FAQs on Flashcards: Rational Numbers

Question 1

1. What counts as a rational number and what doesn't?

Accepted Answer

Ans. 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. Examples include 3/4, -5/2, and 7 (since 7 = 7/1). Irrational numbers like π and √2 cannot be written this way, so they're not rational numbers.

Question 2

2. How do I add and subtract rational numbers with different denominators?

Accepted Answer

Ans. To add or subtract rational numbers with different denominators, first find the lowest common multiple (LCM) of the denominators. Convert both fractions to equivalent fractions using this common denominator, then add or subtract the numerators. For example, 1/3 + 1/4 becomes 4/12 + 3/12 = 7/12. Keep the denominator the same throughout.

Question 3

3. Why do I get different-looking answers when I multiply rational numbers-am I doing it wrong?

Accepted Answer

Ans. Multiplying rational numbers means multiplying numerators together and denominators together: (a/b) × (c/d) = (ac)/(bd). The result looks different because you haven't simplified it yet. Always reduce the final fraction to its simplest form by dividing both numerator and denominator by their greatest common divisor (GCD).

Question 4

4. Can a negative number be a rational number, and how does the negative sign work?

Accepted Answer

Ans. Yes, negative numbers are absolutely rational numbers. A negative rational number can have the negative sign in the numerator, denominator, or in front of the fraction-they're all equivalent: -3/4 = 3/(-4) = -(3/4). When dividing rational numbers, remember that a negative divided by a positive (or vice versa) gives a negative result.

Question 5

5. What's the difference between rational numbers and integers, and are all integers rational?

Accepted Answer

Ans. Integers are whole numbers (positive, negative, or zero), while rational numbers include integers plus all fractions and decimals that terminate or repeat. Every integer is a rational number because any integer n can be written as n/1. However, not every rational number is an integer-for example, 5/8 is rational but not an integer.

Flashcards: Rational Numbers

Mathematics (Maths) Class 8

FAQs on Flashcards: Rational Numbers

Mathematics (Maths) Class 8

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