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Practice Class 8 Maths Chapter 1 Rational Numbers MCQ Questions with Answers based on NCERT syllabus. Learn rational numbers, additive inverse, multiplicative inverse, properties of rational numbers, 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: Easy to Moderate
Based On: NCERT Latest Syllabus
Introduction:
Rational Numbers is the first chapter of Class 8 Mathematics that introduces students to the properties and operations of rational numbers. Students learn about addition, subtraction, multiplication, division, additive inverse, multiplicative inverse, and various properties of rational numbers. These concepts build 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?
The concepts of rational numbers are widely used in mathematics and daily life. Understanding these concepts strengthens problem-solving abilities and prepares students for 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 is a rational number?
A) $$\sqrt{7}$$
B) $$\pi$$
C) $$\frac{5}{8}$$
D) $$\sqrt{13}$$
Answer:
$$\frac{5}{8}$$
Useful Formula for this Question:
A rational number can be expressed in the form:
$$\frac{p}{q}, \quad q \ne 0$$
Concept Behind This Question:
Students should identify numbers that can be expressed as fractions of integers.
Step-by-Step Solution:
- $$\sqrt{7}$$ is irrational because 7 is not a perfect square.
- $$\pi$$ is an irrational number.
- $$\frac{5}{8}$$ is already in the form $$\frac{p}{q}$$.
- $$\sqrt{13}$$ is irrational because 13 is not a perfect square.
Therefore:
$$\frac{5}{8}$$ is a rational number.
Hence, the correct answer is:
$$\frac{5}{8}$$
Exam Tip:
Every integer and fraction is a rational number.
Q2. What is the additive inverse of:
$$\frac{7}{9}$$ ?
A) $$\frac{9}{7}$$
B) $$-\frac{7}{9}$$
C) $$\frac{7}{-9}$$
D) Both B and C
Answer:
Both B and C
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 of a number is obtained by changing its sign.
Therefore:
$$\frac{7}{9} \rightarrow -\frac{7}{9}$$
Also,
$$\frac{7}{-9} = -\frac{7}{9}$$
Hence, both represent the same value.
Therefore, the correct answer is:
Both B and C
Exam Tip:
The sum of a number and its additive inverse is always zero.
Q3. What is the multiplicative inverse of:
$$-\frac{4}{11}$$ ?
A) $$-\frac{11}{4}$$
B) $$\frac{11}{4}$$
C) $$\frac{4}{11}$$
D) $$0$$
Answer:
$$-\frac{11}{4}$$
Useful Formula for this Question:
The multiplicative inverse of:
$$\frac{a}{b}$$
is
$$\frac{b}{a}$$
Concept Behind This Question:
Students should know how to find reciprocals of rational numbers.
Step-by-Step Solution:
Interchange the numerator and denominator while keeping the sign unchanged.
Thus,
$$-\frac{4}{11} \rightarrow -\frac{11}{4}$$
Verification:
$$-\frac{4}{11} \times -\frac{11}{4} = 1$$
Therefore, the correct answer is:
$$-\frac{11}{4}$$
Exam Tip:
Zero does not have a multiplicative inverse.
Q4. Which property is represented by:
$$a+b=b+a$$
A) Closure Property
B) Associative Property
C) Commutative Property
D) Distributive Property
Answer:
Commutative Property
Useful Formula for this Question:
$$a+b=b+a$$
Concept Behind This Question:
Students should identify properties of rational numbers.
Step-by-Step Solution:
The order of numbers changes, but the result remains the same.
Example:
$$2+3=3+2=5$$
Hence, the given expression represents the commutative property.
Therefore, the correct answer is:
Commutative Property
Exam Tip:
Commutative property involves changing the order of numbers.
Q5. Simplify:
$$-\frac{3}{5} \times \frac{10}{9}$$
A) $$-\frac{2}{3}$$
B) $$\frac{2}{3}$$
C) $$-\frac{5}{3}$$
D) $$\frac{3}{2}$$
Answer:
$$-\frac{2}{3}$$
Useful Formula for this Question:
For multiplication of rational numbers:
$$\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}$$
Concept Behind This Question:
Students should multiply and simplify rational numbers correctly.
Step-by-Step Solution:
$$-\frac{3}{5}\times\frac{10}{9}$$
$$=\frac{-30}{45}$$
$$=-\frac{2}{3}$$
Therefore, the correct answer is:
$$-\frac{2}{3}$$
Exam Tip:
Always simplify the fraction to its lowest form.
Important Formulas & Concepts
1. Rational Numbers
$$\frac{p}{q}, \quad q \ne 0$$
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
$$(a+b)+c=a+(b+c)$$
$$(a\times b)\times c=a\times(b\times c)$$
6. Distributive Property
$$a(b+c)=ab+ac$$
FAQs
1. What is a rational number?
A rational number is a number that can be expressed as:
$$\frac{p}{q},\quad q\ne0$$
2. What is the additive inverse of a number?
It is the number which gives zero when added to the original number.
3. Does zero have a multiplicative inverse?
No, zero does not have a multiplicative inverse.
4. What is the reciprocal of:
$$\frac{4}{9}$$ ?
The reciprocal is:
$$\frac{9}{4}$$
5. Are integers rational numbers?
Yes, every integer is a rational number because it can be written as:
$$\frac{n}{1}$$
Common Mistakes
❌ Confusing additive inverse with multiplicative inverse.
❌ Dividing by zero.
❌ Ignoring signs during operations.
❌ Incorrect simplification of fractions.
❌ Forgetting reciprocal while division.
Quick Revision Notes
✔ Rational numbers can be expressed in the form:
$$\frac{p}{q}$$
✔ Every integer is a rational number.
✔ Zero has no multiplicative inverse.
✔ Reciprocal means multiplicative inverse.
✔ Rational numbers satisfy various properties.
Conclusion
Rational Numbers is an important 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 for examinations.
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