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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 introduces students to fractions, integers, and their properties. Understanding rational numbers helps students develop 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 widely used in mathematics and everyday life. A clear understanding of rational numbers builds a strong foundation for algebra and advanced mathematical concepts.
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 inverse of:
$$-\frac{11}{15}$$ ?
A) $$\frac{11}{15}$$
B) $$-\frac{11}{15}$$
C) $$\frac{15}{11}$$
D) $$-\frac{15}{11}$$
Answer:
$$\frac{11}{15}$$
Useful Formula for this Question:
The additive inverse of:
$$\frac{a}{b}$$
is
$$-\frac{a}{b}$$
Concept Behind This Question:
Students should understand the concept of additive inverse.
Step-by-Step Solution:
The additive inverse of a number is obtained by changing its sign.
Given number:
$$-\frac{11}{15}$$
Its additive inverse is:
$$\frac{11}{15}$$
Verification:
$$-\frac{11}{15}+\frac{11}{15}=0$$
Therefore, the correct answer is:
$$\frac{11}{15}$$
Exam Tip:
The sum of a number and its additive inverse is always zero.
Q2. Simplify:
$$\frac{5}{9}+\frac{7}{18}$$
A) $$\frac{17}{18}$$
B) $$\frac{1}{2}$$
C) $$\frac{19}{18}$$
D) $$\frac{11}{18}$$
Answer:
$$\frac{17}{18}$$
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 using a common denominator.
Step-by-Step Solution:
LCM of $$9$$ and $$18$$ is:
$$18$$
Convert:
$$\frac{5}{9}=\frac{10}{18}$$
Now,
$$\frac{10}{18}+\frac{7}{18}=\frac{17}{18}$$
Therefore, the correct answer is:
$$\frac{17}{18}$$
Exam Tip:
Find the LCM of denominators before adding unlike fractions.
Q3. Which property is represented by:
$$(a\times b)\times c=a\times(b\times c)$$
A) Closure Property
B) Associative Property
C) Commutative Property
D) Distributive Property
Answer:
Associative Property
Useful Formula for this Question:
$$(a\times b)\times c=a\times(b\times c)$$
Concept Behind This Question:
Students should identify properties of rational numbers.
Step-by-Step Solution:
The grouping of numbers changes, but the product remains the same.
Example:
$$(2\times3)\times4=2\times(3\times4)=24$$
Hence, the given expression represents the associative property.
Therefore, the correct answer is:
Associative Property
Exam Tip:
Associative property changes grouping but not the order of numbers.
Q4. Simplify:
$$\frac{8}{15}\div\frac{4}{9}$$
A) $$\frac{6}{5}$$
B) $$\frac{5}{6}$$
C) $$\frac{12}{5}$$
D) $$\frac{3}{5}$$
Answer:
$$\frac{6}{5}$$
Useful Formula for this Question:
For division:
$$\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}$$
Concept Behind This Question:
Students should divide rational numbers using reciprocals.
Step-by-Step Solution:
$$\frac{8}{15}\div\frac{4}{9}$$
$$=\frac{8}{15}\times\frac{9}{4}$$
Cancelling common factors:
$$=\frac{2}{5}\times3$$
$$=\frac{6}{5}$$
Therefore, the correct answer is:
$$\frac{6}{5}$$
Exam Tip:
Change division into multiplication using the reciprocal.
Q5. Which of the following statements is true?
A) Zero has a multiplicative inverse.
B) Every rational number is an integer.
C) Every integer is a rational number.
D) Rational numbers are not closed under subtraction.
Answer:
Every integer is a rational number.
Useful Formula for this Question:
Every integer can be written in the form:
$$\frac{n}{1}$$
Concept Behind This Question:
Students should know the relationship between integers and rational numbers.
Step-by-Step Solution:
Any integer can be expressed as:
$$\frac{n}{1}$$
Therefore, every integer is a rational number.
Zero has no multiplicative inverse.
Also, rational numbers are closed under subtraction.
Hence, the correct answer is:
Option C
Exam Tip:
All integers are rational numbers, but all rational numbers are not integers.
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. What is an additive inverse?
The additive inverse of a number is the number that gives zero when added to it.
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. Are rational numbers closed under division?
Yes, except division by zero.
5. Can a rational number be negative?
Yes, rational numbers can be positive, negative, or zero.
Common Mistakes
❌ Confusing reciprocal with additive inverse.
❌ Dividing by zero.
❌ Ignoring negative signs.
❌ Not simplifying fractions completely.
❌ Forgetting to use LCM while adding fractions.
Quick Revision Notes
✔ Rational numbers are written 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 a fundamental chapter in Class 8 Mathematics. A clear understanding of operations and properties of rational numbers helps students solve problems accurately and perform well in examinations. Regular MCQ practice strengthens concepts and boosts confidence.
Related links
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