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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: Easy to Moderate
Based On: NCERT Latest Syllabus
Introduction:
Rational Numbers is an important chapter in Class 8 Mathematics that helps students understand fractions, integers, and their properties. Mastering rational numbers improves problem-solving skills and prepares students for advanced mathematical concepts.
What You Will Learn?
✔ Rational Numbers
✔ Properties of Rational Numbers
✔ Additive Inverse
✔ Multiplicative Inverse
✔ Operations on Rational Numbers
✔ Closure Property
✔ Commutative Property
✔ Associative Property
Why This Topic Is Important?
Rational numbers are used in daily life calculations, measurements, and advanced mathematics. A clear understanding of these concepts builds a strong mathematical foundation.
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 numbers is not a rational number?
A) $$\frac{7}{11}$$
B) $$-3$$
C) $$\sqrt{2}$$
D) $$0$$
Answer:
$$\sqrt{2}$$
Useful Formula for this Question:
A rational number can be written in the form:
$$\frac{p}{q}, \quad q \ne 0$$
Concept Behind This Question:
Students should identify numbers that cannot be expressed as fractions.
Step-by-Step Solution:
- $$\frac{7}{11}$$ is rational.
- $$-3=\frac{-3}{1}$$ is rational.
- $$0=\frac{0}{1}$$ is rational.
- $$\sqrt{2}$$ cannot be expressed as:
$$\frac{p}{q}$$
Therefore:
$$\sqrt{2}$$ is not a rational number.
Hence, the correct answer is:
$$\sqrt{2}$$
Exam Tip:
Square roots of non-perfect squares are irrational numbers.
Q2. Find:
$$\frac{5}{6}-\frac{1}{4}$$
A) $$\frac{7}{12}$$
B) $$\frac{1}{12}$$
C) $$\frac{5}{12}$$
D) $$\frac{11}{12}$$
Answer:
$$\frac{7}{12}$$
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 using a common denominator.
Step-by-Step Solution:
LCM of $$6$$ and $$4$$ is:
$$12$$
Therefore,
$$\frac{5}{6}=\frac{10}{12}$$
and
$$\frac{1}{4}=\frac{3}{12}$$
Now,
$$\frac{10}{12}-\frac{3}{12}=\frac{7}{12}$$
Hence, the correct answer is:
$$\frac{7}{12}$$
Exam Tip:
Convert unlike fractions into like fractions before subtraction.
Q3. What is the multiplicative inverse of:
$$-\frac{8}{15}$$ ?
A) $$-\frac{15}{8}$$
B) $$\frac{15}{8}$$
C) $$-\frac{8}{15}$$
D) $$0$$
Answer:
$$-\frac{15}{8}$$
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:
Given number:
$$-\frac{8}{15}$$
Interchanging numerator and denominator gives:
$$-\frac{15}{8}$$
Verification:
$$-\frac{8}{15}\times-\frac{15}{8}=1$$
Therefore, the correct answer is:
$$-\frac{15}{8}$$
Exam Tip:
The reciprocal of a negative rational number is also negative.
Q4. Which property is represented by:
$$(a+b)+c=a+(b+c)$$
A) Closure Property
B) Associative Property
C) Commutative 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 the same.
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, not order.
Q5. Simplify:
$$\frac{3}{7}\times\frac{14}{15}$$
A) $$\frac{2}{5}$$
B) $$\frac{3}{5}$$
C) $$\frac{5}{2}$$
D) $$\frac{7}{5}$$
Answer:
$$\frac{2}{5}$$
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.
Step-by-Step Solution:
$$\frac{3}{7}\times\frac{14}{15}$$
Cancelling common factors:
$$=\frac{1}{1}\times\frac{2}{5}$$
$$=\frac{2}{5}$$
Therefore, the correct answer is:
$$\frac{2}{5}$$
Exam Tip:
Use cross-cancellation to simplify calculations quickly.
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
$$(a+b)+c=a+(b+c)$$
$$(a\times b)\times c=a\times(b\times c)$$
6. Distributive Property
$$a(b+c)=ab+ac$$
FAQs
1. Can zero be a rational number?
Yes,
$$0=\frac{0}{1}$$
so it is a rational number.
2. Does zero have a reciprocal?
No, zero has no reciprocal.
3. Are all integers rational numbers?
Yes, because every integer can be written as:
$$\frac{n}{1}$$
4. What is the reciprocal of:
$$-\frac{2}{9}$$ ?
The reciprocal is:
$$-\frac{9}{2}$$
5. Are rational numbers closed under subtraction?
Yes, the difference of two rational numbers is always a rational number.
Common Mistakes
❌ Forgetting to simplify fractions.
❌ Ignoring negative signs.
❌ Confusing reciprocal with additive inverse.
❌ Dividing by zero.
❌ Incorrect cross-cancellation.
Quick Revision Notes
✔ Rational numbers can be written as:
$$\frac{p}{q}$$
✔ Zero is a rational number.
✔ Zero has no multiplicative inverse.
✔ Reciprocal means multiplicative inverse.
✔ Rational numbers satisfy closure property.
Conclusion
Rational Numbers is a fundamental chapter in Class 8 Mathematics. Understanding its properties and operations helps students solve mathematical problems accurately and confidently. Regular MCQ practice improves conceptual understanding and exam performance.
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