Calculate rule of three – simple explanation with examples

We will show you step by step how you can easily create a Calculate rule of three can and explain to you the terms proportional and antiproportional rule of three. You can apply and test your knowledge directly with our exercises at the end of the article&

The rule of three explained simply – When is it needed??

The rule of three Solution methods in mathematics, with which you can calculate an unknown quantity from the ratio between 2 known quantities.

The name "rule of three" is derived from the 3 steps of the calculation path.

Using the rule of three Proportional tasks calculate. Using the rule of three is also a helpful tool in everyday life. Among other things, you can

  • Calculating prices in the supermarket
  • Determine quantities when cooking or baking
  • Calculating percentages

To calculate the rule of three, it is advisable to master multiplication and division. We will show you step by step how to calculate the rule of three in the following sections.

Proportional rule of three

The classical rule of three is also called proportional rule of three. Two quantities or. sizes are in the proportional relationship To each other. So the values increase or decrease in the same proportion: the more of X, the more of Y.


Imagine you want to buy three packs of cookies. One package of cookies costs € 0.75. Then two packages of cookies cost twice as much (€1.50) and three packages of cookies cost three times as much (€2.25). This is a proportional relationship.

Proportional rule of three - example

Calculate proportional rule of three – formula

First, let’s illustrate the calculation path with a table.

The problem in a math paper could be:

"You are standing at the cheese counter in the supermarket and want to buy 3 kg of Gouda. 5 kilograms of Gouda cost 25,50 Euro. How much does 3 kilograms cost?"

The solution is actually quite simple:

  • Step 1: Data collection
    → 5 kg of cheese cost €25.50
  • Step 2: Calculate price for 1 kg
    → 1 kg of cheese costs 25.50 : 5 = 5.10€
  • Step 3: Calculate the price for 3 kg
    → 3 kilograms of cheese cost 5.10 – 3 = 15.30

Proportional rule of three - calculation method

Once you have internalized the calculation method of the proportional rule of three, you can also work without a table and instead directly use the Formula apply

Proportional rule of three: Formula

Antiproportional rule of three resp. inverse rule of three

The antiproportional rule of three is also called the inverse rule of three. In the antiproportional rule of three, two quantities are in a antiproportional relationship. So here it is: The more of size X, the less of size Y.


Imagine that a new delivery of goods arrives at the supermarket. Three workers should sort the goods into the shelves. You need 10 hours. However, if three additional workers are requested, all of them will need six together only half as much time, thus 5 hours.

Calculate antiproportional rule of three – formula

Also in this case you can illustrate the calculation way very well with a table. But first let’s have a look at an example task.

"Three employees of the tax office need 32 hours to finish the accounting of an important customer. How many hours are needed in total if eight employees work on the payroll?"

Again, the calculation path consists of 3 steps:

  • Step 1: Data collection
    → 3 employees require 32 working hours
  • Step 2: Calculate hours for one employee
    → 1 employee alone requires 32 hours – 3 = 96 working hours
  • Step 3: Calculate hours for 8 employees
    → 8 employees need 96 hours : 8 = 12 working hours

Actually quite simple or? The most important step is to recognize that this is an antiproportional allocation because the more employees working on the same project, the less total time is required.

Antiproportional rule of three - example

The table serves as an illustration. Of course, you can also just solve it with Formula Determine:

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