Fraction Calculator & Simplifier

A tape measure reads 7 5/8, the blade takes 3/16 out of every cut, and the arithmetic that follows is why most people go looking for a fraction calculator in the first place. Fraction Calculator & Simplifier works the way you were taught it: common denominator, combine, reduce. Those moves are printed underneath the answer rather than collapsing into a single number you have to trust.

Nothing converts to a floating-point number on the way through. In binary doubles 0.1 + 0.2 lands on 0.30000000000000004, and a chain of thirds drifts further with every operation. Numerators and denominators are held as BigInt values instead, so 126/294 reduces to 3/7 by exact integer division and the answer stays exact however many steps came before it.

The boxes take whichever notation you already have in front of you. A ratio like 7/2, a mixed measurement like 3 1/2, a plain decimal like 3.5 and a repeating decimal written 0.8(3) all resolve to the same internal rational. Every keystroke is handled in the tab, so nothing you type is sent anywhere.

A Real Example: Taking 2 3/16 Off a 7 5/8 Board

Load Sample fills the first box with 7 5/8, the second with 2 3/16, and selects Subtract. Four cards answer in four notations at once, and the panel beneath them shows how each was reached.

• Both mixed numbers become improper first: 7 5/8 is 61/8, and 2 3/16 is 35/16.
• The lowest common denominator of 8 and 16 is 16, which restates the first fraction as 122/16.
• Subtracting numerators gives 122 − 35 = 87, so the raw result is 87/16.
• The GCD of 87 and 16 is 1. Nothing divides out, and the step list says so instead of skipping the check.
• The cards read 87/16, 5 7/16, 5.4375 and 543.75%. The mixed number is the one that goes back to the tape measure.

How It Calculates Each of the Four Operations

• Add and Subtract raise both sides to a common denominator found as a / gcd(a,b) × b, combine the numerators, and reduce once at the end rather than after every stage.
• Multiply goes straight across, numerator by numerator and denominator by denominator. Reduction is still deferred to the final step, so you see the unreduced product it came from.
• Divide inverts the second fraction and multiplies. That is why a divisor resolving to zero stops with Dividing by 0 has no result — the second fraction resolves to zero.
• Compare never converts to decimal at all. Cross-multiplication settles 7/12 against 9/16 by 7 × 16 = 112 beating 9 × 12 = 108, leaving no rounding to argue about.
• Reduction is the Euclidean algorithm run on BigInt values, which is what turns 126/294 into 3/7 after dividing both parts by a GCD of 42.

Precision, and Where the Digits Stop

Fractions are exact. Their decimal forms sometimes are not, and each card tells you which of the two you are reading.

• A terminating expansion is printed whole and labelled as terminating. 9/16 is 0.5625, with nothing rounded away behind it.
• A repeating expansion is bracketed rather than truncated. 7/12 prints as 0.58(3) and reports a cycle 1 digit long; 3/7 prints as 0.(428571) with a cycle of 6.
• Long division runs for at most 120 digits. 1/97 fits, since its cycle is 96 digits and it is shown in full, while 1/9999991 does not and ends in an ellipsis with the card saying the cycle is longer than that.
• Any single number you type is capped at 30 digits. A 34-digit numerator turns the box red under Each number is capped at 30 digits — this one has 34.
• Typing 0.8(3) is not the same as typing 0.8333. The brackets mark the block that repeats, so the first becomes exactly 5/6 while the second is taken at face value as 8333/10000. Almost nobody tries this on a first visit.
• Signs are normalised before anything runs, so -7/-14 reads as 1/2 and a negative denominator never reaches the working.