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Practice Class 8 Maths Chapter 1 Rational Numbers MCQ Questions with Answers based on NCERT syllabus. Learn rational numbers, additive inverse, multiplicative inverse, closure property, 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 the properties and operations of rational numbers. Understanding these concepts develops logical reasoning and strengthens the foundation for higher mathematics.
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 daily life calculations. Mastering this chapter improves computational skills and problem-solving abilities.
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 equivalent to:
$$\frac{3}{5}$$ ?
A) $$\frac{6}{10}$$
B) $$\frac{9}{15}$$
C) $$\frac{12}{20}$$
D) All of these
Answer:
All of these
Useful Formula for this Question:
Equivalent rational numbers are obtained by multiplying or dividing the numerator and denominator by the same non-zero integer.
Concept Behind This Question:
Students should identify equivalent rational numbers.
Step-by-Step Solution:
$$\frac{6}{10}=\frac{3}{5}$$
$$\frac{9}{15}=\frac{3}{5}$$
$$\frac{12}{20}=\frac{3}{5}$$
Therefore, all the given fractions are equal to:
$$\frac{3}{5}$$
Hence, the correct answer is:
All of these
Exam Tip:
Equivalent fractions represent the same rational number.
Q2. Simplify:
$$\frac{7}{15}+\frac{2}{5}$$
A) $$\frac{13}{15}$$
B) $$\frac{11}{15}$$
C) $$\frac{9}{15}$$
D) $$\frac{1}{15}$$
Answer:
$$\frac{13}{15}$$
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 using like fractions.
Step-by-Step Solution:
Convert:
$$\frac{2}{5}=\frac{6}{15}$$
Now,
$$\frac{7}{15}+\frac{6}{15}=\frac{13}{15}$$
Therefore, the correct answer is:
$$\frac{13}{15}$$
Exam Tip:
Convert unlike fractions into like fractions before addition.
Q3. Which of the following statements is false?
A) Every integer is a rational number.
B) Rational numbers are closed under multiplication.
C) Zero has a multiplicative inverse.
D) Rational numbers are closed under addition.
Answer:
Zero has a multiplicative inverse.
Useful Formula for this Question:
A multiplicative inverse exists only for non-zero rational numbers.
Concept Behind This Question:
Students should understand multiplicative inverse.
Step-by-Step Solution:
- Every integer can be written as:
$$\frac{n}{1}$$
Hence, integers are rational numbers.
- Rational numbers are closed under addition and multiplication.
- Zero does not have a multiplicative inverse because:
$$\frac{1}{0}$$
is undefined.
Therefore, the false statement is:
“Zero has a multiplicative inverse.”
Hence, the correct answer is:
Option C
Exam Tip:
Always remember that zero has no reciprocal.
Q4. Simplify:
$$-\frac{4}{9}\times\left(-\frac{3}{8}\right)$$
A) $$\frac{1}{6}$$
B) $$-\frac{1}{6}$$
C) $$\frac{3}{4}$$
D) $$-\frac{3}{4}$$
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 apply sign rules and multiplication of rational numbers.
Step-by-Step Solution:
$$-\frac{4}{9}\times\left(-\frac{3}{8}\right)$$
Positive sign because negative × negative = positive.
$$=\frac{12}{72}$$
$$=\frac{1}{6}$$
Therefore, the correct answer is:
$$\frac{1}{6}$$
Exam Tip:
The product of two negative numbers is positive.
Q5. Find:
$$\frac{5}{6}\div\left(-\frac{10}{9}\right)$$
A) $$-\frac{3}{4}$$
B) $$\frac{3}{4}$$
C) $$-\frac{4}{3}$$
D) $$\frac{4}{3}$$
Answer:
$$-\frac{3}{4}$$
Useful Formula for this Question:
For division:
$$\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}$$
Concept Behind This Question:
Students should divide rational numbers using reciprocals.
Step-by-Step Solution:
$$\frac{5}{6}\div\left(-\frac{10}{9}\right)$$
$$=\frac{5}{6}\times\left(-\frac{9}{10}\right)$$
Cancelling common factors:
$$=-\frac{1}{2}\times\frac{3}{2}$$
$$=-\frac{3}{4}$$
Therefore, the correct answer is:
$$-\frac{3}{4}$$
Exam Tip:
Convert division into multiplication by taking the reciprocal of the divisor.
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. Distributive Property
$$a(b+c)=ab+ac$$
FAQs
1. What is a rational number?
A rational number can be expressed as:
$$\frac{p}{q}, \quad q\ne0$$
2. Does zero have a reciprocal?
No, zero does not have a reciprocal.
3. Can rational numbers be negative?
Yes, rational numbers can be positive, negative, or zero.
4. Are rational numbers closed under subtraction?
Yes, the difference of two rational numbers is always a rational number.
5. Are all fractions rational numbers?
Yes, if the denominator is not zero.
Common Mistakes
❌ Ignoring negative signs while calculations.
❌ Dividing by zero.
❌ Confusing additive inverse with reciprocal.
❌ Forgetting to simplify fractions.
❌ Not taking the reciprocal during division.
Quick Revision Notes
✔ Rational numbers are written as:
$$\frac{p}{q}$$
✔ Every integer is a rational number.
✔ Zero is a rational number but has no reciprocal.
✔ Rational numbers are closed under addition and multiplication.
✔ Division by zero is not defined.
Conclusion
Rational Numbers is an essential chapter in Class 8 Mathematics. A thorough understanding of rational numbers and their properties helps students solve problems efficiently and perform well in examinations. Regular MCQ practice improves speed, accuracy, and conceptual understanding.
Related links
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