Simplest Form Calculator
Enter the numerator and denominator to reduce your fraction to its lowest terms.
What is the Simplest Form of a Fraction?
The simplest form (also known as the "reduced form" or "lowest terms") of a fraction is a representation where the numerator and denominator are as small as possible. This happens when the only common factor between the numerator and the denominator is 1. In other words, they are coprime.
Using a simplest form calculator helps students, woodworkers, and chefs quickly interpret measurements without doing manual long division or complex factorization.
How to Calculate Simplest Form Manually
To reduce a fraction by hand, follow these three steps:
- Find the factors of both the numerator and the denominator.
- Identify the Greatest Common Divisor (GCD), which is the largest number that divides into both evenly.
- Divide both the top and bottom numbers by that GCD.
Example: Simplify 12/30
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- The Greatest Common Divisor (GCD) is 6.
- 12 ÷ 6 = 2
- 30 ÷ 6 = 5
- Simplest Form: 2/5
Common Fractions in Simplest Form
| Original Fraction | GCD | Simplest Form |
|---|---|---|
| 50/100 | 50 | 1/2 |
| 21/49 | 7 | 3/7 |
| 18/24 | 6 | 3/4 |
Why Simplifying Fractions Matters
Simplifying fractions makes numbers easier to work with in complex math problems. It also makes it much easier to compare different fractions. For instance, it is difficult to immediately see that 25/75 and 40/120 are the same, but once they are both reduced to 1/3, the relationship becomes crystal clear.