Fraction Calculator

Fractions come up constantly in math coursework — combining measurements, working through algebra, or just checking a homework answer — and the arithmetic gets error-prone fast once you're finding common denominators or cross-multiplying by hand. This tool takes two fractions and an operation (add, subtract, multiply, or divide) and returns the exact simplified result, so you can check your own work or skip straight to the next step of a larger problem.

Every result is automatically reduced to lowest terms — the same simplification you'd do by hand, using the greatest common divisor of the numerator and denominator. You'll also see the decimal equivalent, and if the result is an improper fraction (numerator larger than the denominator), its mixed-number form too, so you can read the answer however your assignment expects it.

A couple of rules to keep in mind: neither denominator can be zero (that's not a valid fraction), and when dividing, the second fraction's numerator can't be zero either, since that would mean dividing by zero. Both numerators and denominators should be whole numbers — if you're starting from a decimal, convert it to a fraction first.

A worked example

Say you're adding 3/4 and 5/6. Cross-multiply into a common denominator: (3 × 6 + 5 × 4) / (4 × 6) = (18 + 20) / 24 = 38/24. That fraction isn't in lowest terms yet — the greatest common divisor of 38 and 24 is 2, so dividing both by 2 simplifies it to 19/12. Since the numerator is larger than the denominator, this calculator also shows it as a mixed number: 1 whole plus 7/12 remaining (12 fits into 19 once, with 7 left over), and as a decimal: 19 ÷ 12 = 1.5833.

A common misconception

The single most common fraction-arithmetic mistake is adding or subtracting numerators and denominators straight across — treating 3/4 + 5/6 as (3+5)/(4+6) = 8/10. That's wrong; fractions only add correctly once they share a common denominator, which is exactly why this calculator cross-multiplies rather than combining the numbers directly. That pitfall is specific to addition and subtraction — multiplication genuinely does work straight across (numerator × numerator, denominator × denominator), which is part of why the two operations get confused.

Cases worth double-checking

Mixed numbers (like 1½) can't be entered directly — this tool expects a plain numerator and denominator, so convert a mixed number to an improper fraction first (multiply the whole number by the denominator and add the numerator: 1½ becomes (1×2+1)/2 = 3/2). Negative fractions work correctly regardless of which term carries the minus sign, but the simplified result always normalizes the sign onto the numerator with a positive denominator, so −3/4 and 3/−4 both simplify to the same −3/4. And a whole number is just a fraction with a denominator of 1 — enter 5 as 5/1 if you need to combine it with another fraction.

Reading your result

Which form of the answer to use depends on what you're doing with it next. The simplified fraction is generally the expected form for a homework answer unless told otherwise; the mixed number is often preferred when the result represents a real-world quantity, like a length or a recipe measurement, since “1 and 7/12” is easier to picture than “19/12.” The decimal is most useful when you need to compare the result against another number quickly, or feed it into a further calculation that doesn't use fractions.

Fractions vs. decimals vs. percentages

All three are different notations for the same underlying value — 3/4, 0.75, and 75% all represent an identical quantity. Fractions are exact and show the relationship between parts and a whole clearly, which is why they're the standard form in algebra and geometry. Decimals are easier to compare at a glance and to type into most calculators, but some fractions (like 1/3) only convert to a decimal that repeats forever, so a decimal answer is sometimes a rounded approximation rather than an exact value the way the fraction itself is.