Working with fractions by hand means finding common denominators, multiplying numerators, and simplifying results — all steps where small arithmetic slips are easy to make. This calculator performs addition, subtraction, multiplication, and division on two fractions and automatically reduces the answer to its simplest form.
The formulas
After computing the raw result, the calculator simplifies it by dividing both the numerator and denominator by their greatest common divisor (GCD).
Worked examples
| Expression | Result |
|---|---|
| 1/2 + 1/3 | 5/6 |
| 3/4 − 1/4 | 1/2 |
| 2/3 × 3/5 | 2/5 |
| 1/2 ÷ 1/4 | 2 |
Step-by-step: adding fractions by hand
- Find a common denominator — multiplying the two denominators always works, even if it isn't the smallest possible one.
- Convert each fraction to that common denominator.
- Add or subtract the numerators, keeping the denominator unchanged.
- Simplify the result by dividing both parts by their greatest common divisor.
Common mistakes
- Adding numerators and denominators directly without finding a common denominator first — 1/2 + 1/3 is not 2/5.
- Forgetting to simplify. 4/8 is a correct but unsimplified answer; 1/2 is the fully reduced form.
- Flipping the wrong fraction when dividing. Only the second fraction (the divisor) gets flipped into its reciprocal.
Frequently asked questions
How do you add two fractions?
Find a common denominator, convert both fractions to that denominator, add the numerators, and simplify the result.
How do you divide fractions?
Multiply the first fraction by the reciprocal (flipped version) of the second fraction, then simplify.
How do I simplify a fraction?
Divide both the numerator and denominator by their greatest common divisor (GCD) until no common factor remains.
References
- Khan Academy — Free lessons on fraction arithmetic