# Maths Ace Class 7 Solutions Chapter 4

## Maths Ace Class 7 Solutions Chapter 4 Rational Numbers

Welcome to NCTB Solutions. Here with this post we are going to help 7th class students for the Solutions of Maths Ace Prime Class 7 Math Book, Chapter 4, Rational Numbers. Here students can easily find step by step solutions of all the problems for Rational Numbers, Exercise 4.1, 4.2, 4.3, 4.4 and 4.5 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 4 solutions.

Rational Numbers Exercise 4.1 Solution :

Question no – (2)

Solution :

(a) – 33

= Negative

(b) 89/-22

= Negative

(c) – 12/-32

= Positive

(d) Given,  + 21/-23

= Negative

(e)  – (- 27)

= Positive

(f) – 5

= Negative

Rational Numbers Exercise 4.2 Solution :

Question no – (1)

Solution :

(a) 35/14

= 5/2

(b) 81/-108

= 9/-12

(c) – 146/365

= -146/365

(d) 6/-42

= 1/-7

Question no – (2)

Solution :

(a) 12/54 and 54/12

= 2/9 & 9/2

12/54 ≠ 54/12

(b) 11/33 and 5/7

= 13/33 ≠ 5/7

(c) 2/9 and 14/63

= 2/9 & 2/9

2/9 = 14/63

(d) 3/-7 and – 9/21

= 3/-7 & – 3/7

= – 3/7 & – 3/7

– 3/7 = – 3/7

Question no – (3)

Solution :

(a) 24/45 and 15/8

= 24/34 & 15/8

= 24 × 8 = 192

= 45 × 15 = 675

(b) 14/28 and 3/9

= 14/28 & 3/9

= 14 × 9 = 126

= 28 × 3 = 84

(c) 3/5 and 15/25

= 3/5 & 15/25

= 3 × 25 = 75

= 5 × 15 = 75

(d)  – 13/52 and – 17/65

= – 13/52 & – 17/65

= – 13 × 65 = – 845

= – 52 × – 17 = – 884

Question no – (4)

Solution :

As per the question, 2/9

= 2 × 6/9 × 6

= 12/54

Question no – (5)

Solution :

(a) 23/46 < 81/99

(b) -1/5 < – 1/7

(c) – 9/17 < 6/-19

(d) 12/56 < 21/65

Question no – (6)

Solution :

(a) 3/7, 21/49, 22/66

= 22/66 < 21/49

= 3/7

(b) 11/-15, -7/10, -3/20, 7/-30

= 11/-15 < -7/10 < 7/-30 < -3/20

Question no – (7)

Solution :

(a) 33/77, 14/63, 2/6

= 33/77 > 2/6 > 14/63

(b) – 3, -3/5, – 8/3, 1/9

= 1/9 > -3/5 > -8/3 > – 3

Question no – (9)

Solution :

Given, Four the rational numbers is

= 42/396, 41/396, 40/396, 38/396

Question no – (10)

Solution :

Given, The Five rational numbers between – 1/5 and – 1/7 are,

= – 27/140, – 26/140, 25/140, – 23/140, – 22/140

Question no – (11)

Solution :

(a) 5/7

= 5/7

(b) – 3/8

= 3/8

(c) – 13/- 16

= 13/16

(d) 20/- 29

= 20/29

Rational Numbers Exercise 4.3 Solution :

Question no – (1)

Solution :

(a) 2/9 and 5/9

= 2 + 5/9

= 7/9

(b) – 1/9 and 1/7

= – 7+ 9/63

= 2/63

(c) 3/921 and 2/71

= 2134 + 1842/65391

= 2085/65391

= 685/21791

(d) 5/-9 and – 7/5

= – 5 – 7/9

= – 12/9

= – 4/3

(e) -1/-9 and 1/18

= – 2 + 1/18

= 3/18

= 1/6

(f) 2/11 and – 1/121

= 22 + 1/121

= 23/121

Question no – (2)

Solution :

(a) – 1/3 + 2/21

= – 7 + 2/21

= – 5/21

(b) – 1/5 + 3/7

= 7 + 15/35

= 22/35

(c) 1/2 + – 71/17

= 17 – 142/34

= – 125/34

(d) – 1/5 + – 1/4

= 4 + 5/20

= 1/20

(e) 1/33 + 2/99

= 3 + 2/99

= 5/99

(f) 1/5 + – 3/7 + 2/35

= 7 – 15 + 2/35

= – 6/35

Question no – (3)

Solution :

(a) 1/2 from 1/7

= 1/7 – 1/2

= 2 – 7/14

= – 5/14

(b) 2/11 from – 21/2

= – 21/2 – 2/21

= – 441 – 4/42

= – 445/42

(c) – 22/3 from 9/31

= 9/31 – -22/3

= 27 + 682/93

= 709/93

(d) 11/5 from 21/53

= 21/53 – 583/265

= – 478/265

(e) 1/9 from 1/27

= 3 – 1/9

= 2/9

(f) – 6/17 from 5/51

= 15 + 6/51

= 21/51

= 7/17

Question no – (4)

Solution :

(a) – 7/6 + 3/5 + 1/3

= – 35 + 18 + 10/30

= – 7/30

(b) 1/8 + 7/12 + (- 2/9)

= 9 + 42 – 16/72

= 35/72

(c) 2/5 + -11/15 + (- 7/50)

= 60 – 110 – 21/150

= – 71/150

(d) 1/3 + 2 4/5 – (- 7/10)

= 1/3 + 14/5 + 7/10

= 10 + 84 + 21/30

= 115/30

= 23/6

(e) 10 1/2 – 5 1/4 – 1 1/2

= 21/2 – 21/4 – 3/2

= 42 – 21 – 6/4

= 15/4

(f) 5 3/5 – 2 2/5 + 3 1/2

= 28/5 – 8/3 + 7/2

= 168 – 80 + 105/30

= 193/30

Rational Numbers Exercise 4.4 Solution :

Question no – (1)

Solution :

(a) 11/7 × (- 31/54)

= – 341/378

(b) 13/9 × (- 27/91)

= – 3/7

(c) 69//-5 × (- 125/23)

= 3 × 75

= 75

(d) 1/17 × 9/15 × 17/12

= 5 × 4

= 1/20

(e) 4/3 × (- 23/51) × 7/11

= – 664/1683

(f) 8/35 × (- 7/51) × 17/35

= – 8/525

Question no – (2)

Solution :

(a) 12/7 ÷ 4/343

= 12/7 × 343/4

= 147

(b) 3/121 ÷ 1/11

= 3/121 × 11

= 3/11

(c) 11/13 ÷ (- 4/39)

= 11/3 × 39/- 4

= – 13/4

(d) 1/2 ÷ (- 4/6)

= 1/2 × 6/-4

= – 3/4

(e) (- 7/8) ÷ 14/32

= – 7/8 × 32/14

= – 2

(f) 11/16 ÷ (- 23/121)

= 11/16 × 121/-3

= 1331/- 368

Question no – (3)

Solution :

(a) – (i) – 1/6 × 4/-5 × 10/16

= 1/6 × 4/-5 × 10/10

= 1/12

(ii) (4/7 ÷ 16/21) ÷ 5/-8

= (4/7 × 21/16) ÷ 5/8

= 3/4 ÷ 8/5

= 6/5

(b) (multiplicative inverse of 3 1/2)/(additive inverse of 2 5/8)

= M.I of 7/2/A.I of 21/8

(c) (24/4 × 2/5) – (1/5 × – 10/3)

= 12/5 + 2/3

= 36 + 10/15

= 46/15

Rational Numbers Exercise 4.5 Solution :

Question no – (1)

Solution :

(a) 15/8

= 1.875

(b) 23/10

= 2.3

(c) 3/16

= 0.1875

(d) 7/9

= 22.5

(e) 7/9

= 0.777

(f) 55/13

= 4/2307

(g) 19/11

= 1.727

(h) 16/7

= 2.285

Question – (2)

Solution :

(a) 2.305

= Rational number.

(b) 0.416

= Rational number.

(c) 2.2360679…

(d) 0.833333…

= Rational number.

Question no – (3)

Solution :

Let, Total book = 1

read of book = 1 – (1/22 + 5/9)

= 1 – (9 + 110/198)

= 1 – 119/198

= 198 – 119/198

= 79/198

Therefore, 79/198 part of the book is left to be read.

Question no – (4)

Solution :

Discount of shop A,

= 400 × 1/7

= 57.14

Discount of shop B,

= 400 × 3/31

= 1200/31

= 38.70

Price of shop A,

= 400 – 57.14

= 342.86

Price of shop B,

= 400 – 38.70

= 361.30

Shop A is the better offer at = 342.86

Question no – (5)

Solution :

Let, number = x

According to the question

= 9x/5 – 5x/7 = 70

or, 63x – 25x/35 = 70

or, 38x/35 = 70

or, x = 70 × 35/38

= 2450/38

= 64.47

Hence, the number is 64.47

Question no – (6)

Solution :

Distance cover in 1 hour

= 189 1/3/4 4/9 = 568/3/40/9

= 568/3 × 9/40

= 42.6 km

Thus, the distance covered in one hour is 42.6 km.

Question no – (7)

Solution :

Area of table cloth,

= 2 1/3 × 2 1/3

= 7/3 × 7/3

= 49/9 m2

Therefore, the area of the table cloth will be 49/9 m2

Next Chapter Solution :

Updated: June 16, 2023 — 4:06 pm