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**Frank Learning Maths Class 8 Solutions Chapter 1 Rational Numbers**

Welcome to NCTB Solution. Here with this post we are going to help 8th class students for the Solutions of Frank Learning Maths Class 8 Book, Chapter 1 Rational Numbers. Here students can easily find step by step solutions of all the problems for Rational Numbers. Here students will find solutions for Exercise 1.1, 1.2, and 1.3. Exercise wise proper solutions for every problems. All the problem are solved with easily understandable methods so that all the students can understand easily. Here in this post all Mathematic solutions are based on the CBSE latest curriculum.

**Rational Numbers Exercise 1.1 Solution**

**Question no – (1) **

**Solution : **

**(a)** |-7/24|

= 7/24

**(b)** |7/13 + -9/13|

= |7/13 – 9/13|

= |-2/13|

= 2/13

**(c)** |-16/35| + |-11/21|

= 16/35 + 11/21

= 48 + 55/105

= 103/105

**(d)** |-14/27| – |-3/20|

= 14/27 – 3/20

= 280 – 81/540

= 199/540

**Question no – (2)**

**Solution : **

**(a)** 7/-13 _ 8/15

= 7/-13 < 8/15

= -7 × 15/13 × 15, -8 × 13/15 × 13

= – 105/13 × 15 **<** -104/15 × 13

**(b)** 5/8 _ -9/14

= 5/8 > -9/14

= 5 × 7/8 × 7 -9 × 4/14 × 4

= 35/56 **>** -36/56

**(c)** -11/16 _ 13/-16

= -11/16 > -13/16

**(d)** -9/-13 _ 36/52

= -9/-13 = 36/52

= 9 × 4/13 × 4, 36/52

= 36/52 **=** 36/52

**Question no – (3)**

**Solution :**

**(a)** In Standard form :

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

**(b) **In Standard form :

= -5/6, 3, -13/-4, 17/-6, -21/12, -12/9

**Question no – (4)**

**Solution : **

**(a)** In standard form :

= 7/8, -5/3, -15/16, 1/4, -7/5

**(b)** In standard form :

= -5/6, -3, 13/4, -17/6, -7/4, -4/3

**Question no –** **(5)**

**Solution :**

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

= -5 + 12/13

= 7/13

**(b)** Given, -8/15 + -7/15

= -8/15 + -7/15

= – 8 – 7/15

= 15/15

= – 1

**(c)** Given, 21/25 – 16/15 + 7/25

= 21 – 16 + 7/15

= 12/25

**(d)** Given, 5/12 – 7/36

= 5/12 – 7/36

= 15 – 7/36

= 8/36

= 2/9

**(e)** Given, -8/17 + -4/51

= – 24 ÷ 4/51

= -28/51

**(f)** Given, -5/16 + 7/24 – 13/48

= 15 + 14-13/48

= 147/84

= -7/24

**Question no – (6)**

**Solution :**

**(a)** 8/-9 × 16/-7

= 128/63

**(b)** 6/7 × -49/36

= 6/7 × -49/36

= -7/6

**(c)** -11/9 × -81/88

= -11/9 × -81/88

= 9/8

**(d)** -5/9 × 49/56 × -72/35

= -5/9 × 49/56 × -72/35

= 1

**(e)** -13/9 ÷ 26/27

= – 13/9 × 27/26

= -3/2

**(f)** -25/7 ÷ 15/14

= -25/7 × 14/15

= -10/3

**Question no – (7)**

**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 – (8)**

**Solution : **

**(a)** -5/12 = __25__/60 = 35/__84__

**(b)** -14/63 = __2__/-9 = -18/__81__

**Question no – (9)**

**Solution : **

**(a)** -8/13, 64/-104

= -8/13, 64/-104

= 8/13

**∴ **[Equivalent]

**(b)** -11/15, 33/-60

= -11/15, 33/-60

= 71/20

**∴ **[Not Equivalent]

**(c)** -5/11, -15/-44

= -5/11, -15/-44

**∴ **[Not Equivalent]

**(d)** -5/7, -15/28

= -5/7, -15/28

**∴ **[Not Equivalent]

**Question no – (10)**

**Solution : **

**(a)** -11/8 = 33/-24

**(b)** -12/9 < 12/9

**(c)** 75/125 > 150/-300

**(d)** -8/3 < -12/8

**Rational Numbers Exercise 1.2 Solution**

**Question no – (1) **

**Solution : **

**(a)** -12/7 + 2/5 =__ 2/5__ + -12/7

**(b)** -2/3 + [-3/7 + (-9/4)] = [- 2/3 + -3/7] + __9/4__

**(c)** – 12/5 + ** 0** =

**+ -12/5 = – 12/5**

__0__**(d)** 3/-5 + ** 3/5** = 0 = [3/5 + -3/5]

**(e)** – 12/5 × __ 5/7 __= 5/7 ×

__[- 12/5]__

**(f)** 2/3 × [(-2/5) × 3/7] = [2/3 × ** (3/7)]** × (-2/5)

**(g)** 2/7 × ** 1 **= 1 ×

__=__

**2/7**

__2/7__**(h)** 2/3 × (5/7 – 1/3) = 2/3 ×__ (5/7)__

**– 2/3 ×**

__(1/3)__**Question no – (2) **

**Solution :**

**(a)** 1/8 + 5/12 + 2/7 + 7/12 + 9/7 + -5/16

= 2 – 5/16 + 12/12 + 11/7

= = 3/16 + 11/17 + 1

= -21 + 176 + 112/112

= 267/112…(Simplified)

**(b)** 11/12 + -17/4 + -4/9 + -15/8 + 13/6

= 11 + 26/12 + -34/ – 15/8 + -4/9

= 37/12 – 49/8 – 4/9

= 222- 441- 32/72

= 251/72…(Simplified)

**(c)** -7/11 + 2/3 + -3/22 + -9/4 + 13/12

= -14 – 3/22 +2/3 + -27 + 13/12

= = -17/22 + 2/3 – 14/12

= – 17/22 + 4 – 7/6

= -17/22 – 3/62

= – 17/-11/22

= – 28/22

= – 14/11…(Simplified)

**(d)** 11/12 × -7/8 × -8/15 × 9/-11

= 11/12 × -7/8 × 8/15 × 9/-11

= -7/20…(Simplified)

**(e)** -8/25 × -35/54 ÷ 28/39 × 63/-52

= – 8/25 × -35/54 × 39/28 × -63/52

= – 7/20…(Simplified)

**(f)** 36/49 ÷ 27/-42 × 26/-45 ÷ 65/-81

= 36/49 × -42/27 × -26/45 × -81/65

= – 42 × 24/49 × 25

= – 1008/1225…(Simplified)

**Question no – (3) **

**Solution : **

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

a = -7/3,

b = 5/-4,

c = 9/8

**∴** L.H.S

= a × (b × c)

= – 7/3 × (- 5/4 × 9/8)

= 105/32

**∴** R.H.S

= (a × b) × c

= (-1/3 × 5/-4) × 9/8

= 105/32

∴ L.H.S = R.H.S…(Verified)

**(b) **Given, a = 5/7,

b = -7/18,

c = 4/9

**∴** L.H.S = 5/7 × (-7/18 × 4/9)

= – 10/81

**∴** R.H.S = (5/7 × -7/18) × 4/9

= – 10/81

**∴** L.H.S = R.H.S…[Verified]

**Question no – (4) **

**Solution : **

**(a) **Given, a = -12/5,

b = -15/4,,

c = 7/6

L.H.S = 12/5 × (-15/4 + 7/6)

= – 12/5 × -45/ + 14/12

= 12/5 × -31/12

= 31/5

R.H.S = (- 12/5 × -15/4) + (12/5 × 7/6)

= – 9 – 14/5

= 45 – 14/5

= 31/5

**∴** L.H.S = R.H.S…(Verified)

**(b) **As per the given question,

a = -6/7,

b = -13/14,

c = 5/21

**∴** L.H.S = 6/7 × (- 13/14 + 5/21)

= 6- 6/7 × -39 + 10/42

= 6/7 × 29/42

= 29/49

**∴** R.H.S = (- 6/7 × -13/14) + (- 6/7 × 5/21)

= 39 – 10/49

= 29/49

**∴** L.H.S = R.H.S…(Verified)

**Question no – (5) **

**Solution : **

**(a)** 2/3 + -4/5 + (-2/3) + 1 + -7/5

= 2/3 + -4/5 + -2/3 + 1 + -7/5

= – 4/5 + 7/5 + 1

= – 11/5 + 1

= 6/5

**(b)** 5/7 + -4/9 + 4 + -13/3 + 6/21

= 5 + 2/7 + -4 – 39/9 + 4

= 1 – 43/9 + 4

= 9 -43 + 36/9

= 9/2

**(c)** 11/14 + (-5/7) + 1+ (13/20)

= 11 – 10/14 + 20 – 13/20

= 10 + 49/140

= 59/140

**(d)** 4/9 + 1/5 + (-4/3) + 9/10

= 4 – 82/9 + 2 + 9/10

= -8/9 + 11/10

= – 80 + 99/90

= 19/99

**(6) Simplify the following using properties of rational number**

**Solution : **

**(a)** 7/9 × -1/2 + 3/5 × 4/7 × – 7/9 × (3/2)

= (7/9 × -1/2) + (3/5 × 4/7) – [1/3 × (-3/2)

= (- 1/2 × (7/9 – 7/3) + (3/5 × 4/7)

= – 1/2 × (7/9 – 7/3) + (3/5 × 4/7)

= – 1/2 × – 14/9 + 3/5 × 4/7

= 7/9 + 12/35

= 245 + 18/315

= 353/315…(Simplified)

**(b)** (-2/7 × -4/9) + 2/3 × 1/5 + (-3/5 × -4/9)

= (-2/7 × -4/9) + (2/3 × 1/5) + (-3/5 × -4/9)

= – 4/9 × (-2/7 + -3/5) + (2/3 × 1/5)

= – 4/9 × – 10 – 21/35 + 2/3 × 1/5

= – 4/9 × – 31/35

= – 2/3 × 62/105 + 2/3 × 1/5

= 2/3 × (62/105 + 1/5)

= 2/3 × (62 + 21/105)

= 2/3 × 83/105

= 246/315…(Simplified)

**Question no – (7) **

**Solution : **

According to the question,

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

One of them is = 10/3

Other one = ?

Let the another one be x

x × 10/3 = -8/9

= 8 = – 8/9 × 3/10

= 4/15

Thus, the other one will be 4/15

**Question no – (8) **

**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

Hence, the answer will be – 25/11

**Question no – (9) **

**Solution : **

Let x must be subtracted,

**∴** – 9/14 – x = 11/18

= – 9/14 – 11/18 = x

= 81 – 77/126 = x

= – 158/126 = x

or, x = 79/63

**∴** x = – 1 16/63

Thus, – 1 16/63 must be subtracted to get 11/18.

**Question no – (10) **

**Solution : **

= 5/9 + – 8/7

= 35 – 72/63

= – 37/63

= 7/8 × 3/8

= 21/40

**∴** – 37/63 × 40/21

= – 1480/1323

Thus, the answer will be – 1480/1323

**Question no – (11) **

**Solution : **

As per the given question,

The sum of two rational numbers is = 8/25

One of them is = 3/16

The other = ?

Let, the another one be x

= x + 3/16 = 8/25

= x = 8/25 – 3/16

= 128 – 75/400

= 53/400

Therefore, the other one will be 53/400

**Question no – (12) **

**Solution : **

**(a)** 3/5 × (35/24 + 10/27)

= 3/5 × 35/24 + 3/5 × 10/27

= 7/8 + 2/9

= 63+16/72

= 79/72

**(b)** -7/3 × (12/5 – 4/21)

= – 7/3 × 12/5 – 7/3 × 4/21

= 28/5 + 4/9

= – 252 + 20/45

= 232/45

**(c)** -2/5 × 3/4 + 5/7 × -3/4 × 1/5

= 2/5 × -3/4 + 1/7 × (- 3/4)

= – 3/4 × (2/5 + 1/7)

= – 3/4 × 19/35

= 57/140

**(d)** 9/16 × 4/21 + -5/8 + 9/16 + -3/14

= 3/28 + – 10 + 9/16 + -3/14

= 3 – 6/28 – 1/16

= 3/28 – 1/16

= – 12 – 7/112

= -19/112

**Question no – (13) **

**Solution : **

= 84 4/5 litres = 424/5 litres

= 11 = 2/3 litres = 35/3 litres

= 424/5 – 35/3 = 1272/-175/15

= 1097/15 litres

Therefore, the container can hold more 1097/15 litres oil.

**Question no – (14) **

**Solution : **

= 25 – 37/3 – 38/5

= 25 × 15 – 185 – 114/15

= 3 – 75 – 299/15

= 76/15 kg

Thus, the weight of the cakes in the box will be 76/15 kg.

**Question no – (15) **

**Solution : **

According to the question,

Length is = 102/3 m

Breadth is = 93/4 m

∴ Area = 32/3 × 39/4 m^{2}

= 104 m^{2}

Therefore, the area of a rectangle will be 104 m^{2}

**Rational Numbers Exercise 1.2 Solution**

**Question no – (2) **

**Solution : **

**(a)** -3/5 = (Left)

**(b)** 7/9 = (Right)

**(c)** -11/-13 = (Left)

**(d)** 25/-29 = (Left)

**(e)** 1/10 = (Right)

**(f)** -15/7 = (Left)

**Question no – (3) **

**Solution : **

Given, = -1, + 1

1^{st} = 1/2 (- 1 + 1) = 0

2^{nd} = 1/2 (- 1 + 0) = -1/2

3^{nd} = 1/2 (0 + 1) = 1/2

4^{th} = 1/2 (0 – -1/2) = – 1/4

5^{th} = 1/2 (0 + 1/2) = 1/4

**Question no – (4) **

**Solution : **

Between 2 and 3

= 20/10

= 30/10

**∴** 21/10, 22/10 , 23/10, 24/10, 25/10

(One the rational numbers)

**Question no – (5)**

**Solution : **

**(a)** Given, 1/2 and 2/3

= 3/6 and 4/6

= 30/60 and 40/60

**∴** 31/60, 32/60, 33/60, 34/60, 35/60, 36/60, 37/60, 38/60, 39/60, 40/60

**(b)** Given, -3/4 and -4/5

= -15/20 and – 16/20

**∴** -151/200, -152/200, -153/200, -154/200, -155/200, -156/200, -158/200, -159/200, 160/200.

**∴** Ten rational numbers between -3/4 and -4/5 are, -151/200, -152/200, -153/200, -154/200, -155/200, -156/200, -158/200, -159/200, 160/200.

**(c)** Given, 2/7 and 2

= 2 and 14

**∴** 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3.

**∴** Ten rational numbers between 2/7 and 2 are 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3.

**(d) Given, **-3 and -7/5

= -15 and -7

**∴** -7.1, -7/7.3, -7.4, -7.5, -7.6, -7.7, -7.8, -7.9, -8

**∴** Ten rational numbers between -3 and -7/5 are, -7.1, -7/7.3, -7.4, -7.5, -7.6, -7.7, -7.8, -7.9, -8

**Question no – (6) **

**Solution : **

Given, + 1, + 2

= 10/10, 20/10

= 11/10, 12/10, 13/10, 14/10, 15/10, 16/10

**∴ **Six rational numbers which are greater than +1 and less than +2 are, 11/10, 12/10, 13/10, 14/10, 15/10, 16/10

**Next Chapter Solutions : **