Rational Numbers MCQs with solutions based on properties operations and number line concepts
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 Class 8 Maths Chapter 1 Rational Numbers MCQ Questions with Answers
1. What are rational numbers in Class 8 Maths Chapter 1?
A rational number is any number that can be written in the form p/q, where p and q are integers and q ≠ 0. In Class 8 Maths Chapter 1, rational numbers include positive fractions, negative fractions, whole numbers, and zero.
- Examples: 3/4, -5/7, 2 (since 2 = 2/1), 0 (since 0 = 0/1)
- The denominator can never be zero.
2. How do you find the reciprocal of a rational number?
The reciprocal of a rational number p/q is q/p, provided p ≠ 0. To find the reciprocal, simply interchange the numerator and denominator.
- Example: Reciprocal of 3/5 is 5/3.
- Reciprocal of -7/4 is -4/7.
- Zero has no reciprocal because division by zero is not defined.
3. What is the standard form of a rational number?
A rational number is in standard form when its denominator is positive and the numerator and denominator have no common factor other than 1. This means the fraction is in its simplest form.
- Example: 6/8 is not in standard form.
- Simplify: 6/8 = 3/4, which is the standard form.
4. How do you add rational numbers?
To add rational numbers, first make the denominators equal, then add the numerators and simplify. Follow these steps:
- Find the LCM of the denominators.
- Convert fractions to like denominators.
- Add numerators and keep the same denominator.
- Simplify the result.
5. How do you subtract rational numbers?
To subtract rational numbers, convert them into like fractions and subtract the numerators. The denominator remains the same.
- Example: 5/6 − 1/4
- LCM of 6 and 4 is 12.
- Convert: 5/6 = 10/12 and 1/4 = 3/12
- Subtract: 10/12 − 3/12 = 7/12
6. What are the properties of rational numbers?
Rational numbers follow important mathematical properties such as closure, commutative, associative, and distributive properties. Key properties include:
- Closure property: The sum, difference, and product of rational numbers is always rational.
- Commutative property: a + b = b + a and a × b = b × a.
- Associative property: (a + b) + c = a + (b + c).
- Distributive property: a × (b + c) = a×b + a×c.
7. How do you multiply rational numbers?
To multiply rational numbers, multiply the numerators together and the denominators together, then simplify. The formula is (a/b) × (c/d) = (ac)/(bd).
- Example: (2/3) × (5/7) = 10/21
- Since 10 and 21 have no common factor, the final answer is 10/21.
8. How do you divide rational numbers?
To divide rational numbers, multiply the first fraction by the reciprocal of the second fraction. The formula is (a/b) ÷ (c/d) = (a/b) × (d/c).
- Example: (3/4) ÷ (2/5)
- Take reciprocal of 2/5 → 5/2
- Multiply: (3/4) × (5/2) = 15/8
- Final answer: 15/8
9. What is the additive inverse of a rational number?
The additive inverse of a rational number is the number that when added to it gives 0. It is obtained by changing the sign of the number.
- Example: Additive inverse of 5/7 is -5/7.
- Because 5/7 + (−5/7) = 0.
10. How do MCQs from Class 8 Maths Chapter 1 Rational Numbers usually come?
MCQs from Class 8 Maths Chapter 1 Rational Numbers usually test concepts like properties, standard form, operations, and reciprocals. Common question types include:
- Finding the reciprocal or additive inverse
- Identifying the correct standard form
- Solving addition, subtraction, multiplication, or division
- Checking properties like commutative or distributive property
