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Class 8 Maths Chapter 1 Rational Numbers based on NCERT syllabus. Learn rational numbers, properties of rational numbers, additive inverse, multiplicative inverse, and operations on rational numbers with 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 introduces students to the properties and operations of rational numbers. Understanding rational numbers helps in solving mathematical problems efficiently and forms the basis 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?
Rational numbers are used in daily life calculations, measurements, and advanced mathematical concepts. Mastering this topic improves logical reasoning and problem-solving skills.
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 multiplicative identity for rational numbers?
A) $$0$$
B) $$1$$
C) $$-1$$
D) $$10$$
Answer:
$$1$$
Useful Formula for this Question:
For every rational number:
$$a \times 1 = a$$
Concept Behind This Question:
Students should know the identity elements of rational numbers.
Step-by-Step Solution:
The multiplicative identity is the number which leaves a rational number unchanged after multiplication.
For any rational number:
$$a \times 1 = a$$
Therefore:
$$1$$ is the multiplicative identity.
Hence, the correct answer is:
$$1$$
Exam Tip:
Remember that $$0$$ is the additive identity, while $$1$$ is the multiplicative identity.
Q2. Find:
$$-\frac{3}{8}+\frac{5}{8}$$
A) $$\frac{1}{4}$$
B) $$-\frac{1}{4}$$
C) $$1$$
D) $$\frac{1}{8}$$
Answer:
$$\frac{1}{4}$$
Useful Formula for this Question:
For like fractions:
$$\frac{a}{b}+\frac{c}{b}=\frac{a+c}{b}$$
Concept Behind This Question:
Students should add rational numbers having the same denominator.
Step-by-Step Solution:
$$-\frac{3}{8}+\frac{5}{8}$$
$$=\frac{-3+5}{8}$$
$$=\frac{2}{8}$$
$$=\frac{1}{4}$$
Therefore, the correct answer is:
$$\frac{1}{4}$$
Exam Tip:
Always simplify the final answer to its lowest form.
Q3. Which of the following rational numbers is equal to:
$$\frac{2}{3}$$ ?
A) $$\frac{4}{6}$$
B) $$\frac{6}{9}$$
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:
$$\frac{4}{6}=\frac{2}{3}$$
$$\frac{6}{9}=\frac{2}{3}$$
$$\frac{8}{12}=\frac{2}{3}$$
Thus, all the given fractions are equivalent to:
$$\frac{2}{3}$$
Hence, the correct answer is:
All of these
Exam Tip:
Equivalent fractions represent the same rational number.
Q4. Which property is represented by:
$$a \times (b+c)=ab+ac$$
A) Closure Property
B) Associative Property
C) Commutative Property
D) Distributive 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:
The multiplication of a number over addition is distributed to each term inside the bracket.
Example:
$$2(3+4)=2\times3+2\times4$$
$$=6+8=14$$
Hence, the given expression represents the distributive property.
Therefore, the correct answer is:
Distributive Property
Exam Tip:
Distributive property connects multiplication with addition or subtraction.
Q5. Simplify:
$$\frac{5}{12}\div\frac{10}{18}$$
A) $$\frac{3}{4}$$
B) $$\frac{5}{6}$$
C) $$\frac{2}{3}$$
D) $$\frac{4}{5}$$
Answer:
$$\frac{3}{4}$$
Useful Formula for this Question:
For division of rational numbers:
$$\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}$$
Concept Behind This Question:
Students should divide rational numbers using reciprocals.
Step-by-Step Solution:
$$\frac{5}{12}\div\frac{10}{18}$$
$$=\frac{5}{12}\times\frac{18}{10}$$
Cancelling common factors:
$$=\frac{1}{2}\times\frac{3}{2}$$
$$=\frac{3}{4}$$
Therefore, the correct answer is:
$$\frac{3}{4}$$
Exam Tip:
Division of fractions means multiplication by the reciprocal.
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. Distributive Property
$$a(b+c)=ab+ac$$
FAQs
1. What is the additive identity of rational numbers?
The additive identity is:
$$0$$
because
$$a+0=a$$
2. What is the multiplicative identity of rational numbers?
The multiplicative identity is:
$$1$$
because
$$a\times1=a$$
3. Can zero be a rational number?
Yes,
$$0=\frac{0}{1}$$
is a rational number.
4. What is the reciprocal of:
$$\frac{7}{8}$$ ?
The reciprocal is:
$$\frac{8}{7}$$
5. Are rational numbers closed under division?
Yes, except when division by zero occurs.
Common Mistakes
❌ Forgetting to take the reciprocal while dividing fractions.
❌ Ignoring negative signs.
❌ Dividing by zero.
❌ Not simplifying fractions.
❌ Confusing identity with inverse.
Quick Revision Notes
✔ Rational numbers are written in the form:
$$\frac{p}{q}$$
✔ $$0$$ is the additive identity.
✔ $$1$$ is the multiplicative identity.
✔ Division of fractions means multiplication by reciprocal.
✔ Rational numbers satisfy various properties.
Conclusion
Rational Numbers is an essential chapter in Class 8 Mathematics. Understanding identities, inverses, and properties of rational numbers helps students solve problems efficiently and build a strong mathematical foundation. Regular MCQ practice enhances accuracy, confidence, and exam performance.
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