Solved Multiple Choice Questions on Rational Numbers for Class 8
The concept of Class 8 Maths Chapter 1 Rational Numbers MCQs is essential in mathematics and helps students prepare for exams using objective-type questions. Practicing rational numbers MCQs sharpens problem-solving skills and brings clarity about number properties, calculations, and logic.
Understanding Class 8 Maths Chapter 1 Rational Numbers MCQs
Rational numbers are numbers that can be written in the form p/q, where p and q are integers and q ≠ 0. In Class 8 Maths Chapter 1, students learn to identify, compare, add, subtract, multiply, and divide rational numbers. Practicing MCQ questions targets exam speed, error reduction, and correct understanding of the difference between rational, irrational, fraction, and integer numbers.
Key Points and Formulae Used in Rational Numbers
The main properties and formulas used in rational numbers are:
2. Additive Identity: 0
3. Multiplicative Identity: 1
4. Reciprocal: If a/b, reciprocal is b/a (a, b ≠ 0)
5. Closure, Commutative, and Associative properties (for addition and multiplication)
Here’s a helpful table to understand different properties of Class 8 rational numbers MCQs more clearly:
Properties of Rational Numbers Table
| Property | Addition | Multiplication | Subtraction | Division |
|---|---|---|---|---|
| Closure | Yes | Yes | Yes | No (Division by 0 not allowed) |
| Commutative | Yes | Yes | No | No |
| Associative | Yes | Yes | No | No |
| Identity | 0 | 1 | 0 | 1 |
This table helps students see which arithmetic operations on rational numbers follow common properties and which do not.
Class 8 Maths Chapter 1 Rational Numbers – Solved MCQs
Practice these important MCQs for Class 8 Maths Chapter 1 Rational Numbers. Answers and explanations are given after each question for better clarity.
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1. An integer can be:
A. Only Positive
B. Only Negative
C. Both positive and negative
D. None of the above
Answer: C
Explanation: Integers include both positive and negative numbers (…,-3,-2,-1,0,1,2,3,…)
2. A rational number can be represented in the form:
A. p/q
B. pq
C. p+q
D. p-q
Answer: A
Explanation: Rational numbers have the form p/q, where p, q are integers, q ≠ 0.
3. The value of ½ × ⅗ is:
A. ½
B. 3/10
C. ⅗
D. ⅖
Answer: B
Explanation: (1/2) × (3/5) = 3/10
4. (½) ÷ (⅗) = ?
A. 3/10
B. ⅗
C. 6/5
D. ⅚
Answer: D
Explanation: (1/2) ÷ (3/5) = (1/2) × (5/3) = 5/6 or ⅚
5. The additive identity of rational numbers is:
A. 0
B. 1
C. -1
D. 2
Answer: A
Explanation: Any number + 0 = the number itself.
6. What is the sum of ⅔ and 4/9?
A. 6/3
B. 6/9
C. 10/9
D. 10/3
Answer: C
Step 1: \(2/3 + 4/9 = (2×3)/(3×3) + 4/9 = 6/9 + 4/9 = 10/9\)
7. The reciprocal of 1/9 is:
A. 9
B. 1
C. 0
D. None of these
Answer: A
Explanation: 1/9 × 9 = 1
8. Which of the following is commutative for rational numbers?
A. Addition and subtraction
B. Addition and multiplication
C. Multiplication and division
D. Subtraction and division
Answer: B
Explanation: Addition and multiplication are commutative.
9. Find the additive inverse of 11/7.
A. 7/11
B. -7/11
C. 11/7
D. -11/7
Answer: D
Explanation: Additive inverse of a/b is -a/b.
10. What is the value of 100 divided by 0?
A. 0
B. 100
C. 1
D. Undefined
Answer: D
Explanation: Division by zero is undefined.
Step-by-Step Solutions – Examples
Let’s solve a sample rational number question step by step.
1. What is the sum of 2/3 and 4/9?Step 1: Find LCM of denominators 3 and 9 = 9.
Step 2: Convert 2/3 to denominator 9: (2/3) × (3/3) = 6/9
Step 3: Now, 6/9 + 4/9 = 10/9.
Final Answer: 10/9
2. What should be subtracted from -2/3 to get -1?
Step 1: Let x be the number to subtract.
-2/3 – x = -1
Step 2: Rearranged: -2/3 + 1 = x
Step 3: x = 1 - 2/3 = (3/3) - (2/3) = (1/3)
Final Answer: 1/3
Common Mistakes to Avoid
- Assuming all fractions are rational numbers without checking if the denominator is zero.
- Dividing by zero in MCQs (always undefined).
- Confusing associative, commutative, and closure properties for all operations.
- Mixing up reciprocal and additive inverse.
Quick Answer Key Table
| Q. No. | Correct Answer |
|---|---|
| 1 | C |
| 2 | A |
| 3 | B |
| 4 | D |
| 5 | A |
| 6 | C |
| 7 | A |
| 8 | B |
| 9 | D |
| 10 | D |
Tips for Class 8 Rational Numbers MCQs
- Always check if a number is in p/q form with q ≠ 0 before calling it rational.
- Memorise identities: 0 is the additive identity, 1 is the multiplicative identity.
- Be cautious with division and order of operations (BODMAS).
- Revisit properties before exams: closure, commutative, associative, and distributive laws.
- Practice time-bound MCQs for board-style questions.
Practice Problems – More for You
- Is 0 a rational number?
- Express -7/8 as a rational number.
- Which of these is NOT a rational number: 4/7, 3/0, -11/9?
- What is the product of -2/5 and 3?
- Find a rational number between 1/2 and 3/4.
Related Resources
- Rational Numbers - Class 8 Core Concepts
- Difference Between Fraction and Rational Number
- Rational Numbers Worksheet
- Decimal Expansion of Rational Numbers
- Comparison of Rational Numbers
- Operations on Rational Numbers
- Number System MCQs
- Multiplying Fractions
- Types of Numbers
- Difference Between Rational and Irrational Numbers
- Numbers
- Fractions
We explored the idea of Class 8 Maths Chapter 1 Rational Numbers MCQs, how to solve them with step-by-step examples, tips for exams, and common mistakes to avoid. Practice regularly and use resources from Vedantu for improved exam results.
FAQs on MCQs on Rational Numbers: Class 8 Maths Chapter 1 Practice
Q1: What are rational numbers with examples for Class 8?
A rational number is any number that can be expressed as a fraction p/q, where p and q are integers and q ≠ 0. Examples include 1/2, -3/4, 0, and 5 (since 5 = 5/1). Rational numbers can be positive, negative, or zero.
Q2: How to distinguish rational and irrational numbers in MCQs?
To distinguish rational and irrational numbers in MCQs: Rational numbers have decimal expansions that are either terminating or recurring, and can be written as fractions p/q. Irrational numbers cannot be expressed as fractions and have non-terminating, non-repeating decimals. Examples of irrational numbers include √2 and π.
Q3: Which is the correct definition of a rational number?
A rational number is defined as any number that can be expressed in the form p/q, where p and q are integers, and q ≠ 0. This definition includes all integers, fractions, and finite or recurring decimals.
Q4: Can you provide solved MCQs from Chapter 1 Rational Numbers?
Yes, the page offers a series of solved MCQs on rational numbers from Chapter 1, each with four options and detailed step-by-step explanations. These help students practice and understand concepts such as number operations, properties, and definitions aligned with the NCERT syllabus.
Q5: How do I download a PDF of Class 8 Maths MCQ Chapter 1?
You can download the PDF of Class 8 Maths Chapter 1 Rational Numbers MCQs by clicking on the provided download link or button on the page. This PDF allows for offline revision and easy printing, supporting mobile and daily study needs.
Q6: Why do students confuse rational numbers with fractions in board questions?
Students often confuse rational numbers with fractions because all fractions are rational numbers, but not all rational numbers are simple fractions. For example, integers like 5 and terminating decimals like 0.75 are rational but not fractions shown in standard form. Clarifying this helps avoid mistakes in MCQs.
Q7: Why is 0 considered a rational number in MCQs?
Zero (0) is considered a rational number because it can be expressed as 0/1 (or 0/q, with q ≠ 0). It fits the definition of rational numbers being expressible as p/q, where both are integers and the denominator is non-zero.
Q8: What are common mistakes students make in rational number MCQs?
Common mistakes include:
1. Confusing irrational numbers as rational.
2. Forgetting that the denominator cannot be zero.
3. Misapplying properties like associativity to division.
4. Mixing up additive and multiplicative identities.
5. Ignoring sign rules when multiplying or dividing rational numbers.
Q9: Why do examiners include 'None of these' in rational number MCQs?
The option 'None of these' is included to test students' careful evaluation and to reduce guessing. It encourages learners to verify calculations instead of selecting the closest option, improving accuracy and critical thinking in rational number problems.
Q10: How do online MCQ tests support exam time management?
Online MCQ tests help students manage exam time by:
1. Providing instant feedback for quick corrections.
2. Simulating exam conditions with timed quizzes.
3. Allowing repeated practice to increase familiarity.
4. Enabling learning on mobile devices anywhere.
These features enhance speed and accuracy for board exam success.
