Simplifying Fractions Calculator
Reduce any fraction to its lowest terms. Get the GCD, step-by-step solution, decimal, and percentage equivalents instantly.
| Property | Value |
|---|
| Original Fraction | Simplified | GCD | Decimal | Percentage |
|---|---|---|---|---|
| 2/4 | 1/2 | 2 | 0.5 | 50% |
| 4/8 | 1/2 | 4 | 0.5 | 50% |
| 6/9 | 2/3 | 3 | 0.6667 | 66.67% |
| 8/12 | 2/3 | 4 | 0.6667 | 66.67% |
| 10/15 | 2/3 | 5 | 0.6667 | 66.67% |
| 12/16 | 3/4 | 4 | 0.75 | 75% |
| 15/20 | 3/4 | 5 | 0.75 | 75% |
| 16/24 | 2/3 | 8 | 0.6667 | 66.67% |
| 18/24 | 3/4 | 6 | 0.75 | 75% |
| 25/100 | 1/4 | 25 | 0.25 | 25% |
How to Simplify a Fraction
Simplifying a fraction means reducing it to its lowest terms, where the numerator and denominator share no common factor other than 1. The process requires finding the greatest common divisor and dividing both parts of the fraction by it.
Step-by-Step Method
- Write down the numerator and denominator of your fraction
- Find all factors of the numerator
- Find all factors of the denominator
- Identify the greatest common divisor (the largest shared factor)
- Divide both the numerator and denominator by the GCD
- The resulting fraction is in its simplest form
Example: Simplify 18/24. Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. GCD = 6. So 18 ÷ 6 = 3 and 24 ÷ 6 = 4. Simplified: 3/4.
The Euclidean Algorithm for GCD
For large numbers, the Euclidean algorithm is the fastest way to find the GCD. Divide the larger number by the smaller, then replace the larger with the smaller and the smaller with the remainder. Repeat until the remainder is 0. The last non-zero remainder is the GCD.
Example for GCD of 48 and 36: 48 ÷ 36 = 1 remainder 12. Then 36 ÷ 12 = 3 remainder 0. GCD = 12.
Types of Fractions
Understanding fraction types helps with simplification:
- Proper fraction: Numerator is smaller than denominator (e.g. 3/4)
- Improper fraction: Numerator is larger than or equal to the denominator (e.g. 7/4)
- Mixed number: A whole number combined with a proper fraction (e.g. 1 and 3/4)
- Equivalent fractions: Different fractions that represent the same value (e.g. 1/2 = 2/4 = 3/6)
Converting Fractions to Decimals and Percentages
Converting fractions to other forms is straightforward once simplified. Divide the numerator by the denominator to get a decimal. Multiply the decimal by 100 to get the percentage. For example, 3/4 = 0.75 = 75%.
Frequently Asked Questions
To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by the GCD. For example, 8/12 has a GCD of 4, so 8÷4=2 and 12÷4=3, giving 2/3.
The GCD, or greatest common divisor, is the largest number that divides both the numerator and denominator evenly. Dividing both by the GCD reduces the fraction to its lowest terms in a single step.
A fraction is fully simplified when the GCD of the numerator and denominator is 1, meaning no integer other than 1 divides both evenly. This is called lowest terms or simplest form.
An improper fraction is simplified the same way as a regular fraction: divide both numerator and denominator by their GCD. You can also convert it to a mixed number by dividing the numerator by the denominator and expressing the remainder as a fraction.
To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. To get a percentage, multiply the decimal by 100 to get 75%.