Use the rule of three to calculate percentages

Percentage calculation - notes on the rule of three

• The rule of three includes tasks that are proportional Assignments goes. In the rule of three, two quantities are assigned to each other, which decrease or decrease proportionally. enlarge. For example, if one of the two sizes doubles, so does the other. A well-known example of proportional allocation is weight and price.
• However, many are unaware that the Percentage calculation is based on a proportional assignment. Here the quantity and percentage are assigned to one another: the larger the quantity, the larger the percentage.
• In the percentage calculation one has to do with the quantities basic value G, the percentage value P and the percentage p (in%).
• There is an equation between these quantities: G: 100% = P: p%. In principle, you are also familiar with such ratio equations from the rule of three.
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• If two of the three quantities G, P and p are known, the missing quantity can be calculated from this ratio equation - just like in the rule of three.


Percentage, basic value, percentage value - the math expert explains the terms

Percentage value, base value and percentage - it can make your head spin. …

Percentage calculation - use the rule of three to calculate the percentage

In the first example, the base value is 1350 euros, for example a purchase price. You will receive a 3% bonus when paying in cash. How much is the purchase price?

• In this exercise you will first assign the sizes. G = 1350 euros (this corresponds to 100%). p = 3% is the bonus and what is sought is the bonus deduction, the percentage value P (in euros).
• 1350: 100 = P: 3. By multiplying by 3 you get P = 1350 x 3: 100 = 40.50 euros. The price is therefore 1350 - 40.50 = 1309.50 euros.
• An alternative approach, in which the final price is obtained immediately, would be to set p = 97% for this task. The calculated P is then the price after deducting the 3% bonus.

How to calculate the basic value G

In this second example, the base value is unknown. For example, you know that during quality controls, around 1.5% of lightbulbs are defective (and cannot be sold). You have now sorted out 6 defective lightbulbs from the samples. But what was the basic number of lightbulbs that were tested?

1. Again, assign the sizes in this exercise. The following applies: p = 1.5% and P = 6 (the defective bulbs). Find the basic set G.
2. You put the sizes in the formula of three: G: 100% = P: p% and get G: 100 = 6: 1.5.
3. Multiply the ratio equation by 100 and you get directly G = 6: 1.5 x 100 = 400.
4. So there were 400 lightbulbs tested.