How to use this calculator
- Enter the first fraction. If it’s a mixed number like 1 1/2, put the whole number in the first box; otherwise leave it at 0.
- Choose the operation: add, subtract, multiply or divide.
- Enter the second fraction the same way.
The result shows the answer as a fraction in lowest terms, as a mixed number and as a decimal, plus the percent and reciprocal. The step-by-step solution walks through the same method you’d use on paper: converting mixed numbers, finding the least common denominator, combining, simplifying with the greatest common divisor and converting back.
The arithmetic is exact. The calculator works with whole numbers at every stage, as you would by hand, so you never see a rounding error like 0.30000000000000004. That holds even for numerators and denominators in the trillions.
The rules for each operation
Adding and subtracting need a common denominator. With fractions a/b and c/d:
Multiplying the denominators always works, but using the least common denominator keeps the numbers small. The LCD is the denominators’ product divided by their greatest common divisor: LCD(4, 6) = 4 × 6 ÷ 2 = 12.
Multiplying goes straight across, top times top and bottom times bottom:
Dividing is multiplying by the reciprocal of the second fraction:
Mixed numbers become improper fractions first: whole × denominator + numerator, over the denominator. So 2 1/4 = (2 × 4 + 1)/4 = 9/4.
Worked examples
Adding mixed numbers: 1 1/2 + 2/3.
- Convert: 1 1/2 = (1 × 2 + 1)/2 = 3/2.
- The LCD of 2 and 3 is 6, since they share no common factor.
- Rewrite: 3/2 = 9/6 and 2/3 = 4/6.
- Add the numerators: (9 + 4)/6 = 13/6.
- GCD(13, 6) = 1, so it’s already in lowest terms.
- As a mixed number: 13 ÷ 6 = 2 remainder 1, so 2 1/6. As a decimal, 2.1666…, where the 6 repeats.
Subtracting: 3/4 − 5/6. GCD(4, 6) = 2, so the LCD is 4 × 6 ÷ 2 = 12. Then 3/4 = 9/12 and 5/6 = 10/12, and 9/12 − 10/12 = −1/12, about −0.083333.
Multiplying mixed numbers: 2 1/4 × 1 1/3. Convert to 9/4 × 4/3, multiply across to get 36/12, and divide top and bottom by their GCD of 12 to get exactly 3.
Dividing: 3/4 ÷ 2/3. Flip the second fraction and multiply: 3/4 × 3/2 = 9/8, which is 1 1/8 or 1.125.
Adding with a shared factor: 5/12 + 3/8. GCD(12, 8) = 4, so the LCD is 12 × 8 ÷ 4 = 24, not 96. Then 10/24 + 9/24 = 19/24.
Finding the GCD with Euclid’s algorithm
To simplify a fraction, you divide by the greatest common divisor of the numerator and denominator. For big numbers, listing factors is slow. Euclid’s algorithm is faster: divide the larger number by the smaller, keep the remainder, and repeat until the remainder is 0. The last non-zero remainder is the GCD.
For 8/30: 30 = 3 × 8 + 6, then 8 = 1 × 6 + 2, then 6 = 3 × 2 + 0. The GCD is 2, so 8/30 = 4/15. The calculator shows these lines in its steps whenever the chain is short enough to be useful.
Common fractions as decimals and percents
| Fraction | Decimal | Repeating notation | Percent |
|---|---|---|---|
| 1/2 | 0.5 | exact | 50% |
| 1/3 | 0.333333… | 0.(3) | 33.3333% |
| 2/3 | 0.666667… | 0.(6) | 66.6667% |
| 1/4 | 0.25 | exact | 25% |
| 3/4 | 0.75 | exact | 75% |
| 1/5 | 0.2 | exact | 20% |
| 1/6 | 0.166667… | 0.1(6) | 16.6667% |
| 1/7 | 0.142857… | 0.(142857) | 14.2857% |
| 1/8 | 0.125 | exact | 12.5% |
| 3/8 | 0.375 | exact | 37.5% |
| 1/9 | 0.111111… | 0.(1) | 11.1111% |
| 1/12 | 0.083333… | 0.08(3) | 8.3333% |
Digits in parentheses repeat forever. Decimals that don’t end are rounded to 6 places in the results, and percents to 4. To go the other way, from a percent to a fraction, use the percentage calculator.
Tips and common mistakes
- Don’t add denominators. 1/2 + 1/3 is not 2/5. Rewrite both over 6 first: 3/6 + 2/6 = 5/6.
- Simplify early when multiplying. In 9/4 × 4/3, the 4s cancel, and you can see the answer is 9/3 = 3 before multiplying anything out.
- Only flip the second fraction when dividing, never the first.
- Keep the sign in one place. The calculator moves any minus sign to the numerator, so 3/(−4) is shown as −3/4.
- A zero denominator is undefined. The calculator flags it, along with any division by a fraction equal to zero.
Assumptions
Entries must be whole numbers up to one trillion in size. A minus sign on the whole number applies to the whole mixed number: −1 1/2 means −(1 + 1/2) = −3/2, which is the standard convention in math textbooks. Results are always reduced to lowest terms, and the decimal shown is exact when it terminates within 6 decimal places.
Frequently asked questions
How do you add fractions with different denominators?
Rewrite both fractions over a common denominator, ideally the least common denominator (LCD), then add the numerators and keep the denominator. For 1/6 + 1/10, the LCD is 30, so the sum is 5/30 + 3/30 = 8/30, which simplifies to 4/15.
How do you multiply fractions?
Multiply the numerators together and the denominators together, then simplify. For 2/3 × 3/4 that's 6/12, which reduces to 1/2. You don't need a common denominator to multiply.
How do you divide fractions?
Flip the second fraction (take its reciprocal) and multiply. So 3/4 ÷ 2/3 becomes 3/4 × 3/2 = 9/8, or 1 1/8 as a mixed number. Dividing by a fraction that equals zero is undefined.
How do I enter a mixed number like 2 1/4?
Type the whole number (2) in the Whole box, then 1 as the numerator and 4 as the denominator. For a simple fraction leave Whole at 0. For a negative mixed number, put the minus sign on the whole number, so −2 1/4 means −(2 + 1/4).
How do you simplify a fraction?
Divide the numerator and denominator by their greatest common divisor (GCD). For 36/12 the GCD is 12, so it simplifies to 3/1, which is just 3. If the GCD is 1, the fraction is already in lowest terms.
Why do some fractions give repeating decimals?
A fraction in lowest terms has a terminating decimal only when its denominator has no prime factors other than 2 and 5. So 3/8 = 0.375 ends, but 1/3 = 0.333… and 1/7 = 0.142857142857… repeat forever. The calculator shows the repeating block in parentheses, such as 2.1(6).
Updated November 2026. Results are estimates for educational purposes and depend on the inputs you provide.