Fraction Calculator
Simplify fractions and convert to decimals, percents, and mixed numbers.
What it does
A fraction in lowest terms divides top and bottom by their greatest common divisor, the largest number splitting both evenly. Euclid finds it fast: replace the pair by the smaller number and the remainder, and repeat until nothing remains.
The tool above reduces your fraction that way, then shows the decimal, the percent, and the mixed number form for improper fractions.
Signs belong up front. A negative over a negative is positive, and the tool keeps the single minus on the numerator so forms stay tidy.
How to use
- Enter whole numbers for top and bottom.
- Read the simplest form first and use it for further math.
- Take the decimal for calculators and the percent for comparisons.
- Use the mixed number for measurements and everyday talk.
Formula
- GCD
- Largest number splitting both parts evenly.
- a mod b
- Remainder driving each Euclid step.
- num / den
- Decimal value of the fraction.
Dividing by the GCD keeps the value identical while shrinking the numbers. Zero over anything is simply zero, while anything over zero has no answer.
Worked example
Example: simplify 12/16
Numerator 12, denominator 16.
- Euclid: 16 mod 12 = 4, then 12 mod 4 = 0, so GCD is 4.
- Divide: 12 / 4 = 3, 16 / 4 = 4. Simplest form 3/4.
- Decimal: 12 / 16 = 0.75.
- Percent: 0.75 x 100 = 75 %.
- Mixed: 3/4 is proper, so it stays 3/4.
Reference table
| As written | Simplest | Decimal |
|---|---|---|
| 2/4 | 1/2 | 0.5 |
| 3/9 | 1/3 | 0.333333 |
| 6/8 | 3/4 | 0.75 |
| 10/15 | 2/3 | 0.666667 |
| 7/4 | 7/4 = 1 3/4 | 1.75 |
Limits
- Whole numbers only. Decimals need conversion first.
- Zero denominator has no answer.
- Very large numbers exceed the input guard.
- Repeating decimals round at six places here.
Common mistakes
- Adding tops and bottoms directly. Fractions need a common denominator first.
- Stopping one step early. 12/16 to 6/8 is not finished; 3/4 is.
- Dropping the sign. Keep one minus in front and track it.
- Dividing by zero and expecting an answer.
- Rounding the decimal before converting onward. Convert exact, round last.
Try it yourself
Quick checks. Answers sit tucked under each question.
Simplify 15/25?
GCD is 5. Then 3/5, which is 0.6 or 60%.
7/3 as a mixed number?
7 / 3 = 2 remainder 1, so 2 1/3.
Questions
What is the fastest way to simplify?
Divide top and bottom by their greatest common divisor in one step instead of chipping away.
How do decimals repeat?
When the reduced denominator holds primes beyond 2 and 5. Thirds and sixths repeat; halves, quarters, and fifths terminate.
What is an improper fraction?
Top at least as big as bottom, like 7/4. As a mixed number that is 1 3/4.
Can the tool handle negatives?
Yes. Signs fold to the front, so -3/4 and 3/-4 both read -3/4.
Why keep simplest form?
Smaller numbers cut errors in later steps and match expected school answers.