Rational Number Calculator – Simplify Fractions
Simplify fractions and convert rational numbers
How to Use
- Enter the numerator (top number) of your fraction
- Enter the denominator (bottom number) of your fraction
- Select the operation you want to perform
- Click calculate to see the result
What is a Rational Number?
A rational number is any number that can be expressed as a fraction p/q, where p and q are integers and q ≠ 0. The word 'rational' comes from 'ratio', as these numbers represent ratios between integers.
Examples of rational numbers include 1/2, 3/4, -5/3, 7 (which is 7/1), and 0.25 (which is 1/4). All integers, fractions, and terminating or repeating decimals are rational numbers.
How to Simplify Fractions
To simplify a fraction, divide both the numerator and denominator by their Greatest Common Divisor (GCD). The GCD is the largest number that divides both numbers evenly.
- Find the GCD of the numerator and denominator
- Divide both numbers by the GCD
- The result is the simplified fraction
Example: To simplify 12/18, find GCD(12, 18) = 6, then 12÷6 = 2 and 18÷6 = 3, so 12/18 = 2/3.
Proper vs Improper Fractions
- Proper fraction: The numerator is less than the denominator (e.g., 3/4, 1/2)
- Improper fraction: The numerator is greater than or equal to the denominator (e.g., 5/3, 7/4)
- Mixed number: A whole number combined with a proper fraction (e.g., 1 2/3, 2 1/4)
Converting to Mixed Numbers
To convert an improper fraction to a mixed number:
- Divide the numerator by the denominator
- The quotient becomes the whole number
- The remainder becomes the new numerator
- Keep the same denominator
Example: 11/4 = 2 remainder 3, so 11/4 = 2 3/4
Frequently Asked Questions
- What is the difference between rational and irrational numbers?
- Rational numbers can be expressed as fractions (p/q where q≠0), while irrational numbers cannot. Examples of irrational numbers include π, √2, and e. Irrational numbers have non-terminating, non-repeating decimal expansions.
- How do I know if a fraction is in its simplest form?
- A fraction is in its simplest form when the numerator and denominator share no common factors other than 1. This means their GCD equals 1. For example, 3/4 is simplified, but 6/8 is not (GCD = 2).
- Can negative numbers be rational?
- Yes! Negative numbers can be rational. For example, -3/4, -5, and -0.25 are all rational numbers. The negative sign can be placed with the numerator, denominator, or in front of the fraction.
- Is zero a rational number?
- Yes, zero is a rational number because it can be expressed as 0/1 or 0/n for any non-zero integer n. Zero is the only number that is neither positive nor negative.