DigiKitFraction Calculator
Enter two fractions or mixed numbers, choose an operation and get the simplified result, the mixed number and the decimal value.
How each operation works
- Add or subtract: bring both fractions to a common denominator, then add or subtract the numerators. The calculator uses a/b + c/d = (a×d + c×b) ÷ (b×d), then simplifies.
- Multiply: multiply the numerators and multiply the denominators: a/b × c/d = (a×c) ÷ (b×d).
- Divide: multiply by the reciprocal of the second fraction: a/b ÷ c/d = (a×d) ÷ (b×c). Dividing by a fraction whose numerator is 0 is not possible.
Every result is simplified by dividing the numerator and denominator by their greatest common divisor, and a negative sign is always carried by the numerator.
Worked examples
| Problem | Result | Mixed number | Decimal |
|---|---|---|---|
| 1/2 + 1/3 | 5/6 | — | 0.833333 |
| 3/4 − 5/6 | −1/12 | — | −0.083333 |
| 1 1/2 × 2/3 | 1 | — | 1 |
| 2/3 ÷ 4/9 | 3/2 | 1 1/2 | 1.5 |
| 7 ÷ 2 | 7/2 | 3 1/2 | 3.5 |
Take 1/2 + 1/3. The common denominator is 6, so 3/6 + 2/6 = 5/6. For 2/3 ÷ 4/9, flip the second fraction and multiply: 2/3 × 9/4 = 18/12, which simplifies to 3/2.
How to enter fractions
- A fraction:
3/4. - A mixed number:
1 1/2(whole number, a space, then the fraction). - A whole number:
5. - A negative value: put the minus sign first, such as
-3/4or-1 1/2.
Fraction to decimal reference
| Fraction | Decimal | Fraction | Decimal |
|---|---|---|---|
| 1/2 | 0.5 | 1/8 | 0.125 |
| 1/4 | 0.25 | 3/8 | 0.375 |
| 3/4 | 0.75 | 5/8 | 0.625 |
| 1/3 | 0.3333… | 2/3 | 0.6667… |
Why a common denominator is needed
You can only add or subtract pieces of the same size. 1/2 and 1/3 are different-sized pieces, so you cut both into sixths first: 1/2 = 3/6 and 1/3 = 2/6. The calculator finds a common denominator by multiplying the two denominators and then simplifies, so the answer is the same as one found with the smallest common denominator.
Things to keep in mind
- The calculator accepts whole numbers, fractions and mixed numbers. It does not accept decimals such as 0.5; write them as fractions (1/2) first.
- The decimal is rounded to six places and may be an approximation for fractions like 1/3.
- Very large numerators or denominators are rejected to avoid inaccurate results.
- A denominator of 0 is not valid, and the calculator will tell you so.
Frequently asked questions
How do I enter a mixed number?
Type the whole number, a space and then the fraction, for example 2 3/4. The calculator converts it to an improper fraction internally.
Does it simplify the answer?
Yes. The result is always reduced to lowest terms. If the result is larger than 1, it also shows the mixed-number form.
Can I use decimals?
Not directly. Convert the decimal to a fraction first, for example 0.25 becomes 1/4.
Why does dividing by zero fail?
Division by zero is undefined. The calculator shows an error when the second fraction equals 0 or when a denominator is 0.
Is my data stored?
No. Everything is calculated in your browser.