Fraction Calculator

You cannot add or subtract fractions directly unless they share a common denominator. The calculator finds the least common multiple (LCM) of the two denominators, rewrites both fractions using that shared denominator, then adds or subtracts the numerators.

For example, to add 1/4 + 1/6, the LCM of 4 and 6 is 12. Rewrite as 3/12 + 2/12 = 5/12. Using the least common multiple, rather than just multiplying the denominators together, keeps the numbers smaller and easier to simplify.

Multiplication is the most direct fraction operation: multiply the numerators together and the denominators together. For example, 2/3 × 3/5 = (2 × 3) ÷ (3 × 5) = 6/15, which simplifies to 2/5.

Division flips the second fraction (its reciprocal) and then multiplies: a/b ÷ c/d = a/b × d/c. Dividing by a fraction is really asking "how many times does this fraction fit into the other one?", and inverting turns that question into an equivalent multiplication.

After every operation, the calculator divides the numerator and denominator by their greatest common divisor (GCD) to reduce the fraction to its simplest form. For example, 6/15 has a GCD of 3, so dividing both by 3 gives 2/5.

Simplifying does not change the value of a fraction — 6/15 and 2/5 represent exactly the same quantity — it just makes the result easier to read and compare against other fractions.

A mixed number, like 1¾, combines a whole number and a proper fraction. Before performing arithmetic, it is usually easiest to convert to an improper fraction: multiply the whole number by the denominator, add the numerator, and keep the same denominator. 1¾ becomes (1 × 4 + 3) ÷ 4 = 7/4.

After calculating, you can convert back to a mixed number by dividing the numerator by the denominator: the quotient becomes the whole number, and the remainder becomes the new numerator over the same denominator.

Some fractions, like 1/3, produce a repeating decimal (0.3333...) that a screen or calculator must eventually round, silently losing a tiny sliver of precision. Fractions carry that value exactly forever, which matters in fields like engineering tolerances, recipe scaling, and financial contracts where rounding errors can compound across many calculations.

Carpentry and construction measurements are a classic everyday example: a tape measure marked in eighths or sixteenths of an inch is really a fraction-based system, and adding measurements like 3 3/8" and 2 5/8" is far more natural using fraction arithmetic than by first converting everything to decimal inches and back again.

Cooking is one of the most common places ordinary people use fraction arithmetic without thinking of it that way. Doubling a recipe that calls for 3/4 cup of an ingredient means multiplying 3/4 by 2, giving 6/4, which simplifies to 1½ cups — exactly the same fraction-multiplication logic used throughout this page.

Halving a recipe works the same way in reverse: multiply each ingredient fraction by 1/2. When halving produces an awkward fraction like 3/8 cup, most measuring sets do not have that exact marking, so cooks often round to the nearest practical measurement or combine smaller standard measures to approximate it closely.

When you need the same ratio expressed as a percent instead (for example, “what percent of the original recipe is this scaled batch?”), the Percentage Calculator converts between those two representations quickly, and the Scientific Calculator handles messier mixed expressions that go beyond fraction arithmetic alone.