Fraction Calculator
Add, subtract, multiply, or divide any two fractions. Results are simplified to lowest terms automatically.
Simplify a fraction
Fraction ↔ Decimal
Common fraction conversions
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333333 | 33.3333% |
| 2/3 | 0.666667 | 66.6667% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/10 | 0.1 | 10% |
How to add, subtract, multiply and divide fractions
Addition and subtraction
You can only add or subtract fractions that share the same denominator. To combine 1/4 and 1/6, find a common denominator (12): 1/4 = 3/12 and 1/6 = 2/12, so 1/4 + 1/6 = 5/12. The lowest common denominator is the least common multiple of the two denominators.
Multiplication
Straightforward: multiply the numerators together and the denominators together, then simplify. So 2/3 × 4/5 = 8/15 (already in lowest terms because 8 and 15 share no factors).
Division
Flip the second fraction (take its reciprocal) and multiply. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8. This is why dividing by a fraction less than one gives a bigger answer — you are asking "how many halves fit in three-quarters?"
Simplifying
Divide numerator and denominator by their greatest common divisor. For 18/24, the GCD is 6, so 18/24 = 3/4. Every rational answer this calculator returns is already simplified.
Fractions, decimals and percentages
Any fraction can be converted to a decimal by dividing the numerator by the denominator, and any decimal that terminates or repeats can be written as a fraction. Some quick conversions worth memorising:
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.3% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1666… | 16.7% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.1 | 10% |
Mixed numbers and improper fractions
A mixed number like 2 3/5 combines a whole number and a fraction. An improper fraction like 13/5 puts the same value in a single fraction (5 × 2 + 3 = 13). Most calculators — including this one — work with improper fractions internally because they are easier to combine. Convert back to a mixed number by dividing (13 ÷ 5 = 2 remainder 3, which is 2 3/5).
Common mistakes with fractions
- Adding numerators and denominators. 1/2 + 1/3 is not 2/5 — that would be less than 1/2. Find a common denominator first.
- Flipping the wrong fraction when dividing. In a ÷ b, flip b (the second one), not a.
- Forgetting to simplify. 4/8 and 1/2 are the same number; convention is to give the simplest form.
- Rounding too early. If you convert 1/3 to 0.33 and then work with that, tiny errors compound. Keep it as a fraction as long as possible.
Frequently asked questions
Why does this calculator show the answer in lowest terms?
By mathematical convention a fraction is "in its simplest form" when the numerator and denominator share no common factor other than 1. Answers like 6/8 are correct but 3/4 is the accepted form.
Can I enter negative fractions?
Yes — put the minus sign on either the numerator or the whole fraction. -3/4 and 3/-4 are treated identically. Two negatives cancel: -3/-4 is the same as 3/4.
How is a decimal converted back to a fraction?
For a terminating decimal, count the digits after the point: 0.375 has three, so it becomes 375/1000, which simplifies to 3/8. For a recurring decimal there is a bit more algebra involved — see any standard textbook.
What is the difference between a fraction and a ratio?
A ratio compares two quantities of the same kind (5 boys to 4 girls = 5:4). A fraction compares a part to a whole (5 out of 9 children are boys = 5/9). Ratios and fractions look similar but mean different things.
Do I need to convert fractions to decimals before comparing them?
Not necessarily. Cross-multiply: to compare 5/7 and 3/4, compute 5 × 4 = 20 and 3 × 7 = 21. The bigger cross product corresponds to the bigger fraction, so 3/4 > 5/7. Faster than doing two long divisions.