About the Fraction Calculator
“Fraction calculator” is one of the biggest calculator searches in existence, and nearly every result converts to decimals internally and rounds. This one does exact rational arithmetic — integers only, all the way through — and shows the steps: the common denominator, the combined numerator, and the simplification with Euclid’s algorithm written out line by line.
The parts nobody else bothers with: repeating decimals converted exactly (0.8333… becomes 5/6, with the algebraic proof), and a tape-measure mode that rounds to 16ths, 32nds or 64ths of an inch and admits the error. Validated in Node before shipping: 121,972 assertions, including every small-fraction operation checked against a BigInt reference.
3/4, 1 2/3, -5, 2.5, 0.8(3), 0.8333...Twelve random problems at the difficulty of the one you just did, with an answer key on the second page. New problems every time.
How to Use the Fraction Calculator
Type two values, pick the operation, calculate. The inputs accept everything a maths class or a job site
throws around — proper and improper fractions, mixed numbers (1 2/3), whole numbers,
decimals, and repeating decimals written either with an ellipsis (0.8333...) or in
parenthesis notation (0.8(3)). The answer comes back three ways — simplified fraction,
mixed number, exact decimal — with the working shown underneath.
Adding Fractions: the Method the Steps Show
To add 1 2/3 and 3/4: convert the mixed number to an improper fraction (5/3), find the least common denominator of 3 and 4 (12), scale both fractions to it (20/12 and 9/12), add the numerators (29/12), and simplify — already in lowest terms, so the mixed form is 2 5/12. Every one of those steps appears in the panel, with the greatest common divisor computed by Euclid’s algorithm and, for subscribers, the algorithm itself written out line by line.
Repeating Decimals Are Fractions in Disguise
Every repeating decimal is exactly a ratio of integers, and the conversion is two lines of algebra: multiply to align the repeating block with itself, subtract, divide. 0.8333… is 5/6 exactly; 0.142857142857… is 1/7; even 0.999… collapses to exactly 1. The tool detects the repeating block from what you typed, refuses to guess when the pattern is not actually repeating, and shows the subtraction as a proof rather than asking you to take its word.
Related tools: the Scientific Calculator for decimal work, the Percentage Calculator for the percent view of the same idea, and the Ratio Calculator for scaling recipes and plans. Browse every Math & Science tool for more.
Frequently Asked Questions
Why does exact arithmetic matter for fractions?
Because 1/3 is not 0.333333. A calculator that converts to decimals immediately carries a rounding error through every later step, and answers like 1/3 + 1/3 + 1/3 come out as 0.999999. This tool never leaves the integers: numerators and denominators are combined with exact integer arithmetic, simplified with the Euclidean algorithm, and only rendered as a decimal at the end — with the repeating part detected exactly rather than truncated.
How do you convert a repeating decimal to a fraction?
With the standard identity: call the number x, multiply by the right powers of ten to line the repeating block up with itself, and subtract. For 0.8333…: 10x = 8.333… and 100x = 83.33…, so 100x − 10x = 75, giving x = 75/90 = 5/6. The tool detects the repeating block automatically when you type an ellipsis (0.8333…) or write it in parentheses (0.8(3)), and shows this subtraction as the proof.
What do 16ths, 32nds and 64ths mode do?
Tape measures and machinist rules divide inches into halves of halves — 16ths on most tapes, 32nds and 64ths on precision rules. Inch mode rounds any decimal measurement to the nearest such fraction and tells you the error you accepted (0.7" is 11/16, which is 0.0125" short). Exact ties round to the even numerator, the machinist convention.
How are mixed numbers with negative signs read?
The sign applies to the whole quantity: −2 1/3 means −(2 + 1/3) = −7/3, matching how the number is spoken. Improper fractions, negatives in either position of a plain fraction, and whole numbers all parse; a zero denominator is rejected with an explanation rather than a silent wrong answer.
How was this calculator tested?
Against an independent implementation and published identities, in Node, before shipping: every combination of numerators and denominators from −9/1 to 9/9 through all four operations — 115,425 cases — compared against a BigInt rational reference; decimal expansions cross-checked against big-integer long division for every denominator to 97 (including 1/97's 96-digit repeating block); round-trips fraction → decimal text → fraction for every proper fraction to /64; and the textbook identities (1/3 = 0.3̄, 1/7 = 0.142857̄, 5/6 = 0.83̄). 121,972 assertions, zero failures.
