Add, subtract, multiply, divide, compare and simplify fractions of any size, exactly. Reads mixed numbers and repeating decimals, and gives the decimal expansion with its repeating cycle.
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Exact arithmetic on rationals, with both evaluation conventions named and the precedence table the parser runs on printed on the page.
Aspect ratios reduced exactly by the greatest common divisor, with the reduction multiplied back as a check, resizes that say whether they are exact, and named ratios that carry a note where the name is not the ratio.
Exact ages and date differences worked out on the calendar itself, with no arithmetic on milliseconds, so the answer is the same in every time zone. Shows which days are not 86,400 seconds long.
A measurement comes out as -15/4 of an inch and you want it as a mixed number, plus the exact decimal.
Expression
-15/4
Result
-15/4 = -3 3/4 = -3.75, and 1/7 = 0.(142857)
A mixed number below zero is where a calculator usually goes wrong: taking the floor of -3.75 gives -4 and printing "-4 1/4" reads as -4.25, a whole unit out. The magnitude is split and the sign put back, which is what "minus three and three quarters" means. The decimal is the exact expansion with its repeating cycle rather than six rounded digits, because a fraction that does not terminate repeats for ever and the cycle is the answer: 0.142857 is not one seventh. Every value is a pair of whole numbers of any size, so nothing is a decimal approximation at any point.
Add, subtract, multiply, divide, compare and simplify fractions of any size, with nothing rounded on the way. Type them however you write them: 3/4, 1 2/3, -5/8, 0.75 or 0.(3).
Every value here is a pair of whole numbers of any size, in lowest terms, with the sign on the numerator. Nothing is a decimal approximation at any point: one third is one third and not 0.3333333333333333, two eighteen-digit denominators add exactly, and a comparison is done by cross multiplying so two fractions a millionth apart are still ordered correctly.
**What you can type.** One box per fraction, because a fraction is one value. It reads 3/4, an improper fraction like 11/4, a negative like -5/8, a mixed number like 1 2/3, a plain decimal like 0.75, a percentage like 12%, and a repeating decimal written 0.(3). Anything it cannot read is refused BY NAME rather than truncated: 1e3 is not read as 1, 2.7 is not read as 2, and a denominator of zero is refused rather than quietly becoming one.
**What comes back.** The answer in lowest terms and, where they differ, the unreduced form the textbook writes first. The mixed number, correct below zero: -7/2 is minus three and a half, and the obvious floor-and-modulo version writes it as "-4 1/2", which is minus four and a half. The decimal expansion with its REPEATING CYCLE rather than six rounded digits, because a decimal expansion of a fraction either stops or repeats and the cycle is the exact answer: one seventh is 0.(142857), where 0.142857 is not one seventh. The prime factorisation of both parts, which is also the reason a decimal stops or does not: it terminates exactly when the denominator has no prime factor but 2 and 5.
**The working, and a check.** The lowest common denominator is shown being found, both fractions rewritten over it, and the GCD divided out. Underneath, the answer is written back from its own mixed form and the identity is stated, so the page checks itself rather than only asserting.
Six operations: add, subtract, multiply, divide, compare, and simplify one fraction on its own.
The common denominator, the rewriting and the simplification are each on the page, in the order they are written by hand.
Two thirds of a cup and a half more, as a fraction you can measure rather than 1.1666666666666667.
Adding sixteenths and eighths, with the answer in lowest terms and as a mixed number.
Is 0.333333 one third? Compare them and see that it is not, and by exactly how much.
Yes, as "1 2/3", with a space. Improper fractions, decimals, percentages and repeating decimals written 0.(3) are all read too, and the tool shows the fraction it read.
A fraction is two whole numbers. Reading 2.7 as 2 would silently answer a different question, which is what a parseInt-based calculator does.
It is refused with the reason, and no answer is produced. Nothing is divided by zero and nothing is quietly turned into a one.
The digits in brackets repeat for ever. A fraction that does not terminate has a repeating cycle, and printing the cycle is exact where printing six digits is not.
Any size. The arithmetic is on whole numbers with no 53-bit limit, so twenty-digit numerators are as exact as single digits.
Because that is what it is: minus (three and a half). Taking the floor of -3.5 gives -4 and writing "-4 1/2" reads as -4.5, which is a different number.
Every calculation runs locally in your browser. Your numbers and expressions are not transmitted or stored.