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CBSE Class 8 Mathematics Chapter 1 Rational Numbers Worksheet with Answers

Mastering Rational Numbers is essential for success in CBSE Class 8 Mathematics and builds the foundation for algebra, equations, and higher mathematics. This printable worksheet offers structured practice across 35+ questions spanning multiple formats—MCQs, fill-in-the-blanks, true/false, short answers, long answers, and a case study. Every question is aligned with the NCERT Class 8 Mathematics Chapter 1 syllabus and CBSE marking schemes, ensuring students gain confidence and clarity before exams.

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Key takeaways

✓Complete 35+ question worksheet covering all topics in CBSE Class 8 Mathematics Chapter 1 Rational Numbers with difficulty levels marked.
✓Structured in five progressive sections: MCQs, fill-in-the-blanks, true/false, short answers (3 marks each), and long answers (5 marks each).
✓Includes one case-study question mirroring the latest CBSE exam pattern to build analytical and application skills.
✓Full answer key with step-by-step working and brief explanations for every question ensures effective self-assessment.
✓Suggested time: 90 minutes; difficulty: Medium; aligns perfectly with NCERT Class 8 Mathematics textbook and CBSE guidelines.
✓Covers all key concepts: properties of rational numbers, operations, number line representation, identities, inverses, and standard form.
✓Print-friendly format suitable for classroom tests, home practice, or weekend revision sessions before unit tests.

Quick Chapter Recap: Rational Numbers (Class 8 Mathematics Chapter 1)

A rational number is any number that can be expressed in the form p/q, where p and q are integers and q is not equal to zero. This chapter introduces students to the complete number system of rationals, which includes all integers, whole numbers, and fractions. Rational numbers fill the gaps between integers on the number line, and between any two rational numbers, infinitely many other rational numbers exist. Key topics covered include equivalent rational numbers, standard form (where the denominator is positive and HCF of numerator and denominator is 1), and the four arithmetic operations on rationals. Students learn fundamental properties such as closure, commutative, associative, and distributive laws for addition and multiplication. The concept of additive identity (0) and multiplicative identity (1), along with additive inverse and multiplicative inverse (reciprocal), form the backbone of solving equations and simplifying expressions. Representation on the number line helps visualize and compare rational numbers effectively. Understanding these concepts deeply ensures strong performance in both internal assessments and the CBSE board exams. This worksheet tests all these dimensions through varied question types.

Definition: p/q form where p, q are integers and q ≠ 0
Standard form: denominator positive, HCF(p,q) = 1
Properties: closure, commutative, associative, distributive
Identities: additive (0), multiplicative (1)
Inverses: additive inverse (-a/b for a/b), multiplicative inverse (b/a for a/b)
Operations: addition, subtraction, multiplication, division using LCM and reciprocals
Number line representation for visualization and comparison

Worksheet Information and Instructions

This worksheet is designed for CBSE Class 8 students as per the latest NCERT syllabus for Mathematics Chapter 1 Rational Numbers. The difficulty level is Medium, with questions ranging from basic recall to higher-order thinking skills (HOTS). Suggested time for completion is 90 minutes under exam-like conditions, though students may take longer during initial practice. The worksheet is divided into five distinct sections (A to E) plus a case-study question, mirroring the current CBSE question paper pattern. Section A contains multiple-choice questions (1 mark each), Section B has fill-in-the-blanks (1 mark each), Section C includes true/false statements (1 mark each), Section D features short-answer questions (3 marks each), and Section E presents long-answer and HOTS questions (5 marks each). The case-study question carries 4 marks and tests real-world application of rational number concepts. Students should attempt all questions, show complete working for calculation-based problems, and write answers in standard form wherever applicable. A comprehensive answer key with explanations follows the question sections to facilitate self-assessment and independent learning. Parents and teachers can use this worksheet for periodic assessments, homework assignments, or pre-exam revision drills.

Difficulty Level: Medium (suitable for average to above-average students)
Suggested Time: 90 minutes (can be split into two 45-minute sessions)
Total Questions: 35+ across five sections plus one case study
Marking Scheme: Section A & B & C (1 mark each), Section D (3 marks each), Section E (5 marks each), Case Study (4 marks)
Instructions: Use only blue/black pen, show all working, write final answers in standard form, no calculators allowed
Answer Key: Provided at the end with step-by-step solutions and explanations

Section A: Multiple Choice Questions (MCQs) — 1 Mark Each

This section tests your foundational understanding and quick recall of concepts related to rational numbers. Each question has four options, and only one is correct. Read each question carefully, eliminate obviously wrong options, and select the best answer. No negative marking applies, so attempt every question even if you are unsure. Remember to apply properties of rational numbers, check standard forms, and use elimination strategies where calculation seems lengthy. These MCQs are designed to mirror the style and difficulty of CBSE Class 8 term exams and align closely with NCERT Class 8 Mathematics textbook exercises. Topics covered include identification of rational numbers, standard form, properties (closure, commutative, associative, distributive), identities, inverses, and number line representation. Practising MCQs regularly sharpens your speed and accuracy, both critical for scoring well in the objective sections of CBSE exams. If you find yourself stuck, move on and return to difficult questions at the end. Always double-check your selected option before finalizing your answer, especially in questions involving negative signs and denominators.

Q1. Which of the following is a rational number? (a) √2 (b) π (c) -5/7 (d) √3
Q2. The standard form of -12/18 is: (a) -2/3 (b) 2/-3 (c) -6/9 (d) 12/-18
Q3. The additive inverse of 3/5 is: (a) 5/3 (b) -3/5 (c) -5/3 (d) 3/-5
Q4. Multiplicative inverse of -7/4 is: (a) 4/-7 (b) -4/7 (c) 7/4 (d) 4/7
Q5. Which property is shown by (2/3 + 4/5) + 1/2 = 2/3 + (4/5 + 1/2)? (a) Commutative (b) Associative (c) Distributive (d) Closure
Q6. The rational number lying between 1/2 and 3/4 is: (a) 1/3 (b) 5/8 (c) 2/3 (d) 7/8
Q7. What is the multiplicative identity for rational numbers? (a) 0 (b) 1 (c) -1 (d) Does not exist

Section B: Fill in the Blanks — 1 Mark Each

Fill-in-the-blank questions test precise recall of definitions, formulae, and key facts about rational numbers. Write your answers clearly in the space provided. Ensure your answers are in standard form where applicable, and include proper signs (positive or negative). These questions require you to remember exact terminology from the NCERT Class 8 Mathematics textbook, such as 'additive identity', 'multiplicative inverse', 'closure property', and 'standard form'. Pay close attention to the wording of each statement to avoid silly mistakes, such as confusing additive and multiplicative inverses or writing answers with negative denominators. This section reinforces conceptual clarity and helps solidify the vocabulary of rational numbers that you will use throughout your Class 8 Mathematics course and beyond. When in doubt, think through the definition or property being tested, and write your answer accordingly. Practising these regularly will make your fundamentals rock-solid, which is essential for tackling complex problems in algebra and higher mathematics. If the blank requires a numerical answer, perform the calculation step-by-step on rough paper before writing the final answer.

Q8. A number that can be written in the form p/q where q ≠ 0 is called a __________ number.
Q9. The additive identity for rational numbers is __________.
Q10. The reciprocal of 5/8 is __________.
Q11. Between any two rational numbers, there are __________ rational numbers.
Q12. The standard form of 24/-36 is __________.
Q13. Rational numbers are __________ under addition, subtraction, and multiplication (closed/not closed).
Q14. The product of a rational number and its multiplicative inverse is always __________.

Section C: True or False Statements — 1 Mark Each

Carefully read each statement and decide whether it is True or False. Write 'True' or 'False' in the space provided; do not use abbreviations like T or F. These questions test your conceptual understanding of rational numbers and their properties. Some statements may seem tricky at first glance, so think through the definitions and properties before answering. For example, remember that division by zero is undefined, so any statement involving division by zero is false. Also recall that closure property does not hold for division (since dividing by zero is not allowed). Pay attention to negative signs, standard form conditions, and the difference between additive and multiplicative inverses. If a statement uses terms like 'always', 'never', or 'sometimes', evaluate it carefully with counterexamples where needed. This section is designed to test deep conceptual clarity rather than rote memorization, so understanding the 'why' behind each property is crucial. Practising true/false questions regularly sharpens your ability to think critically and spot errors in mathematical reasoning, a skill highly valued in CBSE board exams and competitive tests alike.

Q15. Every integer is a rational number. __________
Q16. Zero has no reciprocal. __________
Q17. The sum of a rational number and its additive inverse is 1. __________
Q18. Rational numbers are closed under division. __________
Q19. The product of two negative rational numbers is always negative. __________
Q20. Between 0 and 1, there are exactly ten rational numbers. __________

Section D: Short Answer Questions (3 Marks Each)

Short-answer questions require you to show complete working and provide explanations where needed. Each question is worth 3 marks, so marks are typically distributed as: 1 mark for method, 1 mark for correct calculation, and 1 mark for the final answer in standard form. Write all steps neatly and logically. Do not skip steps, as partial credit is awarded based on the correctness of your method even if the final answer is wrong. These questions test your ability to apply concepts of rational numbers to solve numerical problems involving addition, subtraction, multiplication, division, finding inverses, simplifying expressions, and using properties of rational numbers. Always write your final answer in standard form (positive denominator, fully reduced fraction). If the question asks for a property, state the property name clearly and illustrate with the given numbers. Use proper mathematical notation and avoid ambiguous expressions. If you make a calculation error, cross it out neatly and rewrite; examiners appreciate clear corrections. This section is the backbone of your internal assessments and term exams, so practice these types of questions extensively. Time management is key: allocate about 4-5 minutes per 3-mark question during the actual exam.

Q21. Find the sum: 3/4 + (-5/6). Express your answer in standard form. (3 marks)
Q22. Multiply 7/9 by the reciprocal of -3/5. Simplify your answer. (3 marks)
Q23. Verify the commutative property of addition for the rational numbers -2/3 and 5/7. (3 marks)
Q24. What should be added to -5/8 to get 3/4? (3 marks)
Q25. Represent the following rational numbers on a number line: 3/2, -1/2, 5/4. (3 marks)

Section E: Long Answer and HOTS Questions (5 Marks Each)

Long-answer questions are worth 5 marks each and test higher-order thinking skills (HOTS), multi-step problem solving, and the ability to apply multiple concepts in one question. These questions often combine operations, properties, and real-world reasoning. Marks are distributed across method, logical steps, intermediate calculations, and final answer, so every line of working counts. Start by reading the question twice to fully understand what is being asked. Break the problem into smaller parts and solve step by step. Use properties of rational numbers wherever applicable and state them explicitly (for example, 'using distributive property' or 'applying closure property'). If the question involves proving or verifying a statement, clearly show both sides of the equation or inequality and conclude with a statement like 'Hence verified' or 'Hence proved'. These questions are designed to differentiate high-scoring students from average performers, so invest time in practicing HOTS questions from NCERT exemplar and previous years' CBSE papers. Always write your final answer in a box or underline it clearly. Allocate about 7-8 minutes per 5-mark question during exams, and do not rush. Logical clarity is more important than speed in long-answer questions.

Q26. Simplify: [(2/3 + 5/6) × 4/5] - [1/2 ÷ 3/4]. Show all steps. (5 marks)
Q27. Find five rational numbers between -1/3 and 2/5 using the method of finding equivalent fractions. (5 marks)
Q28. If the sum of two rational numbers is -3/4 and one of them is 5/8, find the other number. Verify your answer by adding. (5 marks)

Case-Study Based Question (4 Marks)

Case-study questions are a recent addition to the CBSE exam pattern and test your ability to apply mathematical concepts to real-world scenarios. Read the case study carefully, understand the context, and extract the relevant numerical data. Then answer the sub-questions that follow. Marks are distributed as 1 mark for each part, so even if you cannot solve one part, attempt the others. Case studies often involve practical situations like sharing resources, measuring quantities, comparing ratios, planning budgets, or analyzing data—all requiring operations on rational numbers. The key skill tested here is reading comprehension combined with mathematical reasoning. Underline or highlight important numbers and relationships in the passage. Draw diagrams or tables if that helps you visualize the problem. Write your answers clearly, showing working wherever required. These questions prepare you for competitive exams and real-life problem-solving beyond the classroom. They also align with the National Education Policy (NEP) 2020 emphasis on application-based learning. Practising case-study questions from sample papers and CBSE question banks will boost your confidence and scoring ability significantly. Allocate about 6-7 minutes for the entire case-study question during your exam.

Complete Answer Key with Explanations

This section provides detailed answers to all questions in the worksheet, complete with step-by-step working and brief explanations. Use this answer key for self-assessment after attempting the worksheet on your own. Do not refer to the answers while solving the questions; that defeats the purpose of practice. After completing the worksheet, check your answers one by one, and for every mistake, try to understand where you went wrong. Was it a calculation error, a conceptual misunderstanding, or a careless mistake? Write down your mistakes in a separate notebook and redo those questions after a few days. This reflective practice is one of the most effective ways to learn and retain concepts. If you are a parent or teacher, use this answer key to provide immediate feedback and guide the student through corrections. The explanations are written in simple language aligned with NCERT Class 8 Mathematics terminology, so students can follow along independently. For complex questions, multiple methods are sometimes provided to show alternative approaches. Remember, mathematics is not just about getting the right answer—it is about understanding the reasoning and logic behind each step. Consistent practice with this kind of detailed feedback will ensure steady improvement and build the confidence needed to excel in CBSE Class 8 Mathematics exams and beyond.

Section A Answers: Q1(c), Q2(a), Q3(b), Q4(b), Q5(b), Q6(b), Q7(b) — with explanations
Section B Answers: Q8: rational, Q9: 0, Q10: 8/5, Q11: infinitely many, Q12: -2/3, Q13: closed, Q14: 1
Section C Answers: Q15: True, Q16: True, Q17: False, Q18: False, Q19: False, Q20: False
Section D Answers: Full working for Q21-Q25 with marks breakdown
Section E Answers: Full working for Q26-Q28 with marks breakdown
Case-Study Answers: Step-by-step solutions for all four parts with marks

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Mastering CBSE Class 8 Mathematics Chapter 1 Rational Numbers requires more than just solving worksheets—it needs personalized guidance, instant doubt-clearing, and adaptive practice. CBSETUTOR.ai is your 24×7 AI tutor designed specifically for CBSE students from Classes 6 to 12. Simply snap a photo of any problem from your NCERT textbook, worksheet, or exam paper, and get step-by-step solutions with detailed explanations in seconds. Whether you struggle with finding LCM for adding rational numbers, understanding properties, or solving HOTS questions, CBSETUTOR.ai breaks down each concept into bite-sized, easy-to-understand steps. The platform offers unlimited practice questions, chapter-wise tests, and instant feedback—all tailored to the latest CBSE syllabus and NCERT guidelines. Unlike expensive tuition classes that cost thousands per month, CBSETUTOR.ai offers all these features at just ₹999 per month for all subjects and all chapters, with a risk-free 3-day free trial so you can experience the power of AI-driven learning before committing. Parents love the transparency and progress tracking, while students appreciate the flexibility to learn anytime, anywhere, at their own pace. Join thousands of CBSE students who have already improved their marks and confidence with CBSETUTOR.ai—your always-available math companion.

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Frequently asked questions

What is the standard form of a rational number?+

A rational number p/q is in standard form when the denominator q is positive and the HCF of the numerator p and denominator q is 1. For example, -2/3 is in standard form, but 2/-3 or -4/6 are not.

How do I add two rational numbers with different denominators?+

Find the LCM of the denominators, convert both rational numbers to equivalent fractions with that LCM as the common denominator, then add the numerators and simplify. For example, to add 2/3 and 3/5, LCM is 15, so 10/15 + 9/15 = 19/15.

What is the difference between additive inverse and multiplicative inverse?+

The additive inverse of a/b is -a/b, and their sum is 0 (additive identity). The multiplicative inverse (reciprocal) of a/b is b/a, and their product is 1 (multiplicative identity). Do not confuse the two.

Can zero be the denominator of a rational number?+

No, zero can never be the denominator because division by zero is undefined in mathematics. By definition, a rational number is p/q where q ≠ 0. However, zero can be the numerator, giving the rational number 0.

How many rational numbers lie between any two rational numbers?+

Infinitely many rational numbers lie between any two given rational numbers. For example, between 1/2 and 1, you can find 3/4, 5/8, 11/16, and countless others by finding equivalent fractions or taking averages.

What are the properties of rational numbers I must remember for CBSE exams?+

Remember closure (addition, subtraction, multiplication—but not division), commutativity (addition and multiplication), associativity (addition and multiplication), and distributivity (multiplication over addition). Also know the identities (0 for addition, 1 for multiplication) and inverses.

How do I divide one rational number by another?+

To divide a/b by c/d, multiply a/b by the reciprocal of c/d. So (a/b) ÷ (c/d) = (a/b) × (d/c) = (ad)/(bc). Remember to simplify your answer to standard form and ensure the denominator is positive.

Why is this worksheet important for Class 8 Mathematics exams?+

Rational Numbers is a fundamental chapter that forms the base for algebra, linear equations, and higher mathematics. This worksheet covers all question types—MCQs, short answers, long answers, and case studies—matching the exact CBSE exam pattern, ensuring thorough preparation and better marks.

How much time should I spend on this worksheet?+

The suggested time is 90 minutes under exam conditions. However, when practicing for the first time, take your time to understand each question. Speed will improve with regular practice. Aim to complete it in one sitting to simulate exam pressure.

Can I use this worksheet for homework or school assignments?+

Absolutely. This worksheet is designed for versatile use—homework, classroom tests, weekend revision, or self-study. Teachers can print and distribute it, and parents can use it to track their child's progress. The detailed answer key makes it ideal for independent practice at home.

Related resources

Important Questions: CBSE Class 8 Mathematics Chapter 1 Rational Numbers Class 8 Mathematics Chapter 1 Rational Numbers — Formulas & Key Points Rational Numbers for Class 8: The Complete CBSE Guide (2026-27)Linear Equations in One Variable for Class 8: The Complete CBSE Guide (2026-27)AI Tutor for Class 8: The Smart Alternative to Tuition AI Tutor for Class 8 Social Science: Learn Faster with Instant Help NCERT Solutions for Class 9 Mathematics Chapter 1: Number Systems – Complete Guide CBSE Class 9 Mathematics Chapter 1 Number Systems Worksheet with Answers

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