Rational Numbers (Class 8 Mathematics)
Master rational numbers, their properties, and operations. Learn about fractions, decimals, and how to work with numbers expressed as ratios.
TL;DR: Master rational numbers, their properties, and operations. Learn about fractions, decimals, and how to work with numbers expressed as ratios.
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Master rational numbers, their properties, and operations. Learn about fractions, decimals, and how to work with numbers expressed as ratios.
Rational Numbers MCQs with Answers & Explanations
Q1. What is a rational number?
- Only integers
- Any number
- Only positive numbers
- A number that can be expressed as p/q where q ≠ 0 ✓ (correct)
Explanation: A rational number is any number that can be expressed as a fraction p/q where p and q are integers and q is not zero. This includes integers, fractions, and terminating/repeating decimals.
Q2. Which of the following is a rational number?
- 1.5 ✓ (correct)
- π
- √2
- √3
Explanation: 1.5 = 3/2 is a rational number. √2, π, and √3 are irrational numbers as they cannot be expressed as a ratio of integers.
Q3. What is the additive identity of rational numbers?
- ∞
- 0 ✓ (correct)
- -1
- 1
Explanation: The additive identity is 0. Adding 0 to any rational number gives the same number. a + 0 = a for all rational a.
Q4. What is the multiplicative identity of rational numbers?
- -1
- 0
- 1 ✓ (correct)
- ∞
Explanation: The multiplicative identity is 1. Multiplying any rational number by 1 gives the same number. a × 1 = a for all rational a.
Q5. What is the additive inverse of 3/4?
- 4/3
- 1
- 3/4
- -3/4 ✓ (correct)
Explanation: The additive inverse of 3/4 is -3/4. Adding them gives zero: 3/4 + (-3/4) = 0.
Q6. What is the multiplicative inverse of 2/5?
- 5/2 ✓ (correct)
- -2/5
- 0
- 2/5
Explanation: The multiplicative inverse of 2/5 is 5/2. Multiplying them gives one: (2/5) × (5/2) = 1.
Q7. Simplify: 2/3 + 1/4
- 8/12
- 11/12 ✓ (correct)
- 3/7
- 3/12
Explanation: 2/3 + 1/4: LCM of 3 and 4 is 12. So, (2×4)/(3×4) + (1×3)/(4×3) = 8/12 + 3/12 = 11/12.
Q8. Simplify: 3/5 × 10/9
- 3/9
- 5/3
- 2/3 ✓ (correct)
- 30/45
Explanation: (3/5) × (10/9) = (3×10)/(5×9) = 30/45 = 2/3. Cancel common factors.
Q9. Which property states that a + b = b + a?
- Associative
- Identity
- Distributive
- Commutative ✓ (correct)
Explanation: The commutative property states that the order of addition (or multiplication) does not change the result. a + b = b + a.
Q10. What is the value of -2/3 ÷ 4/9?
- -3/2 ✓ (correct)
- 8/27
- -8/27
- -6/4
Explanation: (-2/3) ÷ (4/9) = (-2/3) × (9/4) = (-2×9)/(3×4) = -18/12 = -3/2.
Frequently Asked Questions
Is every integer a rational number?
Yes, every integer is a rational number. Any integer n can be expressed as n/1, which is in the form p/q. For example, 5 = 5/1.
What is the difference between rational and irrational numbers?
Rational numbers can be expressed as p/q (like 1/2, 0.5, 3). Irrational numbers cannot (like √2, π, e). Together they form all real numbers.
More Class 8 Mathematics MCQs
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