Add: 1/2 + 1/3
- Input
- Fraction 1 = 1/2, Fraction 2 = 1/3, Operation = add
- Working
- Common denominator = 6. 1/2 = 3/6 and 1/3 = 2/6. 3/6 + 2/6 = 5/6. 5 and 6 share no common factor, so 5/6 is already in lowest terms.
- Result
- 1/2 + 1/3 = 5/6 (≈ 0.833)
Fraction Calculator
Add, subtract, multiply and divide fractions, then simplify the result to lowest terms and a mixed number, with every common-denominator step shown. Runs entirely in your browser — your numbers never leave this device.
Operator
Result
5/6
1/2 + 1/3 = 5/6
- Decimal
- 0.8333
- Percentage
- 83.3333%
Steps
- Common denominator: 1/2 = 3/6, 1/3 = 2/6
- Add numerators: 3/6 + 2/6 = 5/6
- Already in lowest terms
How it works
a/b + c/d = (a×d + c×b) / (b×d) | a/b − c/d = (a×d − c×b) / (b×d) | a/b × c/d = (a×c) / (b×d) | a/b ÷ c/d = (a×d) / (b×c)
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/8 | 0.125 | 12.5% |
| 1/6 | 0.167… | 16.67% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.333… | 33.33% |
| 3/8 | 0.375 | 37.5% |
| 1/2 | 0.5 | 50% |
| 5/8 | 0.625 | 62.5% |
| 3/4 | 0.75 | 75% |
| 5/6 | 0.833… | 83.33% |
| 7/8 | 0.875 | 87.5% |
For addition and subtraction the calculator first rewrites both fractions over a common denominator — the lowest common multiple of the two denominators — then adds or subtracts the numerators. Multiplication needs no common denominator: multiply straight across. Division flips the second fraction and multiplies, the 'keep, change, flip' rule, because dividing by a fraction is the same as multiplying by its reciprocal.
Every result is simplified by dividing the numerator and denominator by their greatest common factor, and improper fractions (numerator larger than denominator) are also shown as mixed numbers, so 7/4 appears as both 7/4 and 1 3/4. The working shows the common denominator, the rewritten fractions and the simplification step, in the same order you would write them on paper.
Whole numbers are treated as fractions with a denominator of 1, and mixed numbers should be entered as a whole part plus a fraction part. A denominator of zero is rejected with an explanation — a fraction with zero underneath is undefined, not zero — and negative signs are carried through the numerator so the sign of the answer is always clear.
Worked examples
Subtract: 3/4 − 1/6
- Input
- Fraction 1 = 3/4, Fraction 2 = 1/6, Operation = subtract
- Working
- Common denominator = 12. 3/4 = 9/12 and 1/6 = 2/12. 9/12 − 2/12 = 7/12. 7 is prime and does not divide 12, so the answer is already simplified.
- Result
- 3/4 − 1/6 = 7/12 (≈ 0.583)
Divide: 5/8 ÷ 2/3
- Input
- Fraction 1 = 5/8, Fraction 2 = 2/3, Operation = divide
- Working
- Flip the second fraction and multiply: 5/8 × 3/2 = (5×3) / (8×2) = 15/16. 15 and 16 share no common factor, so no simplification is needed.
- Result
- 5/8 ÷ 2/3 = 15/16 (= 0.9375)
Frequently asked questions
Why do I need a common denominator to add fractions but not to multiply them?
Addition combines pieces, and pieces must be the same size before they can be counted together — sixths can be added to sixths, but halves and thirds cannot until both are rewritten as sixths. Multiplication is a scaling operation, not a combining one, so the numerators and denominators simply multiply straight across.
How does the calculator simplify a fraction?
It finds the greatest common factor of the numerator and denominator and divides both by it. For example, 18/30 has a GCF of 6, so it becomes 3/5. If the GCF is 1, the fraction is already in its lowest terms and is left unchanged.
What is a mixed number and when is it shown?
A mixed number combines a whole number with a proper fraction, such as 1 3/4 for 7/4. The calculator shows it whenever the result is improper (the numerator is bigger than the denominator), alongside the simplified improper fraction, because recipes, measurements and school answers often expect the mixed form.
Why does dividing by a fraction mean flipping it?
Dividing by a number is the same as multiplying by its reciprocal — dividing by 2 is multiplying by 1/2. The same rule holds for fractions: dividing by 2/3 is multiplying by 3/2. You can check it: (5/8 ÷ 2/3) × 2/3 gets you back to exactly 5/8.
Can I enter a fraction with a zero denominator?
No, and the calculator explains why instead of guessing. A denominator of zero would mean splitting something into zero parts, which is undefined in mathematics. A zero numerator is fine, though: 0/5 is simply 0.
Does this fraction calculator upload my numbers?
No. It runs 100% in your browser, so the fractions you enter are calculated on your own device and are never uploaded, stored or shared. There is nothing to sign up for and no record of your calculations once you close the page.
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