Fraction Calculator
Add, subtract, multiply, or divide fractions and mixed numbers, or convert between decimals and fractions. Every answer is simplified, with the working shown underneath.
Your fractions
Results
Result
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Fraction A
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Fraction B
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Comparison
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Show the mathHow it was calculated
Adding, subtracting, multiplying, dividing
To add or subtract fractions, first give them a common denominator, then add or subtract the numerators. To multiply, multiply the numerators together and the denominators together. To divide, multiply by the second fraction's reciprocal (flip its numerator and denominator). This calculator handles all four automatically, including mixed numbers, and always simplifies the result to lowest terms.
Worked example: 2/3 + 3/4. The denominators differ, so multiply them to get a common denominator of 12. Then 2/3 = 8/12 and 3/4 = 9/12, and 8/12 + 9/12 = 17/12. The GCD of 17 and 12 is 1, so it can't be reduced, and as a mixed number it is 1 5/12. Open "Show the math" under the result to see the same steps for your own fractions. One case has no answer: dividing by a fraction worth zero, such as 0/3. The calculator says so instead of returning a number.
Fraction to decimal, and back
A fraction converts to a decimal by dividing the numerator by the denominator (3/4 = 3 ÷ 4 = 0.75). Going the other way, a decimal converts to a fraction by reading its digits as a numerator over a power of 10 (0.75 = 75/100), then simplifying (75/100 = 3/4). Switch to "Decimal → Fraction" mode above to convert instantly in either direction — every fraction on this page also shows its decimal equivalent.
Mixed numbers vs. improper fractions
A mixed number (like 1 ⅓) combines a whole number with a proper fraction. An improper fraction (like 4/3) has a numerator larger than its denominator, expressing the same value without a separate whole part. This calculator accepts mixed numbers as input and shows results both ways — as a simplified fraction and as a mixed number — so you can use whichever form you need.
Comparing fractions
To tell which of two fractions is bigger, cross-multiply: for a/b vs. c/d, compare a×d against b×c. This avoids finding a common denominator first, and works even when the fractions look very different in size. In Arithmetic mode, this calculator runs that comparison automatically on Fraction A and Fraction B, regardless of which operation is selected.
Fraction to decimal chart
These are the fractions that come up most often in recipes, measurements and homework. Decimals are rounded to four places, and "…" marks a decimal that repeats forever. Multiply a decimal by 100 to get the percentage, or use the percentage calculator for anything beyond a quick lookup.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.3333… | 33.33% |
| 2/3 | 0.6667… | 66.67% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1667… | 16.67% |
| 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% |
| 1/12 | 0.0833… | 8.33% |
| 1/16 | 0.0625 | 6.25% |
A fraction gives a terminating decimal only when its simplified denominator has no prime factors other than 2 and 5. That is why eighths and sixteenths end neatly while thirds, sixths and twelfths repeat.
Inch fractions in decimals and mm
US tape measures, drill bits and lumber are marked in halves, quarters, eighths and sixteenths of an inch. Since 1 inch is exactly 25.4 mm, each fraction converts exactly:
| Inches | Decimal inches | Millimetres |
|---|---|---|
| 1/16" | 0.0625 | 1.5875 |
| 1/8" | 0.125 | 3.175 |
| 3/16" | 0.1875 | 4.7625 |
| 1/4" | 0.25 | 6.35 |
| 3/8" | 0.375 | 9.525 |
| 1/2" | 0.5 | 12.7 |
| 5/8" | 0.625 | 15.875 |
| 3/4" | 0.75 | 19.05 |
| 7/8" | 0.875 | 22.225 |
Adding measurements is fraction arithmetic: a 2 3/8" board plus a 1 5/16" board is 2 6/16 + 1 5/16 = 3 11/16". Enter them as mixed numbers above to check. For metric lengths, the cm to inches converter goes the other way, and the tile calculator uses these measurements to estimate a whole floor.
Frequently asked questions
How do I convert a fraction to a decimal without a calculator?
Divide the numerator by the denominator using long division — 3 ÷ 4 = 0.75, for example. This calculator does that division instantly for both fractions you enter, and for the result of whatever operation you choose, so you always see the decimal equivalent alongside the fraction.
How do I put or type a fraction into a calculator?
On this calculator, enter the whole number part (if any), numerator, and denominator into their own fields — for example, 1 ⅓ becomes whole=1, numerator=1, denominator=3. Most physical scientific calculators use a dedicated fraction key (often labeled a b/c or ⌟) that moves the cursor between numerator and denominator slots the same way.
How do I turn a decimal into a fraction?
Switch to "Decimal → Fraction" mode above, enter your decimal, and this calculator converts it exactly — reading the digits after the decimal point to build a fraction over a power of 10, then simplifying. For example, 0.75 becomes 75/100, which simplifies to 3/4.
How do I know which fraction is bigger?
Cross-multiply: for a/b vs c/d, compare a×d against b×c — whichever product is larger belongs to the larger fraction. This calculator does that comparison automatically every time you enter two fractions in Arithmetic mode, regardless of which operation you've selected.
How do I simplify or reduce a fraction?
Divide the numerator and denominator by their greatest common divisor (GCD) — for 8/12, the GCD is 4, so it reduces to 2/3. To simplify a single fraction here, enter it as Fraction A, choose Divide as the operation, and enter 1/1 as Fraction B — every result on this calculator is automatically reduced to lowest terms, so the answer shown is your fraction fully simplified.
How do I turn a repeating decimal like 0.333… into a fraction?
Repeating decimals need a small algebra trick. Let x = 0.333…, so 10x = 3.333…; subtract to get 9x = 3, and x = 3/9 = 1/3. Two repeating digits use 100x instead: 0.272727… becomes 99x = 27, or 3/11. The converter above reads only the digits you type, so 0.333 becomes 333/1000, not 1/3.
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