A fraction calculator that shows its working
This free fraction calculator adds, subtracts, multiplies and divides fractions and mixed numbers, then gives the answer in lowest terms, as a mixed number, as an exact decimal and as a percentage. Every answer comes with the working a teacher expects to see: the common denominator, the rewritten fractions, the GCD used to simplify and the final conversion.
More modes cover the other jobs students meet constantly: Simplify reduces any fraction using Euclid’s algorithm; Decimal → fraction turns decimals — including repeating ones such as 0.333… — into exact fractions; Convert takes a fraction, mixed number, decimal or percentage and gives every other form; and Chart prints a fraction to decimal and percent chart from 1/1 to 1/20 or 1/30. All arithmetic uses big integers, so nothing is rounded.
How to use the Fraction Calculator
- Choose a mode at the top: Calculate, Simplify, Decimal → fraction, Convert (type 2 3/4, 0.375 or 37.5%) or Chart.
- For a calculation, type each fraction: the optional whole number on the left, the numerator above the line and the denominator below it.
- Pick the operation (+, −, × or ÷) from the box between the two fractions.
- Read the answer in the result panel — the simplified fraction, plus the mixed-number form when the fraction is improper.
- Check the exact decimal and percentage in the tiles below, then follow the numbered steps to see how the answer was reached.
- Use “Copy result” to paste the simplified fraction into your notes, or in Chart mode press Print, Download PDF or PNG.
Fraction Calculator features
Mixed numbers built in
Enter 2¾ as 2, 3 and 4. Mixed numbers are converted to improper fractions automatically, and the step is shown.
Teacher-style steps
Least common denominator, equivalent fractions, keep-change-flip for division and the GCD used to simplify — all with your numbers.
Exact repeating decimals
1/6 is shown as 0.1(6) with the repeating digit marked, rather than a rounded 0.166667.
Decimal to fraction
Converts terminating decimals like 2.125 and repeating decimals like 0.(142857) into exact fractions, and suggests a simple approximation for long decimals.
Fraction ⇄ decimal ⇄ percent
Convert mode reads 3/8, 2 3/4, 0.(6) or 12.5% and shows the simplest fraction, mixed number, exact decimal and exact percentage, such as 1/3 = 33.(3)%.
Printable conversion chart
Unit fractions 1/1 to 1/N, or every fraction up to denominator N (10, 12, 16, 20 or 30), with repeating digits under a bar — print it, or save a vector PDF or PNG on A4, Letter, A5 or Legal.
How fraction arithmetic works
Adding and subtracting: fractions can only be added when they share a denominator. Find the least common denominator (the LCM of the denominators), scale each fraction up to it, then add or subtract the numerators. Example: 1/2 + 2/3 → LCD 6 → 3/6 + 4/6 = 7/6 = 1 1/6.
Multiplying: multiply straight across — numerator × numerator over denominator × denominator. 3/4 × 2/5 = 6/20, which simplifies to 3/10. No common denominator is needed.
Dividing: keep the first fraction, change ÷ to ×, and flip the second fraction. 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. This works because dividing by a number is the same as multiplying by its reciprocal.
Simplifying: divide the numerator and denominator by their greatest common divisor. For 84/126 the GCD is 42, so 84/126 = 2/3. The LCM and GCD Calculator shows the factor tables behind both numbers.
Turning repeating decimals into fractions
For a repeating decimal, multiply it by a power of ten so the repeating part lines up, then subtract. For x = 0.1666…, 100x = 16.666… and 10x = 1.666…; subtracting gives 90x = 15, so x = 15/90 = 1/6. The calculator does exactly this when you type 0.1(6), and shows each line.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.(3) = 0.333… | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/6 | 0.1(6) = 0.1666… | 16.67% |
| 1/7 | 0.(142857) | 14.29% |
| 1/8 | 0.125 | 12.5% |
| 1/9 | 0.(1) = 0.111… | 11.11% |
| 3/16 | 0.1875 | 18.75% |
Common fraction mistakes
- Adding the denominators. 1/2 + 1/3 is not 2/5. Rewrite both over 6 first: 3/6 + 2/6 = 5/6.
- Flipping the wrong fraction. When dividing, only the second fraction (the divisor) is inverted.
- Forgetting the whole number. 2 1/4 × 2 is not 4 1/4 × … — convert to 9/4 first, then multiply: 9/4 × 2 = 9/2 = 4 1/2.
- Stopping before lowest terms. 6/20 is correct but unfinished; most teachers expect 3/10.
- Negative mixed numbers. −1 1/2 means −(1 + 1/2) = −3/2, not −1 + 1/2.
Fraction Calculator FAQ
How do I add fractions with different denominators?
Find the least common denominator, convert each fraction to it, then add the numerators. For 2/5 + 1/4 the LCD is 20, so 8/20 + 5/20 = 13/20. The fraction calculator shows each of these steps with your own numbers.
How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator and add the numerator: 2 3/4 = (2 × 4 + 3)/4 = 11/4. Type 2 3/4 in Convert mode to see the step, the decimal 2.75 and the percentage 275%.
Can I print a fraction to percentage table from 1 to 20?
Yes. Choose Chart, keep “Unit fractions” and N = 20 (or pick 30, or “All fractions” for 1/2 … 19/20), then Print or download the PDF. Repeating decimals such as 1/3 = 0.3 with a bar are shown exactly.
How do I enter a mixed number like 3½?
Type 3 in the whole-number box, 1 as the numerator and 2 as the denominator. Leave the whole-number box empty for an ordinary fraction.
How do I simplify a fraction to lowest terms?
Divide the top and bottom by their greatest common divisor. The Simplify mode finds the GCD with Euclid’s algorithm and shows every division, so you can copy the method.
How do I convert a decimal to a fraction?
Write the decimal over a power of ten and simplify: 0.375 = 375/1000 = 3/8. For repeating decimals, type the repeating digits in brackets, such as 0.(6) for 0.666…, to get the exact fraction 2/3.
Why is my answer shown as an improper fraction and a mixed number?
Both are correct: improper fractions such as 13/6 are easier to keep calculating with, mixed numbers such as 2 1/6 easier to picture.
Can I use negative fractions?
Yes. Put the minus sign on the whole number (−1, 1, 2 for −1½) or on the numerator of a simple fraction (−3 over 4). Subtracting a larger fraction from a smaller one also gives a negative answer.