Fraction Calculator

Add, subtract, multiply, or divide fractions — simplified automatically.

How the calculator works

Addition and subtraction first rewrite both fractions over a common denominator — the product of the two denominators, reduced afterwards — then combine the numerators. Multiplication is the easy one: numerators times numerators, denominators times denominators. Division flips the second fraction and multiplies. In every case the result is then reduced by dividing both parts by their greatest common divisor, and the sign is normalized so the denominator stays positive. Mixed-number conversion divides the numerator by the denominator: the quotient becomes the whole part and the remainder becomes the new numerator, so 7/3 reads as 2 and 1/3. The decimal value is the numerator divided by the denominator, shown to up to six places.

Formula

a/b + c/d = (ad + bc) ÷ (bd)
a/b × c/d = (ac) ÷ (bd)
a/b ÷ c/d = (ad) ÷ (bc)

Where:

  • a/b — the first fraction
  • c/d — the second fraction
  • The result is always simplified by the greatest common divisor

Example

Take 1/2 + 1/3. A common denominator is 6, giving 3/6 + 2/6 = 5/6 ≈ 0.833333 — already in lowest terms. Now try 4/8 ÷ 2/3: flipping the second fraction gives 4/8 × 3/2 = 12/16, which simplifies by the common divisor 4 to a clean 3/4, or 0.75 as a decimal. The same three-line logic covers every operation the calculator performs.

Frequently Asked Questions

Why do I need a common denominator to add fractions?
Fractions name parts of different-sized wholes — thirds and halves are different units, like meters and feet. A common denominator converts both to the same unit so the numerators can be added meaningfully. Multiplication and division never need it, which is why they feel easier.
What does 'simplified' actually mean?
A fraction is simplified when numerator and denominator share no common factor except 1. 3/2 and 6/4 are the same quantity, but 3/2 is the conventionally accepted form. The calculator divides both parts by their greatest common divisor to reach it.
Can I enter whole numbers or negatives?
Yes. Enter a whole number by putting 1 in the denominator (7/1), and make a fraction negative through either the numerator or the denominator — the result is normalized to show the sign on the numerator.
How precise is the decimal output?
It shows up to six decimal places. Repeating decimals such as 1/3 display as 0.333333 — a rounded view of an exact fraction, which is precisely why the fractional form remains the primary result.