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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 deals with fractions, integers, and their properties. Understanding rational numbers helps students solve mathematical problems efficiently and builds a strong 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 used in everyday calculations, measurements, and advanced mathematical concepts. Mastering this chapter improves logical reasoning and computational 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 the reciprocal of:
$$-\frac{5}{12}$$ ?
A) $$-\frac{12}{5}$$
B) $$\frac{12}{5}$$
C) $$-\frac{5}{12}$$
D) $$0$$
Answer:
$$-\frac{12}{5}$$
Useful Formula for this Question:
The reciprocal of:
$$\frac{a}{b}$$
is
$$\frac{b}{a}$$
Concept Behind This Question:
Students should know how to find the reciprocal of rational numbers.
Step-by-Step Solution:
Given rational number:
$$-\frac{5}{12}$$
Interchanging numerator and denominator gives:
$$-\frac{12}{5}$$
Verification:
$$-\frac{5}{12}\times-\frac{12}{5}=1$$
Therefore, the correct answer is:
$$-\frac{12}{5}$$
Exam Tip:
The reciprocal of a negative rational number is also negative.
Q2. Find:
$$\frac{3}{4}+\left(-\frac{5}{8}\right)$$
A) $$\frac{1}{8}$$
B) $$-\frac{1}{8}$$
C) $$\frac{11}{8}$$
D) $$-\frac{11}{8}$$
Answer:
$$\frac{1}{8}$$
Useful Formula for this Question:
For addition of rational numbers:
$$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$$
Concept Behind This Question:
Students should add rational numbers with unlike denominators.
Step-by-Step Solution:
Convert the fractions into like fractions.
$$\frac{3}{4}=\frac{6}{8}$$
Now,
$$\frac{6}{8}+\left(-\frac{5}{8}\right)$$
$$=\frac{1}{8}$$
Therefore, the correct answer is:
$$\frac{1}{8}$$
Exam Tip:
Convert unlike fractions into like fractions before addition or subtraction.
Q3. Which property is represented by:
$$a\times b=b\times a$$
A) Associative Property
B) Closure 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 the properties of rational numbers.
Step-by-Step Solution:
The order of numbers changes, but the product remains the same.
Example:
$$2\times3=3\times2=6$$
Hence, the given expression represents the commutative property.
Therefore, the correct answer is:
Commutative Property
Exam Tip:
Commutative property changes the order of numbers only.
Q4. Find:
$$-\frac{7}{9}\times\frac{3}{14}$$
A) $$-\frac{1}{6}$$
B) $$\frac{1}{6}$$
C) $$-\frac{3}{2}$$
D) $$\frac{3}{2}$$
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 multiply rational numbers correctly.
Step-by-Step Solution:
$$-\frac{7}{9}\times\frac{3}{14}$$
Cancelling common factors:
$$=-\frac{1}{3}\times\frac{1}{2}$$
$$=-\frac{1}{6}$$
Therefore, the correct answer is:
$$-\frac{1}{6}$$
Exam Tip:
Use cross-cancellation to simplify multiplication.
Q5. Which of the following statements is false?
A) Every integer is a rational number.
B) Zero is a rational number.
C) Every rational number has a reciprocal.
D) Rational numbers are closed under addition.
Answer:
Every rational number has a reciprocal.
Useful Formula for this Question:
A reciprocal exists only for non-zero rational numbers.
Concept Behind This Question:
Students should understand the properties of rational numbers.
Step-by-Step Solution:
- Every integer can be written as:
$$\frac{n}{1}$$
Therefore, integers are rational numbers.
- Zero can be written as:
$$\frac{0}{1}$$
Hence, zero is rational.
- Zero does not have a reciprocal.
Thus, the statement:
“Every rational number has a reciprocal”
is false.
Therefore, the correct answer is:
Option C
Exam Tip:
Always remember that zero has no reciprocal.
Important Formulas & Concepts
1. Rational Numbers
$$\frac{p}{q}, \quad q\ne0$$
2. Additive Inverse
$$\frac{a}{b}+\left(-\frac{a}{b}\right)=0$$
3. Multiplicative Inverse
$$\frac{a}{b}\times\frac{b}{a}=1,\quad a\ne0,\ b\ne0$$
4. Commutative Property
$$a+b=b+a$$
$$a\times b=b\times a$$
5. Associative Property
$$(a+b)+c=a+(b+c)$$
6. Distributive Property
$$a(b+c)=ab+ac$$
FAQs
1. What is a reciprocal?
The reciprocal of a number is obtained by interchanging its numerator and denominator.
2. Is zero 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 integers rational numbers?
Yes, because every integer can be expressed as:
$$\frac{n}{1}$$
5. Are rational numbers closed under multiplication?
Yes, the product of two rational numbers is always a rational number.
Common Mistakes
❌ Forgetting reciprocal while division.
❌ Ignoring negative signs.
❌ Dividing by zero.
❌ Confusing additive inverse with multiplicative inverse.
❌ Incorrect simplification of fractions.
Quick Revision Notes
✔ Rational numbers are expressed as:
$$\frac{p}{q}$$
✔ Every integer is a rational number.
✔ Zero is a rational number but has no reciprocal.
✔ Reciprocal means multiplicative inverse.
✔ Rational numbers satisfy closure property.
Conclusion
Rational Numbers is an important chapter in Class 8 Mathematics. A strong understanding of rational numbers and their properties helps students solve mathematical problems efficiently and perform well in examinations. Regular MCQ practice improves confidence, accuracy, and conceptual understanding.
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