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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 a fundamental chapter in Class 8 Mathematics that introduces students to fractions, integers, and their properties. A strong understanding of rational numbers develops logical reasoning and improves 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 helps students build 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 rational numbers is equal to:
$$\frac{24}{36}$$ ?
A) $$\frac{2}{3}$$
B) $$\frac{4}{6}$$
C) $$\frac{8}{12}$$
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:
$$\frac{24}{36}=\frac{2}{3}$$
Also,
$$\frac{4}{6}=\frac{2}{3}$$
and
$$\frac{8}{12}=\frac{2}{3}$$
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:
$$\frac{5}{12}+\frac{7}{18}$$
A) $$\frac{29}{36}$$
B) $$\frac{19}{36}$$
C) $$\frac{17}{36}$$
D) $$\frac{11}{36}$$
Answer:
$$\frac{29}{36}$$
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:
$$12$$
and
$$18$$
is
$$36$$
Convert:
$$\frac{5}{12}=\frac{15}{36}$$
$$\frac{7}{18}=\frac{14}{36}$$
Now,
$$\frac{15}{36}+\frac{14}{36}=\frac{29}{36}$$
Therefore, the correct answer is:
$$\frac{29}{36}$$
Exam Tip:
Convert unlike fractions into like fractions before addition.
Q3. What is the additive inverse of:
$$\frac{9}{14}$$ ?
A) $$-\frac{9}{14}$$
B) $$\frac{14}{9}$$
C) $$\frac{9}{14}$$
D) $$-\frac{14}{9}$$
Answer:
$$-\frac{9}{14}$$
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 changes only the sign of the number.
Given number:
$$\frac{9}{14}$$
Its additive inverse is:
$$-\frac{9}{14}$$
Verification:
$$\frac{9}{14}+\left(-\frac{9}{14}\right)=0$$
Therefore, the correct answer is:
$$-\frac{9}{14}$$
Exam Tip:
The sum of a number and its additive inverse is always zero.
Q4. Which property is represented by:
$$a\times(b+c)=ab+ac$$
A) Commutative Property
B) Closure Property
C) Distributive Property
D) Associative Property
Answer:
Distributive Property
Useful Formula for this Question:
$$a\times(b+c)=ab+ac$$
Concept Behind This Question:
Students should identify different properties of rational numbers.
Step-by-Step Solution:
Multiplication is distributed over addition.
Example:
$$3(4+2)=3\times4+3\times2$$
$$=12+6=18$$
Hence, the given expression represents the distributive property.
Therefore, the correct answer is:
Distributive Property
Exam Tip:
Distributive property links multiplication with addition and subtraction.
Q5. Simplify:
$$-\frac{8}{15}\times\frac{25}{32}$$
A) $$-\frac{5}{12}$$
B) $$\frac{5}{12}$$
C) $$-\frac{4}{5}$$
D) $$\frac{4}{5}$$
Answer:
$$-\frac{5}{12}$$
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:
$$-\frac{8}{15}\times\frac{25}{32}$$
Cancelling common factors:
$$=-\frac{1}{3}\times\frac{5}{4}$$
$$=-\frac{5}{12}$$
Therefore, the correct answer is:
$$-\frac{5}{12}$$
Exam Tip:
Use cross-cancellation before multiplication to simplify calculations.
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 in the form:
$$\frac{p}{q}, \quad q\ne0$$
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 subtraction?
Yes, the difference of two rational numbers is always a rational number.
Common Mistakes
❌ Ignoring negative signs.
❌ Dividing by zero.
❌ Confusing reciprocal with additive inverse.
❌ Not simplifying fractions completely.
❌ Forgetting 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 an important chapter in Class 8 Mathematics. Understanding 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 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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