Fraction rules
a/b + c/d = (ad + bc) / bd
a/b − c/d = (ad − bc) / bd
a/b × c/d = ac / bd
a/b ÷ c/d = ad / bc
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.
Example: 2 1/4 × 1 1/3. Convert to improper fractions: 9/4 × 4/3. Multiply: 36/12. Simplify by the GCD 12: 3.
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.
Frequently asked questions
How do I enter a mixed number?
Type the whole number, a space, then the fraction — for example
2 1/4. Negative numbers work too: -1 1/2. Whole numbers and decimals like 0.75 are also accepted.How do you add fractions with different denominators?
Rewrite both fractions with a common denominator, add the numerators and simplify. 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
How do you divide fractions?
Multiply the first fraction by the reciprocal of the second (flip it). 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1 1/2.
How do you simplify a fraction?
Divide the numerator and denominator by their greatest common divisor (GCD). For 18/24 the GCD is 6, so it simplifies to 3/4.