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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 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
Based On: NCERT Latest Syllabus
Introduction:
Rational Numbers is an important chapter in Class 8 Mathematics that helps students understand fractions, integers, and their properties. Mastering rational numbers improves 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 used in daily life calculations, measurements, and higher mathematics. Understanding these concepts builds a strong foundation for algebra and advanced mathematical topics.
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 lies between:
$$\frac{1}{4}$$
and
$$\frac{3}{4}$$ ?
A) $$\frac{1}{8}$$
B) $$\frac{1}{2}$$
C) $$\frac{7}{8}$$
D) $$1$$
Answer:
$$\frac{1}{2}$$
Useful Formula for this Question:
A rational number lying between two rational numbers can be found using their average.
Concept Behind This Question:
Students should identify rational numbers between two given numbers.
Step-by-Step Solution:
Convert the fractions into decimals:
$$\frac{1}{4}=0.25$$
$$\frac{3}{4}=0.75$$
Now,
$$\frac{1}{2}=0.5$$
Since
$$0.25<0.5<0.75$$
Therefore:
$$\frac{1}{2}$$ lies between
$$\frac{1}{4}$$
and
$$\frac{3}{4}$$
Hence, the correct answer is:
$$\frac{1}{2}$$
Exam Tip:
A number between two rational numbers is also a rational number.
Q2. Simplify:
$$-\frac{5}{12}+\frac{1}{3}$$
A) $$-\frac{1}{12}$$
B) $$\frac{1}{12}$$
C) $$-\frac{3}{12}$$
D) $$\frac{3}{12}$$
Answer:
$$-\frac{1}{12}$$
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:
Convert:
$$\frac{1}{3}=\frac{4}{12}$$
Now,
$$-\frac{5}{12}+\frac{4}{12}$$
$$=\frac{-1}{12}$$
Therefore, the correct answer is:
$$-\frac{1}{12}$$
Exam Tip:
Take special care of negative signs while adding fractions.
Q3. Which of the following rational numbers has no reciprocal?
A) $$\frac{5}{7}$$
B) $$-\frac{9}{11}$$
C) $$0$$
D) $$1$$
Answer:
$$0$$
Useful Formula for this Question:
A rational number has a reciprocal only if it is non-zero.
Concept Behind This Question:
Students should understand multiplicative inverse.
Step-by-Step Solution:
The reciprocal of a number is obtained by interchanging its numerator and denominator.
For:
$$0=\frac{0}{1}$$
its reciprocal would be:
$$\frac{1}{0}$$
which is not defined.
Therefore:
$$0$$ has no reciprocal.
Hence, the correct answer is:
$$0$$
Exam Tip:
Always remember that zero does not have a multiplicative inverse.
Q4. Find:
$$\frac{7}{10}\times\left(-\frac{5}{14}\right)$$
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:
$$\frac{7}{10}\times\left(-\frac{5}{14}\right)$$
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:
A positive number multiplied by a negative number gives a negative result.
Q5. Which property is represented by:
$$a+(b+c)=(a+b)+c$$
A) Commutative Property
B) Associative Property
C) Closure Property
D) Distributive Property
Answer:
Associative Property
Useful Formula for this Question:
$$a+(b+c)=(a+b)+c$$
Concept Behind This Question:
Students should identify the properties of rational numbers.
Step-by-Step Solution:
The grouping of numbers changes, but the sum remains unchanged.
Example:
$$2+(3+4)=(2+3)+4=9$$
Hence, the given expression represents the associative property.
Therefore, the correct answer is:
Associative Property
Exam Tip:
Associative property changes grouping but not the order of numbers.
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 in the form:
$$\frac{p}{q}, \quad q\ne0$$
2. Can zero be a rational number?
Yes,
$$0=\frac{0}{1}$$
Therefore, zero is a rational number.
3. Does zero have a reciprocal?
No, zero has no reciprocal.
4. Are rational numbers closed under addition?
Yes, the sum of two rational numbers is always a rational number.
5. Can a rational number lie between two rational numbers?
Yes, infinitely many rational numbers lie between any two rational numbers.
Common Mistakes
❌ Ignoring negative signs.
❌ Dividing by zero.
❌ Confusing additive inverse with reciprocal.
❌ Not simplifying fractions completely.
❌ Forgetting cross-cancellation in multiplication.
Quick Revision Notes
✔ Rational numbers are written as:
$$\frac{p}{q}$$
✔ Zero is a rational number.
✔ Zero has no reciprocal.
✔ Rational numbers are closed under addition.
✔ Infinitely many rational numbers exist between two rational numbers.
Conclusion
Rational Numbers is a fundamental chapter in Class 8 Mathematics. Understanding the properties and operations of rational numbers helps students solve mathematical problems efficiently and build a strong foundation for higher mathematics. Regular MCQ practice improves conceptual understanding and exam performance.
Related links
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