Enter two fractions and an operation to see the result simplified, as a mixed number, and as a decimal — with the working shown.
Result
Most calculators turn a fraction into a decimal before doing anything with it, and a binary decimal cannot hold one sixth. Add 1/6 to itself six times that way and you get 0.9999999999999999 instead of 1; type 0.1 + 0.2 and you get 0.30000000000000004. The error is tiny and it is real, and in a tool whose only promise is exactness it is the whole ballgame. This calculator keeps the numerator and the denominator as whole numbers from start to finish, so 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 is 1 exactly, with no decimal ever involved.
Adding fractions needs a common denominator, and the one to use is the lowest common multiple, not the product. For 1/6 + 1/10, multiplying the denominators gives 60, which works and then needs simplifying; the LCM is 30, so the sum is 5/30 + 3/30 = 8/30 = 4/15. Same answer, smaller numbers along the way — which matters because a chain of additions on multiplied denominators grows fast enough to leave the range where whole-number arithmetic is still exact.
Simplifying is division by the greatest common divisor. For 6/8 the GCD is 2, so it reduces to 3/4. Turning an improper fraction into a mixed number is the other half of tidying up: 7/3 is 2 1/3, because three goes into seven twice with one third left over. When the fraction is negative the sign belongs to the whole number and nowhere else — −7/3 is −2 1/3, not −2 −1/3. Written the second way it reads as a subtraction and the value comes out wrong.
Dividing by a fraction means multiplying by its reciprocal: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6. The reason is less mysterious than the rule sounds. Dividing by 4/5 asks how many four-fifths fit into the number, and since each fifth fits five times per unit and you want groups of four, you scale by five and share by four. Flipping the second fraction is that sentence written as arithmetic.
Give them a common denominator, add the numerators, then simplify. For 1/6 + 1/10 the lowest common multiple of 6 and 10 is 30, so the sum is 5/30 + 3/30 = 8/30, which reduces to 4/15. Multiplying the denominators would give 60 and the same value, just with larger numbers to reduce afterwards.
A decimal calculator stores 1/6 as the nearest binary fraction, which is slightly off, and the error accumulates. Six of those added together come to 0.9999999999999999. Here the sum is done in whole numbers and comes to 1. If the two ever disagree, the exact one is this one.
Divide the numerator by the denominator: the quotient is the whole part and the remainder stays over the original denominator. 7/3 gives 2 with 1 left over, so 2 1/3. For a negative fraction the sign goes on the whole part only: −7/3 is −2 1/3.
Because dividing by 4/5 is asking how many groups of four-fifths fit inside the number. Each unit holds five fifths, so you multiply by 5, and you want them in groups of four, so you divide by 4 — which is exactly multiplying by 5/4. Worked out: 2/3 ÷ 4/5 = 10/12 = 5/6.
When the numerator and denominator share no common divisor other than 1. Finding the greatest common divisor and dividing both by it gets there in one step: 6/8 has a GCD of 2 and becomes 3/4, which cannot go further because 3 and 4 share nothing.
No. The calculation runs in your browser in a few lines of JavaScript. There is no server to send it to — this site is static files.
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