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Practice Class 8 Maths Chapter 1 Rational Numbers MCQ Questions with Answers based on NCERT syllabus. Learn rational numbers, 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: Moderate to Difficult
Based On: NCERT Latest Syllabus
Introduction:
Rational Numbers is a fundamental chapter in Class 8 Mathematics that introduces students to fractions, integers, and their properties. A strong understanding of rational numbers develops mathematical reasoning and problem-solving skills.
What You Will Learn?
✔ Rational Numbers
✔ Additive Inverse
✔ Multiplicative Inverse
✔ Closure Property
✔ Commutative Property
✔ Associative Property
✔ Distributive Property
✔ Operations on Rational Numbers
Why This Topic Is Important?
Rational numbers are widely used in mathematics, science, and everyday calculations. Understanding their properties helps students build a strong foundation for algebra and higher mathematics.
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:
$$\frac{-15}{20}$$ ?
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:
Simplify:
$$\frac{-15}{20}=-\frac{3}{4}$$
Also,
$$\frac{3}{-4}=-\frac{3}{4}$$
and
$$\frac{-6}{8}=-\frac{3}{4}$$
Therefore, all the given fractions are equivalent.
Hence, the correct answer is:
All of these
Exam Tip:
Equivalent fractions represent the same rational number.
Q2. Simplify:
$$-\frac{7}{12}+\frac{5}{18}$$
A) $$-\frac{11}{36}$$
B) $$\frac{11}{36}$$
C) $$-\frac{1}{36}$$
D) $$\frac{1}{36}$$
Answer:
$$-\frac{11}{36}$$
Useful Formula for this Question:
For addition:
$$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$$
Concept Behind This Question:
Students should add rational numbers with unlike denominators.
Step-by-Step Solution:
LCM of:
$$12$$
and
$$18$$
is
$$36$$
Convert:
$$-\frac{7}{12}=-\frac{21}{36}$$
$$\frac{5}{18}=\frac{10}{36}$$
Now,
$$-\frac{21}{36}+\frac{10}{36}=-\frac{11}{36}$$
Therefore, the correct answer is:
$$-\frac{11}{36}$$
Exam Tip:
Always convert unlike fractions into like fractions before addition.
Q3. What is the multiplicative inverse of:
$$\frac{-13}{7}$$ ?
A) $$-\frac{7}{13}$$
B) $$\frac{7}{13}$$
C) $$-\frac{13}{7}$$
D) $$0$$
Answer:
$$-\frac{7}{13}$$
Useful Formula for this Question:
The multiplicative inverse of:
$$\frac{a}{b}$$
is
$$\frac{b}{a}$$
Concept Behind This Question:
Students should know how to find reciprocals.
Step-by-Step Solution:
Given number:
$$\frac{-13}{7}$$
Interchanging numerator and denominator gives:
$$-\frac{7}{13}$$
Verification:
$$\frac{-13}{7}\times\left(-\frac{7}{13}\right)=1$$
Therefore, the correct answer is:
$$-\frac{7}{13}$$
Exam Tip:
The sign of a rational number remains unchanged in its reciprocal.
Q4. Which property is represented by:
$$a+b=b+a$$
A) Associative Property
B) Closure Property
C) Commutative Property
D) Distributive Property
Answer:
Commutative Property
Useful Formula for this Question:
$$a+b=b+a$$
Concept Behind This Question:
Students should identify properties of rational numbers.
Step-by-Step Solution:
The order of numbers changes, but the sum remains the same.
Example:
$$4+7=7+4=11$$
Hence, the given expression represents the commutative property.
Therefore, the correct answer is:
Commutative Property
Exam Tip:
Commutative property changes order but not the result.
Q5. Simplify:
$$\frac{9}{14}\times\left(-\frac{7}{18}\right)$$
A) $$-\frac{1}{4}$$
B) $$\frac{1}{4}$$
C) $$-\frac{3}{4}$$
D) $$\frac{3}{4}$$
Answer:
$$-\frac{1}{4}$$
Useful Formula for this Question:
For multiplication:
$$\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}$$
Concept Behind This Question:
Students should multiply rational numbers correctly.
Step-by-Step Solution:
$$\frac{9}{14}\times\left(-\frac{7}{18}\right)$$
Cancelling common factors:
$$=\frac{1}{2}\times\left(-\frac{1}{2}\right)$$
$$=-\frac{1}{4}$$
Therefore, the correct answer is:
$$-\frac{1}{4}$$
Exam Tip:
Use cross-cancellation before multiplication to simplify calculations.
Important Formulas & Concepts
1. Rational Numbers
$$\frac{p}{q}, \quad q\ne0$$
2. Additive Identity
$$a+0=a$$
3. Multiplicative Identity
$$a\times1=a$$
4. Additive Inverse
$$\frac{a}{b}+\left(-\frac{a}{b}\right)=0$$
5. Multiplicative Inverse
$$\frac{a}{b}\times\frac{b}{a}=1,\quad a\ne0,\ b\ne0$$
6. Closure Property
Rational numbers are closed under addition, subtraction, and multiplication.
FAQs
1. What is a rational number?
A rational number can be expressed as:
$$\frac{p}{q}, \quad q\ne0$$
2. Does every rational number have a reciprocal?
No, zero does not have a reciprocal.
3. What is the additive identity?
The additive identity is:
$$0$$
because
$$a+0=a$$
4. What is the multiplicative identity?
The multiplicative identity is:
$$1$$
because
$$a\times1=a$$
5. Are rational numbers closed under subtraction?
Yes, the difference of two rational numbers is always a rational number.
Common Mistakes
❌ Ignoring negative signs.
❌ Dividing by zero.
❌ Confusing reciprocal with additive inverse.
❌ Not simplifying fractions.
❌ Forgetting cross-cancellation.
Quick Revision Notes
✔ Rational numbers are written as:
$$\frac{p}{q}$$
✔ Every integer is a rational number.
✔ Zero has no reciprocal.
✔ Rational numbers satisfy closure property.
✔ Division by zero is not defined.
Conclusion
Rational Numbers is an important chapter in Class 8 Mathematics. Understanding the properties and operations of rational numbers helps students solve problems efficiently and build a strong mathematical foundation. Regular MCQ practice improves accuracy, confidence, and exam performance.
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