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**Number Line Prime Class 7 Solutions Chapter 5 Rational Numbers**

Welcome to NCTB Solutions. Here with this post we are going to help 7th class students for the Solutions of Number Line Prime Class 7 Math Book, Chapter 5, Rational Numbers. Here students can easily find step by step solutions of all the problems for Rational Numbers, Exercise 5A, 5B, 5C, 5D, 5E and 5F 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 5 solutions. Here in this post all the solutions are based on latest Syllabus.

**Rational Numbers Exercise 5A Solution :**

**(1) Which of the following are not rational numbers?**

**Solution :**

(c) 5/0

5/0 is not rational number

**(2) Write each of the following integers as a rational number.**

**Solution :**

(a) 42

= 42/1

(b) – 72

= – 72/1

(c) 0

= 0/1

(d) – 17

= -17/1

**Question no – (3)**

**Solution :**

(a) 8/- 11

= – 8/11

(b) – 14/- 19

= 14/19

(c) – 3/- 5

= 3/5

(d) – 28/- 59

= 28/59

**Question no – (4)**

**Solution :**

(a) -7/5

(b) 2/7

(c) -1/4

(d) 15/6

**Question no – (5)**

**Solution :**

(a) 2/5

= 2/5 equivalent to – 2/- 5, 4/10, – 4/- 10, 6/15

(b) – 5/7

= – 5/7 equivalent to 5/- 7, – 15/21, – 10/14, – 20/28

(c) – 6/11

= – 6/11 equivalent to 6/- 11, 12/- 22, – 12/22, – 18/33

(d) 8/- 15

= 8/- 15 equivalent to 16/- 30, – 8/15, 24/- 45, – 24/45

**Question no – (6)**

**Solution :**

(a) – 19/76

= – 1/4

(b) 225/- 625

= – 9/25

(c) 228/384

= 19/32

(d) – 259/- 407

= 259/407

**Question no – (7)**

**Solution :**

(a) 4/3___ 1/2

Given, 4/3

= 4 × 5/7 × 5

= 20/35,

Given, 1/2

= 1 × 3/2 × 3

= 3/6

∴ 8/6 > 3/6 = 4/3 > 3/6

(b) 5/7 ____ 2/7

= 5/7 > 2/7

(c) 4/7____3/5

Given, 4/7

= 4 × 5/7 × 5

= 20/35,

Given, 3/5

= 3 × 7/5 × 7

= 21/35

∴ 20/35 < 21/35 = 4/7 < 3/5

(d) 5/8____3/5

Given, 5/8

= 5 × 5/8 × 5

= 25/40

Given, 3/5

= 3 × 8/5 × 8

= 24/40

∴ 25/40 > 24/40 = 5/8 > 3/5

**Question no – (8)**

**Solution :**

(a) 1/3

|1/3|

= 1/3

(b) – 5/6

|5/6|

= 5/6

(c) 3/- 7

|3/- 7|

= 3/7

(d) – 8/- 5

|- 8/- 5|

= 8/5

**Rational Numbers Exercise 5B Solution :**

**Question no – (1)**

**Solution : **

(a) 1/7 + 4/7

= 1+4/7

=5/7

(b) 9/19 + 3/19

= 9+3/19

= 12/19

(c) 2/5 + 5/6

12+25/30

= 37/30

(d) 15/36 + 65/18

= 15 + 130/36

= 145/36

**Question no – (2) **

**Solution : **

(a) 7/10 and 3/10

7/10 + 3/10

= 7 + 3/10

= 10/10

=1

(b) -6 and 3/20

= – 6 + 3/20

= -120 + 3/20

= – 117/20

(c) 2 1/2 and 7 1/5

= 2 1/2 + 7 1/5

= 5/2 + 36/5

= 25 +72/10

=97/10

(d) – 11/41 and 9/20

= – 11/41 + 9/20

= – 220 + 369/820

= 149/820

**Question no – (3)**

**Solution : **

(a) 3/9 and 8/9

3/9 + 8/9

= 3 + 8/9

= 11/9

(b) 4/11 and 7/11

4/11 + 7/11

= 4 + 7/11

= 11/11

= 1

(c) 13/39 and 18/39

13/39 + 18/39

= 13 + 18/39

= 31/39

(d) -17/20 and 37/30

= -17/20 + 37/30

= -51 + 74/60

= 23/60

**Question no – (4)**

**Solution : **

(a) -3/7

= 3/7

(b) 0

= 0

(c) -2/11

= 2/11

(d) -27/- 83

= – 27/83 or 27/- 83

**Rational Numbers Exercise 5C Solution :**

**Question no – (1) **

**Solution : **

(a) 5/18 – 7/18

= 5 -7/18

= – 2/18

= – 1/9

(b) -1/27 – 1/9

= -1 – 3/27

= – 4/27

(c) 17/25 – -13/20:

= 68 + 65/100

= 133/100

(d) -21/43 – -11/129

= -21/43 + 11/129

= – 63 + 11/129

= – 52/129

**Question no – (2) **

**Solution : **

(a) 2/9, 1/6

= 4 – 3/18

= 1/18

(b) 2 5/16, – 1 9/32

= 37/16 – 41/32

= 74 – 41/32

= 33/32

(c) -6/25, 1 19/20

= – 6/25 – 39/20

= – 24 – 195/100

= – 219/100

(d) -15/27, -29/81

= – 45 + 29/81

= -16/81

**Question no – (3)**

**Solution : **

(a) 3/5 from 8/5

= 3/5 – 8/5

= 3 – 8/5

= – 5/5

= -1

(b) 4/-11 from -3/11

= 4/-11 – -3/11

= -4+3/11

= -1/11

(c) -9/13 from -6/-13

= – 9/13 – -6/-13

= – 9 -6/13

= -15/13

(d) -6/17 from 5/51

= – 6/17 – 5/51

= – 18 – 5/51

= – 23/51

**Question no – (4)**

**Solution :**

Let the other number be x

∴ x + (-7/12) = -11/36

x = -11/36 + 7/12

= -11 + 21/36

= 10/36

= 5/18

**Question no – (5)**

**Solution :**

Let we should subtracted x

∴ -10 – x = 1 3/25

∴ x = -10 – 28/25

= -250 – 28/25

**Question no – (6) **

**Solution :**

Additive inverse of 35/-48 = 35/48

∴ 5 – 35/48

= 240 – 35/48

**Question no – (7)**

**Solution :**

Let, we should add – x

∴ x + (-2/3) = 14/36

∴ x = 14/36 + 2/3

= 14 + 24/36

= 38/36

= 19/18

**Question no – (8) **

**Solution :**

Let the another number be x

∴ 11/15 – x = 2 1/5

∴ x = 11/15 – 11/5

= 11 – 33/15

= -22/15

**Question no – (9)**

**Solution : **

(a) 2/3 + 4/15 -1/3

= 10 + 4/15 – 1/3

= 14/15 – 1/3

= 14 – 5/15

= 9/15

= 3/5

(b) -9/10 + 3/16 – 2/18

= – 648 + 135 – 80/720

= – 593/720

**Rational Numbers Exercise 5D Solution :**

**Question no – (1)**

**Solution : **

(a) 2/9 × 5/13

= 10/117

(b) 7/19 × -38/21

= -2/3

(c) -2/77 × 35/-50

= 1/55

(d) 22/36 × 16/-33

= -11/54

**Question no – (2)**

**Solution : **

(a) 2/7 by 7/2

= 1

(b) – 4/15 by 30/48

= -1

(c) 8/25 by 10

= 16/5

(d) -56/31 by 6/-7

= 48/31

**Question no – (3)**

**Solution :**

-4/15 + 4/15

= 0 by 10/13

= 0 × 10/13

= 0

**Question no – (4)**

**Solution : **

(a) (1/10 + 7/15) × (3/16 + 3/8)

= (3+14/30) × (3+6/16)

= 17/30 × 9/16

= 51/160

(b) (-2/3 + 4/9) × (11/15 – 2/5)

=(- 6 + 4/9) × (11- 6/15)

= -2/9 × 5/15

= -2/18

(c) (1/16 – 5/18) × (5/9 – 7/12)

= (9 – 40/144) × (20-21/36)

= -31/144 × -1/36

= 31/5184

(d) (2/9 + -5/6) × (-3/-8 – ¾)

= (4 -15/18) × (3-6/8)

= -11/18 × -3/8

= 11/48

**Question no – (5)**

**Solution :**

= -2/3 5/9 – (-2/3)

= 5/9 + 2/3

= 5+6/9

= 11/9

∴ 11/9 × (7/3 + -4/15)

= 11/9 × (35-4/15)

= 11/9 × 31/15

= 341/135

**Rational Numbers Exercise 5E Solution :**

**Question no – (1)**

**Solution : **

(a) 2/11

= 11/2

(b) -7/15

= 15/7

(c)-21/-37

= 37/21

(d) 15/-36

= -36/15

**Question no – (2)**

**Solution : **

(a) 20/39 ÷ (-13)

= 20/39 × 1/-13

= -20/507

(b) 12/-13 ÷ 2/7

= -12/13 × 7/2

= -42/13

**Question no – (3)**

**Solution : **

(a) 7/8 by ¼

= 7/8 × 4

= 7/2

= 3.5

(b) 12/13 by 6/13

= 12/13× 13/6

= 2

**Question no – (4)**

**Solution :**

Let, we can multiplied by x

∴ x × (-5/8) = 1/6

∴ x = 1/16 × -8/5

∴ x= 1/10

**Question no – (5)**

**Solution :**

Let, we should multiplied by x

∴ x × (-5/9) = -7/6

∴ x = -7/6 × -9/5

= 21/10

**Question no – (6)**

**Solution :**

Let, we should multiplied by x

∴ x × 11/13 = -65/69

∴ x = – 65/69 × 13/11

∴ x = -65/33

**Question no – (7)**

**Solution :**

Reciprocal of 5/14 is 14/5

∴ Product of (-3/10× 2/15)= -1/25

∴ -1/25 – 14/5

= -1-70/25

= -71/25

**Question no – (8)**

**Solution :**

Sum – (7/10 + -3/5)

= 7-6/10

= 1/10

Reciprocal of – 11/20 = -20/11

1/10 ÷ -20/11

= 1/10 × 11/20

=-11/200

**Question no – (9)**

**Solution : **

(a) 1/3+2/7

= 7+6/21

= 13/21

Reciprocal – 21/13

(b) 7/8 – -9/24

7/8 – (-9/24)

= 7/8 + 9/24

=21 + 9/24

=30/24

= 5/4

Reciprocal – 4/5

(c) 3/11 × -33/42

3/11 × -33/42

= -3/14

Reciprocal = -14/3

**Question no – (10)**

**Solution :**

(a) 4/9 and 5/18.

LCM of 9, 18 = 18

∴ 4/9 = 4×2/9×2

= 8/18

∴ 8/18>7/18>6/18>5/18

∴ Rational numbers are – 7/18, 6/18

(b) 2/5 and 3/10

LMC of 5, 10 is = 10

2/5 = 2×2/5×2 = 4/10

∴ 4/10>3.9/10>3.8/10>3.7/10>…….>3/10

∴ Rational numbers 39/100, 38/100

(c) -9/10 and -9/8

LMC of 10, 8 is – 40

-9/10= -9×4/10×4 = -36/40 , -9/8 = -9×5/8×5 = -45/40

∴ -36/40> -37/40>-38/40>…….>-45/40

∴ Rational numbers are – -37/40, -38/40

(d) -6/7 and 7/14.

LCM of 7, 14 = 14

∴ -6/7 = -6×2/7×2 = -12/14

∴ 7/14>6/14>5/14>….>-11/14>-12/14

∴ Rational numbers are – 6/14, 5/14

**Question no – (11)**

**Solution : **

(a) -7/4

∴ -7/4 = -1.75

(b) 12/25

∴ 12/25 = 0.48

(c) 11/20

∴ 11/20 = 0.55

(d) -17/8

∴ -17/8 = 1.875

**Question no – (12)**

**Solution : **

(a) 0.87

= 87 – 8/90

= 79/90

(b) 2.6

= 2+0.6

= 2 + 6/9

= 6+2/3

= 8/9

(c) 0.23

= 23/99

(d) 0.365

= 365 – 36/900

= 329/900

**Rational Numbers Exercise 5F Solution :**

**Question no – (1) **

**Solution :**

∴ Sartik walk – 1/2 hour 1^{st}

∴ Sartik walk – 1/4 hour 2^{nd} day

∴ 2 days total time – (1/2 +1/4) = 3/4 hour

∴ 2 days time – 3/4 hour.

∴ she walk in 4 days = x × 3/4 hour

**Question no – (2) **

**Solution :**

Noor reads ,

1^{st} day -1/22

2^{nd} day – 5/9

∴ He read = 1/22 + 5/9

= 9+110/198

= 119/198 of the both

Let total book part is – 1

∴ Left to read – 1 – 119/198

= 198 -119/198

= 79/198

**Question no – (3) **

**Solution :**

∴ Headphone cost – 400

∴ A offers 1/7 of amount = 1/7 × 400

∴ B offer 3/31 of amount = 3/31 × 400

LCM of 7 and 31 is 271

∴ 400 × 31/7 × 31

= 12400/217

3 × 7 × 400/31 × 7 = 8400/217

∴ A’s offer is better by

= (12400/217 – 8400/217)

= 4000/217

= 18.43

**Question no – (4)**

**Solution :**

Let the number I x

∴ 9x – 5/7x = 70

∴ 63x – 25x/35 = 70

∴ 38x = 70 × 35

∴ x = 70 × 35/38

**Question no – (5)**

**Solution :**

∴ 4 4/9 hour goes 189 1/3 km

∴ 40/9 hour goes 568/3

∴ 1 hour goes 568/3 × 9/40

= 426/10

= 42.6 km.

**Next Chapter Solution : **