How this calculator works
Every fraction is first turned into an improper fraction (1 1/2 becomes 3/2). To add or subtract, the fractions are put over a common denominator by cross-multiplying; to multiply, numerators and denominators are multiplied straight across; to divide, the second fraction is flipped and multiplied. The result is then reduced by dividing top and bottom by their greatest common divisor, and written as a mixed number if it is bigger than 1.
Assumptions and tips
- Decimals are converted to exact fractions (0.75 = 3/4).
- A negative mixed number like −1 1/2 means −(1 + 1/2) = −3/2.
Worked example
Using the default values in the calculator above:
| Input | Value |
|---|---|
| First fraction | 1 1/2 |
| Operation | + add |
| Second fraction | 2/3 |
| Result | Value |
|---|---|
| Answer | 13/6 |
| Mixed number | 2 1/6 |
| Decimal | 2.166667 |
| Percent | 216.6667 % |
Step by step:
- Write both as improper fractions: 1 1/2 and 2/3
- Common denominator = product of the denominators
- Add the cross-multiplied numerators: (a × d + c × b) ÷ (b × d)
- Simplify by the greatest common divisor and write as a mixed number
Common fraction answers
Worked with this calculator — handy for recipes and measuring.
| Problem | Answer | Decimal |
|---|---|---|
| 1/2 + 1/3 | 5/6 | 0.833333 |
| 3/4 + 1/4 | 1 | 1 |
| 2/3 + 1/4 | 11/12 | 0.916667 |
| 1/2 − 1/3 | 1/6 | 0.166667 |
| 3/4 − 1/8 | 5/8 | 0.625 |
| 3/4 × 1/2 | 3/8 | 0.375 |
| 2/3 × 3/4 | 1/2 | 0.5 |
| 1/2 ÷ 1/4 | 2 | 2 |
| 3/4 ÷ 1/2 | 3/2 | 1.5 |
| 1 1/2 × 2 | 3 | 3 |
| 2 1/4 ÷ 3 | 3/4 | 0.75 |
Common mistakes to avoid
- Adding denominators: 1/2 + 1/3 is 5/6, not 2/5.
- Flipping the first fraction when dividing — flip the second one.
- Forgetting to convert mixed numbers to improper fractions before multiplying.
Frequently asked questions
What is 1 1/2 + 2/3?
3/2 + 2/3 = 9/6 + 4/6 = 13/6 = 2 1/6.
How do you divide fractions?
Keep the first, flip the second, multiply: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1 1/2.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common divisor: 18/24 ÷ 6/6 = 3/4.
What is half of 3/4 cup?
3/4 × 1/2 = 3/8 cup — useful when halving a recipe.
Sources
Built and reviewed by Anirban Kundu, Creator & Editor · M.Sc Physics, 20 years teaching science