Fraction Calculator
Last updated: 2026-06-25
For fraction arithmetic: addition/subtraction a/b ± c/d = (a·d ± c·b)/(b·d), multiplication a/b × c/d = (a·c)/(b·d), division a/b ÷ c/d = (a·d)/(b·c), then reduce by the GCD to lowest terms.
Enter two fractions and an operation below to get the simplified fraction, mixed number and decimal value at once.
Fraction arithmetic
Result in lowest terms
0
Enter integers for numerators and denominators. The result cannot be computed if a denominator is 0, or if the second numerator is 0 in division.
How to use
- Enter the first fraction — Enter the numerator and denominator of the first fraction.
- Choose an operation — Select addition (+), subtraction (−), multiplication (×) or division (÷).
- Enter the second fraction and calculate — Enter the second fraction and press Calculate to see the simplified fraction, mixed number and decimal value.
How fraction arithmetic and reduction work
Each fraction operation follows its own rule. Addition and subtraction require a common denominator, while multiplication and division operate directly on numerators and denominators. At the end, divide by the greatest common divisor (GCD) of the numerator and denominator to reach lowest terms.
| Operation | Formula | Example |
|---|---|---|
| Addition | a/b + c/d = (a·d + c·b) / (b·d) | 1/2 + 1/3 = 5/6 |
| Subtraction | a/b − c/d = (a·d − c·b) / (b·d) | 3/4 − 1/4 = 1/2 |
| Multiplication | a/b × c/d = (a·c) / (b·d) | 2/3 × 3/5 = 2/5 |
| Division | a/b ÷ c/d = (a·d) / (b·c) | 1/2 ÷ 1/4 = 2 |
Reducing a fraction means dividing the numerator and denominator by the same number to get a simpler form. Dividing by their GCD gives lowest terms in one step. By convention the negative sign is placed on the numerator and the denominator is kept positive. The GCD behind reduction can also be checked with the GCD & LCM calculator.
Frequently Asked Questions (FAQ)
How do I reduce a fraction to lowest terms?
Divide the numerator and denominator by their greatest common divisor (GCD). For example, 6/8 becomes 3/4 after dividing both by 2. This calculator simplifies the result automatically.
How do I add and subtract fractions?
If the denominators differ, find a common denominator first. a/b ± c/d = (a·d ± c·b) / (b·d), then reduce to lowest terms. Example: 1/2 + 1/3 = (3+2)/6 = 5/6.
How do I divide fractions?
Multiply by the reciprocal of the divisor (flip its numerator and denominator). a/b ÷ c/d = a/b × d/c = (a·d) / (b·c). Division is undefined if the divisor's numerator is 0.
What is a mixed number?
A mixed number is the sum of a whole number and a proper fraction. For example, 7/3 is 2 and 1/3. This calculator also shows the mixed number for improper fractions.
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Last updated: 2026-06-25