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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, 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. Mastering rational numbers helps students strengthen their 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 extensively in mathematics and real-life calculations. Understanding their properties forms the basis for algebra and 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 equivalent to:
$$\frac{21}{28}$$ ?
A) $$\frac{3}{4}$$
B) $$\frac{6}{8}$$
C) $$\frac{9}{12}$$
D) All of these
Answer:
All of these
Useful Formula for this Question:
Equivalent rational numbers are obtained by multiplying or dividing the numerator and denominator by the same non-zero integer.
Concept Behind This Question:
Students should identify equivalent rational numbers.
Step-by-Step Solution:
Simplify:
$$\frac{21}{28}=\frac{3}{4}$$
Also,
$$\frac{6}{8}=\frac{3}{4}$$
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:
$$-\frac{5}{18}+\frac{7}{9}$$
A) $$\frac{1}{2}$$
B) $$\frac{5}{18}$$
C) $$\frac{1}{18}$$
D) $$\frac{17}{18}$$
Answer:
$$\frac{1}{2}$$
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:
$$\frac{7}{9}=\frac{14}{18}$$
Now,
$$-\frac{5}{18}+\frac{14}{18}=\frac{9}{18}$$
Simplifying further:
$$\frac{9}{18}=\frac{1}{2}$$
Therefore, the correct answer is:
$$\frac{1}{2}$$
Exam Tip:
Always simplify the final answer to its lowest form.
Q3. What is the multiplicative inverse of:
$$\frac{17}{-8}$$ ?
A) $$-\frac{8}{17}$$
B) $$\frac{8}{17}$$
C) $$-\frac{17}{8}$$
D) $$\frac{17}{8}$$
Answer:
$$-\frac{8}{17}$$
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 the reciprocal of rational numbers.
Step-by-Step Solution:
Given number:
$$\frac{17}{-8}=-\frac{17}{8}$$
Interchanging numerator and denominator gives:
$$-\frac{8}{17}$$
Verification:
$$-\frac{17}{8}\times-\frac{8}{17}=1$$
Therefore, the correct answer is:
$$-\frac{8}{17}$$
Exam Tip:
The sign of the rational number remains unchanged in its reciprocal.
Q4. Which property is represented by:
$$(a+b)+c=a+(b+c)$$
A) Closure Property
B) Commutative Property
C) Associative 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 properties of rational numbers.
Step-by-Step Solution:
The grouping of numbers changes, but the result 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 order.
Q5. Simplify:
$$-\frac{9}{20}\times\frac{10}{27}$$
A) $$-\frac{1}{6}$$
B) $$\frac{1}{6}$$
C) $$-\frac{2}{3}$$
D) $$\frac{2}{3}$$
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 and simplify rational numbers correctly.
Step-by-Step Solution:
$$-\frac{9}{20}\times\frac{10}{27}$$
Cancelling common factors:
$$=-\frac{1}{2}\times\frac{1}{3}$$
$$=-\frac{1}{6}$$
Therefore, the correct answer is:
$$-\frac{1}{6}$$
Exam Tip:
Use cross-cancellation to simplify multiplication quickly.
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 a rational number?
A rational number can be expressed as:
$$\frac{p}{q}, \quad q\ne0$$
2. Does zero have a reciprocal?
No, zero does not have a reciprocal.
3. What is the additive identity?
The additive identity is:
$$0$$
because
$$a+0=a$$
4. What is the multiplicative identity?
The multiplicative identity is:
$$1$$
because
$$a\times1=a$$
5. Are rational numbers closed under multiplication?
Yes, the product of two rational numbers is always a rational number.
Common Mistakes
❌ Forgetting to simplify fractions.
❌ Ignoring negative signs.
❌ Dividing by zero.
❌ Confusing reciprocal with additive inverse.
❌ 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 one of the most important chapters in Class 8 Mathematics. A strong understanding of rational numbers and their properties helps students solve problems efficiently and perform well in examinations. Regular MCQ practice improves speed, accuracy, and conceptual understanding.
Related links
- Class 8 Maths Chapter 1 Rational Numbers
- Class 8 Maths additive inverse, multiplicative inverse MCQ
- Class 8 Maths Chapter 1 properties of rational numbers, additive inverse
- Class 8 Maths Chapter 1 Rational Numbers multiplicative
- Class 8 Maths Chapter 1 Rational Numbers
- Class 8 Maths Chapter 1 Rational Numbers, Additive inverse
- Class 8 Maths Chapter 1 Rational Numbers
- Class 8 Maths Chapter 1 Rational Numbers
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