Fraction rules
a/b − c/d = (ad − bc) / bd
a/b × c/d = ac / bd
a/b ÷ c/d = ad / bc
After each operation the result is simplified by dividing the top and bottom by their greatest common divisor. Mixed numbers are first converted to improper fractions: 2 1/4 = (2 × 4 + 1)/4 = 9/4.
Where fractions show up
- Cooking — scaling a recipe by 1 1/2 or halving 3/4 cup. See also cups to grams.
- Construction and woodworking — adding measurements like 5 3/8 in + 2 7/16 in.
- Homework — checking answers and seeing each step.
How to use the calculator
- Type the first fraction as a simple fraction (3/4), a mixed number with a space (1 1/2) or a whole number (5). Negative values work too (−2/3).
- Choose the operation: add, subtract, multiply or divide.
- Type the second fraction and read the simplified answer, its mixed-number form, its decimal value and the working.
Adding fractions step by step
To add or subtract, the fractions need a common denominator. Using the least common denominator (LCD) keeps numbers small:
Dividing fractions
Dividing by a fraction is the same as multiplying by its reciprocal — “keep, change, flip”. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8. A useful check: dividing by a number less than 1 gives a bigger result.
Simplifying fractions
A fraction is in lowest terms when the numerator and denominator have no common factor other than 1. Find the greatest common divisor (GCD) and divide both by it: 18/24 → GCD 6 → 3/4. A quick way to find the GCD is Euclid’s algorithm: repeatedly replace the larger number with the remainder of dividing it by the smaller one until the remainder is 0 (24 mod 18 = 6, 18 mod 6 = 0, so the GCD is 6).
Common fractions as decimals
- 1/2 = 0.5 · 1/3 ≈ 0.333 · 2/3 ≈ 0.667 · 1/4 = 0.25 · 3/4 = 0.75
- 1/5 = 0.2 · 1/8 = 0.125 · 3/8 = 0.375 · 5/8 = 0.625 · 7/8 = 0.875
- 1/16 = 0.0625 · 1/32 = 0.03125 — handy for inch measurements
Common mistakes
- Adding numerators and denominators directly: 1/2 + 1/3 is not 2/5; it is 5/6.
- Multiplying only the whole parts of mixed numbers: 1 1/2 × 2 1/2 is 3 3/4, not 2 1/4. Convert to improper fractions first (3/2 × 5/2 = 15/4).
- Cancelling terms across a plus sign — you can only cancel common factors in multiplication.
Frequently asked questions
How do I enter a mixed number?
2 1/4. Negative numbers work too: -1 1/2. Whole numbers and decimals like 0.75 are also accepted.