Add, subtract, multiply and divide fractions — with every step of the working shown.
Type a whole number (3), a fraction (2/3), a mixed number (1 1/2) or a negative (-5/8). Decimals work too.
13/6
Sum
Simplified fraction—
As a mixed number—
Exact decimal—
Rounded decimal—
As a percentage—
Step by step
Every step is worked in exact whole numbers rather than decimals, so nothing is lost to rounding. Brackets in the decimal mark the digits that recur forever — 0.1(6) means 0.1666… A negative sign belongs to the fraction as a whole, so -1 1/2 is minus one and a half, not minus one plus a half.
About this calculator
Adding and subtracting fractions needs a common denominator because a fraction's denominator says what size the pieces are, and you cannot add pieces of different sizes and get a sensible count. A half and a third are not two of anything — but six of the same size will do, so both get rewritten in sixths, and then the numerators can simply be added. This calculator uses the lowest common multiple rather than just multiplying the denominators together, which keeps the numbers small and usually means less simplifying at the end.
Multiplying needs none of that. Multiplying by 2⁄3 means taking two thirds of something, and that works whatever size the pieces already are — so you multiply the numerators together and the denominators together and you are done. This is the opposite of what most people expect, since addition looks like the easier operation and is in fact the fiddlier one.
Division is multiplication in disguise. Dividing by 1⁄4 asks how many quarters fit into your number, and since four quarters fit into every whole, the answer is four times bigger — which is exactly what multiplying by 4⁄1 does. Flipping the second fraction and multiplying is not a trick to memorise; it is the same question asked the other way round. It also explains why dividing by a fraction smaller than one makes the answer bigger.
Simplifying works by finding the greatest common divisor of the numerator and denominator — the largest whole number that divides both exactly — and dividing both by it. 8⁄12 has a greatest common divisor of 4, so it reduces in one move to 2⁄3. When that divisor is 1 the fraction is already as simple as it gets, and the working above says so rather than leaving a blank step. Doing it in one move with the GCD is why you never need to keep halving and checking.
Two things to watch. A mixed number carries its sign across the whole value, so -1 1/2 is −3⁄2, and reading it as −1 + 1⁄2 is the most common source of a wrong answer in fraction arithmetic. And a fraction is only ever an exact decimal when its simplified denominator is built purely from 2s and 5s — every other denominator recurs forever, which is why the decimal here is shown with brackets rather than rounded off.
Frequently asked questions
How do you add fractions with different denominators?
Rewrite both so they share a denominator, then add the numerators and leave the denominator alone. The quickest shared denominator is the lowest common multiple of the two you have: for halves and thirds that is six, so 1⁄2 becomes 3⁄6, 1⁄3 becomes 2⁄6, and the answer is 5⁄6. Multiplying the denominators together always works too, it just leaves more simplifying to do afterwards.
Why do you flip the second fraction when dividing?
Because dividing asks how many of the second fraction fit into the first, and that is the same as multiplying by its reciprocal. Six divided by a half is twelve, because twelve halves fit into six — and multiplying six by 2⁄1 gives the same twelve. It is not a shortcut; the two questions are identical. It also explains why dividing by something less than one makes the result larger.
How do I turn an improper fraction into a mixed number?
Divide the numerator by the denominator. The whole-number part of that division is the whole number, and the remainder becomes the new numerator over the same denominator. For 13⁄6, six goes into thirteen twice with one left over, so it is 2 1⁄6. The calculator shows this line only when the fraction is actually improper.
What does the bracket in the decimal mean?
It marks the digits that repeat forever. 1⁄6 is 0.1666… with the 6 going on indefinitely, written here as 0.1(6). Showing it this way is exact, where writing 0.1667 would be a rounded approximation. If you need the fraction back from a recurring decimal, the decimal to fraction converter does that conversion exactly.
Can I use negative numbers and mixed numbers together?
Yes. Enter them as you would write them — -1 1/2, -5/8, -3. The minus applies to the entire value, so -1 1/2 is treated as minus one and a half, which is −3⁄2. Signs are carried through the working and the answer is displayed with the minus in front of the whole fraction rather than attached to the numerator.