Solve an expression step by step

Type the expression as it is in the book, with brackets, fractions and powers: out come all the steps in the order they are done, and the result as an exact fraction.

Or try an example:

The calculation happens in your browser: nothing is sent anywhere.

The order things are done in

The order is not a matter of opinion and it is always the same: brackets first, starting with the innermost ones; then powers and roots; then multiplications and divisions, from left to right; additions and subtractions last, again from the left. The page writes one line for each group of operations at the same level, the way you write it in an exercise book, and next to it says which rule it is applying.

There is one trap worth knowing, because it is the first mistake people make at secondary school: -2² is -4, not 4. The minus sign in front is applied AFTER the power, so it reads as «minus the square of two»; if you meant the square of minus two you have to write (-2)². The «read as» line, above the result, spells out every bracket that precedence decided on its own: if what you see there is different from what you had in mind, you have found the mistake before doing any arithmetic. If you only want the number and not the steps, the short way is Scientific calculator.

Fractions stay fractions

The arithmetic is done with whole numbers as big as they need to be, not with the computer's decimals: one third stays one third, it does not turn into 0.333333 with an error that drags on to the end. That is why adding three thirds gives exactly 1 here and not 0.999999: in an expression with fractions, which is THE school case, being exact is not a detail.

Before adding or subtracting two fractions with different denominators, the common denominator line appears, that is the one you would write yourself: the fractions rewritten over the same denominator and then the sum. The final result comes in three forms, because the book may ask for all three: fraction in lowest terms, mixed number when the fraction is greater than one, and decimal, with the repeating part in brackets when the digits repeat. To reduce a single fraction to lowest terms there is Simplify Fractions.

What this tool does not do

It only does numeric expressions: if a letter shows up inside, it says so and stops, instead of guessing. Equations and expressions with letters need a symbolic engine, which is a different job, and a tool that promised steps there as well would not be able to keep the promise.

And roots are done only when they come out exact: √16 is 4 and √(16/9) is 4/3, but √2 is not a fraction, so instead of printing 1.4142 and carrying on as if nothing happened the page says that exactness ends there. It is the same reason why exponents have to be whole numbers. If what you have in front of you is not an expression but an equation with an x, the right place is Quadratic Equation Solver.

How to type the expression

All three kinds of brackets work, round, square and curly, and the order you use them in does not matter: the page reprints them the way the book does, that is round inside, then square, then curly. For divide you can type a colon or a slash, for times an asterisk or the × sign, and a comma for decimals works just like a dot. The power is the ^ sign (2^10) and the square root is √ or a V. The keys above the field are there for exactly this, because on a phone the curly bracket and the root sign are nowhere to be found.