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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
Based On: NCERT Latest Syllabus
Introduction:
Rational Numbers is an important chapter in Class 8 Mathematics that introduces students to operations and properties of rational numbers. Understanding these concepts helps students solve mathematical problems efficiently and strengthens their mathematical foundation.
What You Will Learn?
✔ Rational Numbers
✔ Properties of Rational Numbers
✔ Additive Inverse
✔ Multiplicative Inverse
✔ Closure Property
✔ Commutative Property
✔ Associative Property
✔ Division of Rational Numbers
Why This Topic Is Important?
Rational numbers are used extensively in daily life and advanced mathematics. A clear understanding of rational numbers helps students develop logical thinking 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 is the additive identity for rational numbers?
A) $$0$$
B) $$1$$
C) $$-1$$
D) $$10$$
Answer:
$$0$$
Useful Formula for this Question:
For every rational number:
$$a+0=a$$
Concept Behind This Question:
Students should know the identity elements of rational numbers.
Step-by-Step Solution:
The additive identity is the number which leaves a rational number unchanged after addition.
For any rational number:
$$a+0=a$$
Therefore:
$$0$$ is the additive identity.
Hence, the correct answer is:
$$0$$
Exam Tip:
Remember that $$0$$ is the additive identity, while $$1$$ is the multiplicative identity.
Q2. Simplify:
$$\frac{7}{12}-\frac{1}{3}$$
A) $$\frac{1}{4}$$
B) $$\frac{5}{12}$$
C) $$\frac{3}{4}$$
D) $$\frac{1}{12}$$
Answer:
$$\frac{1}{4}$$
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 correctly.
Step-by-Step Solution:
Convert the fractions into like fractions.
$$\frac{1}{3}=\frac{4}{12}$$
Now,
$$\frac{7}{12}-\frac{4}{12}=\frac{3}{12}$$
$$=\frac{1}{4}$$
Therefore, the correct answer is:
$$\frac{1}{4}$$
Exam Tip:
Always simplify the final answer to its lowest form.
Q3. Which of the following rational numbers is equal to:
$$-\frac{2}{5}$$ ?
A) $$\frac{-4}{10}$$
B) $$\frac{2}{-5}$$
C) $$-\frac{6}{15}$$
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:
$$\frac{-4}{10}=-\frac{2}{5}$$
$$\frac{2}{-5}=-\frac{2}{5}$$
$$-\frac{6}{15}=-\frac{2}{5}$$
Thus, all the given fractions are equal to:
$$-\frac{2}{5}$$
Hence, the correct answer is:
All of these
Exam Tip:
Multiply or divide the numerator and denominator by the same non-zero number to obtain equivalent rational numbers.
Q4. The product of any rational number and its reciprocal is:
A) $$0$$
B) $$1$$
C) The same number
D) Undefined
Answer:
$$1$$
Useful Formula for this Question:
For any non-zero rational number:
$$\frac{a}{b}\times\frac{b}{a}=1$$
Concept Behind This Question:
Students should understand multiplicative inverse.
Step-by-Step Solution:
Let the rational number be:
$$\frac{a}{b}$$
Its reciprocal is:
$$\frac{b}{a}$$
Therefore,
$$\frac{a}{b}\times\frac{b}{a}=1$$
Hence, the correct answer is:
$$1$$
Exam Tip:
Zero does not have a reciprocal.
Q5. Simplify:
$$-\frac{4}{9}\div\frac{2}{3}$$
A) $$-\frac{2}{3}$$
B) $$-\frac{1}{2}$$
C) $$\frac{2}{3}$$
D) $$-\frac{3}{2}$$
Answer:
$$-\frac{2}{3}$$
Useful Formula for this Question:
For division of rational numbers:
$$\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}$$
Concept Behind This Question:
Students should divide rational numbers using reciprocals.
Step-by-Step Solution:
$$-\frac{4}{9}\div\frac{2}{3}$$
$$=-\frac{4}{9}\times\frac{3}{2}$$
Cancelling common factors:
$$=-\frac{2}{3}$$
Therefore, the correct answer is:
$$-\frac{2}{3}$$
Exam Tip:
Replace division by multiplication using 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. Closure Property
Rational numbers are closed under addition, subtraction, and multiplication.
FAQs
1. What is the additive identity of rational numbers?
The additive identity is:
$$0$$
2. What is the multiplicative identity of rational numbers?
The multiplicative identity is:
$$1$$
3. Does every rational number have a reciprocal?
Yes, except:
$$0$$
4. Can negative fractions be rational numbers?
Yes, every negative fraction is a rational number.
5. Are rational numbers closed under multiplication?
Yes, the product of two rational numbers is always a rational number.
Common Mistakes
❌ Forgetting to take reciprocal during division.
❌ Ignoring negative signs.
❌ Dividing by zero.
❌ Not simplifying fractions completely.
❌ Confusing identity with inverse.
Quick Revision Notes
✔ Rational numbers are expressed as:
$$\frac{p}{q}$$
✔ $$0$$ is the additive identity.
✔ $$1$$ is the multiplicative identity.
✔ Reciprocal means multiplicative inverse.
✔ Zero has no reciprocal.
Conclusion
Rational Numbers is a fundamental chapter in Class 8 Mathematics. Understanding operations, identities, and properties of rational numbers helps students solve problems efficiently and excel in examinations. Regular MCQ practice improves speed, accuracy, and conceptual understanding.
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