L space in the tank is unused.

**Question no – (5) **

**Solution :**

Water tank Thickness = 25/32 …(as per the question)

**∴** Outer circle diameter,

= + 25/32 + 25/32

= 50/32

**∴** Inner circle diameter,

= 3.5 – 50/32

= 1120 – 500/320

= 620/320

= 31/16

Hence, the inside diameter of the pipe will be 31/16

**Question no – (6) **

**Solution :**

**First,** Perimeter of rectangle,

= 2 (12 – 1/2 + 5 1/5)

= 2 (25/2 + 26/5)

= 2 × 125 + 52/10

= 177/5

**Now,** Area of rectangle,

= 12 1/2 × 5 1/5

= 25/2 × 25/5

= 65 m^{2}

**∴** Area of a square,

= 1 × 1

= 1m^{2}

So, if there is 4 square, then 4 m^{2} area.

Hence, Unused land,

= 65 – 4

= 61 m^{2}

**Question no – (7) **

**Solution : **

Let, the boy has = x Rs

Then he spend = 3/5x

Remained each,

= x – 3/5x

= 2x/5

then again he spend,

= 2x/5 × 1/4, x/10

Remaining Money,

= 2x/5 – x/10

= 4x – 1x/10

then 3x/10 = 15

= x = 150/3

**∴** x = 50

Therefore, at first he had 50 rupees.

**Next Chapter Solution : **

👉 Chapter 2 👈