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Practice Class 8 Maths Chapter 1 Rational Numbers MCQ Questions with Answers based on NCERT syllabus. Learn properties of rational numbers, additive inverse, multiplicative inverse, and operations on rational numbers with detailed solutions for CBSE exams.
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Chapter Information
Subject: Mathematics
Class: 8
Chapter: Rational Numbers
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Easy to Moderate
Based On: NCERT Latest Syllabus
Introduction:
Rational Numbers is an important chapter in Class 8 Mathematics that deals with the properties and operations of rational numbers. Understanding these concepts helps students solve mathematical problems efficiently and develop a strong foundation for advanced topics.
What You Will Learn?
✔ Rational Numbers
✔ Properties of Rational Numbers
✔ Additive Inverse
✔ Multiplicative Inverse
✔ Operations on Rational Numbers
✔ Closure Property
✔ Distributive Property
✔ Problem-Solving Skills
Why This Topic Is Important?
Rational numbers are widely used in mathematics and daily life. Learning their properties and operations improves logical reasoning and computational skills.
Exam Relevance
These questions are useful for:
✔ CBSE Exams
✔ State Board Exams
✔ School Tests
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. Which of the following rational numbers is equal to:
$$-\frac{3}{4}$$ ?
A) $$\frac{3}{-4}$$
B) $$-\frac{3}{4}$$
C) $$\frac{-6}{8}$$
D) All of these
Answer:
All of these
Useful Formula for this Question:
Equivalent rational numbers have the same value.
Concept Behind This Question:
Students should identify equivalent rational numbers.
Step-by-Step Solution:
$$\frac{3}{-4}=-\frac{3}{4}$$
Also,
$$\frac{-6}{8}=\frac{-3}{4}$$
Thus, all the given numbers are equal to:
$$-\frac{3}{4}$$
Hence, the correct answer is:
All of these
Exam Tip:
Multiplying or dividing the numerator and denominator by the same non-zero number gives an equivalent rational number.
Q2. Find:
$$\frac{2}{5}+\frac{3}{10}$$
A) $$\frac{1}{2}$$
B) $$\frac{7}{10}$$
C) $$\frac{9}{10}$$
D) $$\frac{1}{10}$$
Answer:
$$\frac{7}{10}$$
Useful Formula for this Question:
For addition of fractions:
$$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$$
Concept Behind This Question:
Students should add rational numbers using a common denominator.
Step-by-Step Solution:
LCM of $$5$$ and $$10$$ is:
$$10$$
Therefore,
$$\frac{2}{5}=\frac{4}{10}$$
Now,
$$\frac{4}{10}+\frac{3}{10}=\frac{7}{10}$$
Hence, the correct answer is:
$$\frac{7}{10}$$
Exam Tip:
Convert fractions into like fractions before addition.
Q3. Find the multiplicative inverse of:
$$\frac{9}{-11}$$
A) $$-\frac{11}{9}$$
B) $$\frac{11}{9}$$
C) $$-\frac{9}{11}$$
D) $$\frac{9}{11}$$
Answer:
$$-\frac{11}{9}$$
Useful Formula for this Question:
The multiplicative inverse of:
$$\frac{a}{b}$$
is
$$\frac{b}{a}$$
Concept Behind This Question:
Students should find the reciprocal of rational numbers.
Step-by-Step Solution:
Given number:
$$\frac{9}{-11}=-\frac{9}{11}$$
Interchanging numerator and denominator gives:
$$-\frac{11}{9}$$
Verification:
$$-\frac{9}{11}\times-\frac{11}{9}=1$$
Therefore, the correct answer is:
$$-\frac{11}{9}$$
Exam Tip:
The sign of the rational number remains unchanged in its reciprocal.
Q4. Which of the following statements is true?
A) Rational numbers are not closed under addition.
B) Rational numbers are closed under multiplication.
C) Rational numbers are not closed under subtraction.
D) Rational numbers are not closed under division.
Answer:
Rational numbers are closed under multiplication.
Useful Formula for this Question:
If the operation on two rational numbers gives another rational number, then the set is closed under that operation.
Concept Behind This Question:
Students should understand the closure property of rational numbers.
Step-by-Step Solution:
Rational numbers are closed under:
✔ Addition
✔ Subtraction
✔ Multiplication
✔ Division (except division by zero)
Thus, the true statement is:
Rational numbers are closed under multiplication.
Hence, the correct answer is:
Option B
Exam Tip:
Division by zero is not defined.
Q5. Simplify:
$$-\frac{7}{8}\times\frac{4}{21}$$
A) $$-\frac{1}{6}$$
B) $$\frac{1}{6}$$
C) $$-\frac{2}{3}$$
D) $$\frac{2}{3}$$
Answer:
$$-\frac{1}{6}$$
Useful Formula for this Question:
For multiplication:
$$\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}$$
Concept Behind This Question:
Students should multiply and simplify rational numbers.
Step-by-Step Solution:
$$-\frac{7}{8}\times\frac{4}{21}$$
Cancelling common factors:
$$=-\frac{1}{2}\times\frac{1}{3}$$
$$=-\frac{1}{6}$$
Therefore, the correct answer is:
$$-\frac{1}{6}$$
Exam Tip:
Use cross-cancellation to simplify calculations.
Important Formulas & Concepts
1. Rational Numbers
$$\frac{p}{q}, \quad q\ne0$$
2. Additive Inverse
$$\frac{a}{b}+\left(-\frac{a}{b}\right)=0$$
3. Multiplicative Inverse
$$\frac{a}{b}\times\frac{b}{a}=1,\quad a\ne0,\ b\ne0$$
4. Closure Property
Rational numbers are closed under:
✔ Addition
✔ Subtraction
✔ Multiplication
✔ Division (except by zero)
5. Distributive Property
$$a(b+c)=ab+ac$$
FAQs
1. What are equivalent rational numbers?
Equivalent rational numbers have the same value but different forms.
2. Does every rational number have a reciprocal?
Yes, except zero.
3. Are rational numbers closed under multiplication?
Yes, the product of two rational numbers is always a rational number.
4. Is division by zero defined?
No, division by zero is not defined.
5. Can a negative rational number have a positive reciprocal?
No, the reciprocal of a negative rational number is also negative.
Common Mistakes
❌ Forgetting to take LCM while adding fractions.
❌ Dividing by zero.
❌ Ignoring negative signs.
❌ Not simplifying fractions completely.
❌ Confusing reciprocal with additive inverse.
Quick Revision Notes
✔ Rational numbers can be written as:
$$\frac{p}{q}$$
✔ Zero has no reciprocal.
✔ Rational numbers are closed under addition and multiplication.
✔ Equivalent fractions represent the same value.
✔ Reciprocal means multiplicative inverse.
Conclusion
Rational Numbers is a fundamental chapter in Class 8 Mathematics. Mastering the properties and operations of rational numbers helps students solve problems quickly and accurately. Regular MCQ practice strengthens concepts and boosts exam performance.
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