Math Tools

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Twenty-two calculators, and the working underneath

Fractions with the common denominator written out, every kind of average from one paste, roots simplified the way the exercise asks for them, logarithms to any base, long division and long multiplication in the written layout, a number line you can print, and the five percentage tools people get wrong: discounts that chain, margin against markup, tax added and taken back off, cash rounding, and price per kilo.

Half of these show their working, because the answer was never the hard part. Somebody looking up 3/4 + 2/5 has the answer on the phone in their hand; what they do not have is the twenty, the two expansions and the cancelling — and without those the homework cannot be handed in.

None of the arithmetic is done in floating point. Fractions are exact rationals, money is exact decimal, and a root or a logarithm is computed digit by digit in integer arithmetic to however many places you ask for, with the tool saying whether it landed exactly or stopped. Everything runs inside this browser tab, compiled to WebAssembly; there is no server to send anything to.

Fractions and ratios

Fraction calculator
Adds, subtracts, multiplies and divides fractions, and shows the common denominator.

Ratio calculator
Simplifies a ratio and shares an amount in it so that the parts add up exactly.

Rule of three solver
Solves the missing term of a direct or inverse proportion, and explains which is which.

Lists and averages

Average calculator
Mean, median and mode of a pasted list, with the ones people forget to ask for.

Sum calculator
Adds up a list that arrived as text, exactly, and says what it skipped.

Powers and roots

Exponent calculator
Any exponent, whole or not — with the reciprocal and the root written out.

Root calculator
√72 is 6√2 — the simplified form the exercise asks for, not just the decimal.

Modulo calculator
−7 mod 3 is 2 or −1 depending on the language. Both answers, with the languages.

Shown working

Prices and percentages

Discount calculator
30 % off then 20 % off is 44 % off, not 50 %. Chained discounts, done right.

VAT calculator
Taking 20 % tax back off is a division, not a subtraction. Both directions, shown.

To print

Questions

Why does this round differently from my spreadsheet?
Because it is not using floating point. A spreadsheet stores 2.675 as a binary fraction very slightly below 2.675, so rounding it to two places gives 2.67. These tools keep the digits you typed, which gives 2.68. The same difference is why a column of prices adds up to the penny here.
Is thirty per cent off and then twenty per cent off the same as fifty?
No — it is forty-four per cent off, because the second discount comes off what is left rather than off the original. The discount tool shows both numbers side by side for exactly that reason, and the margin and tax tools do the same for the two other percentage traps.
Can I see how the answer was reached?
For most of them, yes, and it is generated from the same steps the calculation takes rather than reconstructed afterwards. The fraction calculator shows the common denominator, the proportion solver shows the cross-multiplication, and long division and long multiplication produce the written layout rather than just the number.
Is what I type uploaded anywhere?
No. The tools are compiled to WebAssembly and run inside the browser tab. Nothing you type is sent to a server, and you can watch your browser's network panel while you use one to see that nothing leaves the page.