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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 to Difficult
Based On: NCERT Latest Syllabus
Introduction:
Rational Numbers is an important chapter in Class 8 Mathematics that introduces students to fractions, integers, and their properties. Understanding rational numbers helps develop 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 and everyday life. A strong understanding of their properties helps students solve problems efficiently and prepares them for 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:
$$\frac{-18}{24}$$ ?
A) $$-\frac{3}{4}$$
B) $$\frac{3}{-4}$$
C) $$\frac{-9}{12}$$
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:
$$\frac{-18}{24}=-\frac{3}{4}$$
Also,
$$\frac{3}{-4}=-\frac{3}{4}$$
and
$$\frac{-9}{12}=-\frac{3}{4}$$
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:
$$\frac{7}{10}+\frac{3}{20}$$
A) $$\frac{17}{20}$$
B) $$\frac{13}{20}$$
C) $$\frac{19}{20}$$
D) $$\frac{1}{20}$$
Answer:
$$\frac{17}{20}$$
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 a common denominator.
Step-by-Step Solution:
Convert:
$$\frac{7}{10}=\frac{14}{20}$$
Now,
$$\frac{14}{20}+\frac{3}{20}=\frac{17}{20}$$
Therefore, the correct answer is:
$$\frac{17}{20}$$
Exam Tip:
Find the LCM of denominators before addition.
Q3. What is the additive inverse of:
$$\frac{-5}{13}$$ ?
A) $$\frac{5}{13}$$
B) $$-\frac{5}{13}$$
C) $$\frac{13}{5}$$
D) $$-\frac{13}{5}$$
Answer:
$$\frac{5}{13}$$
Useful Formula for this Question:
The additive inverse of:
$$\frac{a}{b}$$
is
$$-\frac{a}{b}$$
Concept Behind This Question:
Students should understand additive inverse.
Step-by-Step Solution:
The additive inverse changes only the sign of the number.
Given number:
$$-\frac{5}{13}$$
Its additive inverse is:
$$\frac{5}{13}$$
Verification:
$$-\frac{5}{13}+\frac{5}{13}=0$$
Therefore, the correct answer is:
$$\frac{5}{13}$$
Exam Tip:
A number and its additive inverse always add up to zero.
Q4. Which property is represented by:
$$a\times b=b\times a$$
A) Closure Property
B) Associative Property
C) Commutative Property
D) Distributive Property
Answer:
Commutative Property
Useful Formula for this Question:
$$a\times b=b\times a$$
Concept Behind This Question:
Students should identify properties of rational numbers.
Step-by-Step Solution:
The order of multiplication changes, but the result remains the same.
Example:
$$4\times5=5\times4=20$$
Hence, the given expression represents the commutative property.
Therefore, the correct answer is:
Commutative Property
Exam Tip:
Commutative property changes the order but not the answer.
Q5. Simplify:
$$\frac{15}{28}\times\left(-\frac{14}{25}\right)$$
A) $$-\frac{3}{10}$$
B) $$\frac{3}{10}$$
C) $$-\frac{5}{6}$$
D) $$\frac{5}{6}$$
Answer:
$$-\frac{3}{10}$$
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:
$$\frac{15}{28}\times\left(-\frac{14}{25}\right)$$
Cancelling common factors:
$$=\frac{3}{2}\times\left(-\frac{1}{5}\right)$$
$$=-\frac{3}{10}$$
Therefore, the correct answer is:
$$-\frac{3}{10}$$
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. Distributive Property
$$a(b+c)=ab+ac$$
FAQs
1. What is an additive inverse?
The additive inverse of a number is the number that gives zero when added to it.
2. Does every rational number have a reciprocal?
No, zero does not have a reciprocal.
3. What is the multiplicative identity?
The multiplicative identity is:
$$1$$
4. Are rational numbers closed under addition?
Yes, the sum of two rational numbers is always a rational number.
5. Can rational numbers be negative?
Yes, rational numbers can be positive, negative, or zero.
Common Mistakes
❌ Ignoring negative signs.
❌ Dividing by zero.
❌ Confusing additive inverse with reciprocal.
❌ Forgetting to simplify fractions.
❌ Errors in cross-cancellation.
Quick Revision Notes
✔ Rational numbers are expressed 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 a fundamental chapter in Class 8 Mathematics. Understanding its properties and operations helps students solve mathematical problems efficiently and perform well in examinations. Regular MCQ practice improves conceptual understanding and confidence.
Related links
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- Class 8 Maths Chapter 1 properties of rational numbers, additive inverse
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