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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, closure property, and operations on rational numbers with 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 and their properties. Understanding rational numbers helps students strengthen their arithmetic skills and prepare for algebraic concepts.
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 used in mathematics, science, and daily-life calculations. A strong understanding of this topic improves logical reasoning and problem-solving 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 equivalent to:
$$\frac{8}{12}$$ ?
A) $$\frac{2}{3}$$
B) $$\frac{4}{6}$$
C) $$\frac{16}{24}$$
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:
Simplify:
$$\frac{8}{12}=\frac{2}{3}$$
Also,
$$\frac{4}{6}=\frac{2}{3}$$
and
$$\frac{16}{24}=\frac{2}{3}$$
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:
$$\frac{11}{15}-\frac{2}{5}$$
A) $$\frac{1}{3}$$
B) $$\frac{5}{15}$$
C) $$\frac{2}{15}$$
D) $$\frac{13}{15}$$
Answer:
$$\frac{1}{3}$$
Useful Formula for this Question:
For subtraction:
$$\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}$$
Concept Behind This Question:
Students should subtract rational numbers using like fractions.
Step-by-Step Solution:
Convert:
$$\frac{2}{5}=\frac{6}{15}$$
Now,
$$\frac{11}{15}-\frac{6}{15}=\frac{5}{15}$$
Simplifying further:
$$\frac{5}{15}=\frac{1}{3}$$
Therefore, the correct answer is:
$$\frac{1}{3}$$
Exam Tip:
Always simplify the final answer to its lowest form.
Q3. Which of the following rational numbers does not have a reciprocal?
A) $$\frac{5}{9}$$
B) $$-\frac{7}{11}$$
C) $$1$$
D) $$0$$
Answer:
$$0$$
Useful Formula for this Question:
A reciprocal exists only for non-zero rational numbers.
Concept Behind This Question:
Students should understand multiplicative inverse.
Step-by-Step Solution:
The reciprocal of:
$$0=\frac{0}{1}$$
would be:
$$\frac{1}{0}$$
which is undefined.
Therefore:
$$0$$ does not have a reciprocal.
Hence, the correct answer is:
$$0$$
Exam Tip:
Always remember that zero has no reciprocal.
Q4. Which property is represented by:
$$a\times(b+c)=ab+ac$$
A) Closure Property
B) Associative Property
C) Distributive Property
D) Commutative Property
Answer:
Distributive Property
Useful Formula for this Question:
$$a\times(b+c)=ab+ac$$
Concept Behind This Question:
Students should identify different properties of rational numbers.
Step-by-Step Solution:
The multiplication operation is distributed over addition.
Example:
$$2(5+3)=2\times5+2\times3$$
$$=10+6=16$$
Hence, the given expression represents the distributive property.
Therefore, the correct answer is:
Distributive Property
Exam Tip:
Distributive property links multiplication with addition and subtraction.
Q5. Simplify:
$$-\frac{6}{7}\times\frac{14}{15}$$
A) $$-\frac{4}{5}$$
B) $$\frac{4}{5}$$
C) $$-\frac{5}{4}$$
D) $$\frac{5}{4}$$
Answer:
$$-\frac{4}{5}$$
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:
$$-\frac{6}{7}\times\frac{14}{15}$$
Cancelling common factors:
$$=-\frac{2}{1}\times\frac{2}{5}$$
$$=-\frac{4}{5}$$
Therefore, the correct answer is:
$$-\frac{4}{5}$$
Exam Tip:
Use cross-cancellation before multiplication to make calculations easier.
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 in the form:
$$\frac{p}{q}, \quad q\ne0$$
2. Does zero have a reciprocal?
No, zero does not have a reciprocal.
3. What is the additive identity?
The additive identity is:
$$0$$
4. What is the multiplicative identity?
The multiplicative identity is:
$$1$$
5. Are rational numbers closed under multiplication?
Yes, the product of two rational numbers is always a rational number.
Common Mistakes
❌ Forgetting to simplify fractions.
❌ Ignoring negative signs.
❌ Dividing by zero.
❌ Confusing reciprocal with additive inverse.
❌ Making errors in cross-cancellation.
Quick Revision Notes
✔ Rational numbers are written in the form:
$$\frac{p}{q}$$
✔ 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 essential chapter in Class 8 Mathematics. A strong understanding of rational numbers and their properties helps students solve problems efficiently and build a solid foundation for higher mathematics. Regular MCQ practice improves speed, accuracy, and conceptual understanding.
Related links
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