Rule of three

What the rule of three does

You know three numbers of a proportion and want the fourth. The calculator fills it in and, more usefully, shows the two steps that get there, so the working can go straight into a homework book.

The important part is choosing the kind of proportion. In a direct one, both quantities grow together: twice the rolls, twice the price. In an inverse one, one grows as the other falls: twice the workers, half the time.

• Direct: x = b × c ÷ a. First work out one unit, then multiply.
• Inverse: x = a × b ÷ c. The product of the pair stays the same, so divide the total work.

The units are optional. If you fill them in, they appear in the labels and in the working, which makes it much easier to check the result is the quantity you actually wanted.

Frequently asked questions

How do I tell a direct proportion from an inverse one?

Ask what happens when the first quantity doubles. If the second doubles too, the proportion is direct. If it halves, it is inverse. Price per item is direct; workers and time are inverse.

Can I enter decimals?

Yes, either way — “6.4” or “6,4”. The result is shown to at most four decimal places, and the copy button gives the plain number.

Why does the first quantity have to be non-zero?

Because the first step divides by it. Without it there is no value for one unit, and the proportion has no solution.

Does it simplify the ratio?

For a direct proportion it also shows the ratio in its lowest terms, so you can see at a glance that 100 : 6.4 is the same as 125 : 8.