Working with fractions
A fraction is a way of writing a part of a whole: the bottom number (the denominator) says how many equal pieces the whole is split into, and the top number (the numerator) says how many of those pieces you have. This calculator adds, subtracts, multiplies and divides any two fractions, then gives you the answer in lowest terms along with its mixed-number and decimal forms — updated live as you type.
How the four operations work
Adding and subtracting require a common denominator: rewrite both fractions over the same bottom number, then add or subtract the tops. Multiplying is simpler — multiply the numerators together and the denominators together. Dividing means multiplying by the reciprocal: flip the second fraction upside down and multiply. Every result is then reduced by the greatest common divisor so it is in its simplest form.
| Operation | Rule | Example |
|---|---|---|
| Add (+) | Common denominator, add numerators | 1/2 + 1/3 = 5/6 |
| Subtract (−) | Common denominator, subtract numerators | 3/4 − 1/4 = 1/2 |
| Multiply (×) | Multiply numerators and denominators | 2/3 × 3/4 = 1/2 |
| Divide (÷) | Multiply by the reciprocal of the second | 1/2 ÷ 1/4 = 2 |
Worked example
Generated by the same engine that powers the calculator, for 1/2 + 1/3.
| Step | Value |
|---|---|
| Common denominator of 2 and 3 | 6 |
| Rewrite | 3/6 + 2/6 |
| Add the numerators | 5/6 |
| Result (already simplified) | 5/6 |
| As a decimal | 0.8333 |
Mixed numbers and decimals
An improper fraction (numerator larger than denominator) can be written as a mixed number — a whole part plus a proper fraction. For instance 7/3 is 2 1/3. Dividing the numerator by the denominator gives the decimal form, which may repeat (5/6 = 0.8333…). The calculator shows all three so you can use whichever fits your work.
Frequently asked questions
How do you add fractions?+
Give both fractions a common denominator, add the numerators, then simplify. For example, 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6.
How do you subtract fractions?+
Use a common denominator, subtract the numerators, then reduce. 3/4 − 1/4 = 2/4 = 1/2.
How do you multiply fractions?+
Multiply the numerators together and the denominators together, then simplify. 2/3 × 3/4 = 6/12 = 1/2.
How do you divide fractions?+
Flip the second fraction (its reciprocal) and multiply. 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2.
What does simplifying a fraction mean?+
Dividing the numerator and denominator by their greatest common divisor so the fraction is in its lowest terms, e.g. 6/12 simplifies to 1/2.
What is a mixed number?+
A whole number plus a proper fraction. An improper fraction like 7/3 equals the mixed number 2 1/3.
Can a fraction have a negative sign?+
Yes. This calculator carries the sign on the numerator, so −1/2, 1/−2 and −(1/2) are all treated as −1/2.
Why can’t you divide by zero?+
Dividing by zero has no defined value, so dividing by a fraction whose numerator is 0 (like 0/5) is undefined — the calculator flags it rather than returning a number.
How do you convert a fraction to a decimal?+
Divide the numerator by the denominator. 5/6 = 5 ÷ 6 ≈ 0.8333.
What is the greatest common divisor (GCD)?+
The largest whole number that divides two numbers exactly. It is used to reduce a fraction to lowest terms; for 12 and 18 the GCD is 6.
Sources
- Wolfram MathWorld — Fraction (rational-number arithmetic)
- Encyclopaedia Britannica — Fraction
- Math is Fun — Fractions (add, subtract, multiply, divide)
Formula and data last reviewed by the TheCalculatorVault team on 26 June 2026. Figures are for general information, not professional advice.
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