RD Sharma Class 8 Solutions Chapter 1 - Rational Numbers Updated for 2025-26

RD Sharma Solutions for Class 8 Maths, Chapter 1 - Rational Numbers, are available here. Prepared by subject experts, these solutions are designed to help students score well. The chapter covers rational numbers, whole numbers, natural numbers, and their representation on a number line. Download the detailed solutions PDF to prepare effectively for your exams.

RD Sharma Class 8 Rational Numbers (2025-26) PDF

By practicing questions from the RD Sharma Class 8 Solutions Rational Numbers PDF, students gain practical knowledge of the chapter. This understanding can be applied not only to other chapters but also to real-life situations. Additionally, students can conveniently access the answers to Rational Numbers, available in PDF format on the Home-Tution website, for easy reference and self-assessment.

Access Answers to Maths RD Sharma Solutions for Class 8 Chapter 1 Rational Numbers

1. Add the following rational numbers:

(i) 5/-9 and 7/3

Solution: Firstly we need to convert the denominators to positive numbers.

5/-9 = (5 × -1)/ (-9 × -1) = -5/9

The denominators are 9 and 3

By taking LCM for 9 and 3 is 9

We rewrite the given fraction in order to get the same denominator

-5/9 = (-5×1) / (9×1) = -5/9 and

7/3 = (7×3) / (3×3) = 21/9

Since the denominators are same we can add them directly

-5/9 + 21/9 = (-5+21)/9 = 16/9

(ii) 3/4 and -5/8

Solution: The denominators are 4 and 8

By taking LCM for 4 and 8 is 8

We rewrite the given fraction in order to get the same denominator

3/4 = (3×2) / (4×2) = 6/8 and

-5/8 = (-5×1) / (8×1) = -5/8

Since the denominators are same we can add them directly

6/8 + -5/8 = (6 + (-5))/8 = (6-5)/8 = 1/8

(iii) -7/27 and 11/18

Solution: The denominators are 27 and 18

By taking LCM for 27 and 18 is 54

We rewrite the given fraction in order to get the same denominator

-7/27 = (-7×2) / (27×2) = -14/54 and

11/18 = (11×3) / (18×3) = 33/54

Now, the denominators are same we can add them directly

-14/54 + 33/54 = (-14+33)/54 = 19/54

(iv) -3 and 3/5

Solution: The denominators are 1 and 5

By taking LCM for 1 and 5 is 5

We rewrite the given fraction in order to get the same denominator

-3/1 = (-3×5) / (1×5) = -15/5 and

3/5 = (3×1) / (5×1) = 3/5

Now, the denominators are same we can add them directly

-15/5 + 3/5 = (-15+3)/5 = -12/5

(v) 31/-4 and -5/8

Solution: Firstly we need to convert the denominators to positive numbers.

31/-4 = (31 × -1)/ (-4 × -1) = -31/4

The denominators are 4 and 8

By taking LCM for 4 and 8 is 8

We rewrite the given fraction in order to get the same denominator

-31/4 = (-31×2) / (4×2) = -62/8 and

-5/8 = (-5×1) / (8×1) = -5/8

Since the denominators are same we can add them directly

-62/8 + (-5)/8 = (-62 + (-5))/8 = (-62-5)/8 = -67/8

(vi) 5/36 and -7/12

Solution: The denominators are 36 and 12

By taking LCM for 36 and 12 is 36

We rewrite the given fraction in order to get the same denominator

5/36 = (5×1) / (36×1) = 5/36 and

-7/12 = (-7×3) / (12×3) = -21/36

Now, the denominators are same we can add them directly

5/36 + -21/36 = (5 + (-21))/36 = 5-21/36 = -16/36 = -4/9

(vii) 7/-18 and 8/27

Solution: Firstly we need to convert the denominators to positive numbers.

7/-18 = (7 × -1)/ (-18 × -1) = -7/18

The denominators are 18 and 27

By taking LCM for 18 and 27 is 54

We rewrite the given fraction in order to get the same denominator

-7/18 = (-7×3) / (18×3) = -21/54 and

8/27 = (8×2) / (27×2) = 16/54

Since the denominators are same we can add them directly

-21/54 + 16/54 = (-21 + 16)/54 = -5/54

(viii) -5/16 and 7/24

Solution: The denominators are 16 and 24

By taking LCM for 16 and 24 is 48

We rewrite the given fraction in order to get the same denominator

-5/16 = (-5×3) / (16×3) = -15/48 and

7/24 = (7×2) / (24×2) = 14/48

Now, the denominators are same we can add them directly

-15/48 + 14/48 = (-15 + 14)/48 = -1/48

2. Add the following rational numbers:

(i) -5/7 and 3/7

(ii) -8/11 and -4/11

(iii) -15/4 and 7/4

(iv) 6/13 and -9/13

Solution:

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

(ii) -8/11 + -4/11 = (-8 + (-4))/11 = (-8-4)/11 = -12/11

(iii) -15/4 + 7/4 = (-15+7)/4 = -8/4

Further dividing by 4 we get,

-8/4 = -2

(iv) 6/13 + -9/13 = (6 + (-9))/13 = (6-9)/13 = -3/13

3.Simplify:

(i) 3 + 5/-7

Solution: Firstly convert the denominator to positive number

5/-7 = (5×-1)/(-7×-1) = -5/7

3/1 + -5/7

Now let us take the LCM for 1 and 7 which is 7

(3×7)/(1×7) + (-5×1)/(7×1)

21/7 + -5/7

Since the denominators are same we can add them directly

(21-5)/7 = 16/7

(ii) 8/9 + -11/6

Solution: let us take the LCM for 9 and 6 which is 18

(8×2)/(9×2) + (-11×3)/(6×3)

16/18 + -33/18

Since the denominators are same we can add them directly

(16-33)/18 = -17/18

(iii) 5/26 + 11/-39

Solution:

11/-39 = (11×-1)/(-39×-1) = -11/39

5/26 + -11/39

Now let us take the LCM for 26 and 39 which is 78

(5×3)/(26×3) + (-11×2)/(39×2)

15/78 + -22/78

Since the denominators are same we can add them directly

(15-22)/78 = -7/78

(iv) 7/9 + 3/-4

Solution: 

3/-4 = (3×-1)/(-4×-1) = -3/4

7/9 + -3/4

Now let us take the LCM for 9 and 4 which is 36

(7×4)/(9×4) + (-3×9)/(4×9)

28/36 + -27/36

Since the denominators are same we can add them directly

(28-27)/36 = 1/36

Benefits of using RD Sharma for Class 8 Maths

• Comprehensive Practice: RD Sharma’s Mathematics book provides numerous questions for each concept, ensuring thorough practice.
• In-depth Conceptual Understanding: Unlike other books, RD Sharma offers detailed explanations of concepts along with numerical problems, making learning more comprehensive.
• Practical Knowledge: This book not only explains the theory but also provides practical applications of mathematical concepts, helping students understand their real-life relevance.
• Focus on Key Topics: Topics like Rational Numbers, which are fundamental, are thoroughly covered. Regular revision strengthens the foundation for more advanced mathematics.
• Exam Preparation: Designed to cover all topics in the syllabus, this book helps you prepare in detail for your exams, giving you the edge to excel.