Vertoq
Fraction Calculator
Enter two fractions and pick an operation to see the result, simplified and as a decimal.
Working with fractions
Fractions are calculated differently depending on whether you're adding/subtracting or multiplying/dividing, and the calculator above automatically simplifies the answer to the smallest possible numerator and denominator.
The methods behind each operation
Addition and subtraction require a common denominator first. 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6, by scaling each fraction so the denominators match before adding or subtracting the numerators.
Multiplication is the simplest of all: multiply numerator by numerator and denominator by denominator, as in 1/2 × 1/3 = 1/6. Division flips the second fraction and multiplies instead, so 1/2 ÷ 1/3 becomes 1/2 × 3/1 = 3/2.
Simplifying a fraction
A fraction is simplified by dividing the numerator and denominator by their greatest common divisor (GCD). 12/16 has a GCD of 4, so both 12 and 16 divide by 4 to give 3/4, the same value in its simplest form.
Mixed numbers and improper fractions
A mixed number like 1½ can be rewritten as an improper fraction (numerator larger than denominator) by multiplying the whole number by the denominator and adding the numerator: 1½ = (1×2+1)/2 = 3/2. The calculator above works with improper fractions, so convert mixed numbers this way before entering them.
Frequently asked questions
Why do fractions need the same denominator to be added?
The denominator shows how many equal parts the whole is divided into. If the parts are different sizes (different denominators), the numerators can't be combined directly, they first need to be rescaled to the same part size.
Does the calculator always give the simplified answer?
Yes, the result is always automatically divided by the greatest common divisor of the numerator and denominator, so you get the answer in its simplest form.
Can I enter negative numbers?
Yes, both the numerator and denominator can be negative, and the sign is handled correctly in the result.