﻿ Rule of three — Math18

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# Rule of three

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## What is the rule of three?

The rule of three is a form that allows the resolution of problems of proportionality between three known values and an unknown, in other words, the rule of three is an operation that allows you to find a fourth term with respect to a given proportion.

## Simple rule of three

A simple rule of three is classified in two ways, direct and inverse.

### Simple direct three rule

It is considered to be direct when one magnitude increases so does the other.
Below is an example to know the unknown using the rule of three

Assuming 4 pallets cost \$ 20. How much do 7 pallets?

Note: It is a problem of direct proportion, since the more pallets you acquire the total cost also increases.

First we must put in a fraction the known data, corresponding to 4 pallets with a total value of 20 dollars:

4 pallets / 20 dollars

It can also be accommodated as follows:

20 dollars / 4 pallets

Now we must match the unknown and the known data that corresponds to 7 palettes, it is important to note that the type of variable is in the same corresponding row, we have variables palettes and the cost that corresponds to pesos. The unknown is usually represented with the letter "x" but can be represented with any letter.

4 pallets / 20 dollars
=
7 pallets /
X

Having the other accommodation with 20 dollars / 4 pallets will have:

20 dollars / 4 pallets
=
X
/ 7 pallets

In the second arrangement it is easier to clear, any accommodation we have at the time of making the corresponding clearances would reach the same equation to find the unknown.
We perform the corresponding clearances:

4 pallets (X) /
20 dollars
= 7 pallets
X = (
7 pallets /
4 pallets
) (20 dollars)

As you can see the type of magnitude, in this case "pallets" is simplified by having "pallets / pallets", therefore, the result of the unknown would be the dollars:

X = (
7 / 4
) (20 dollars) = 35 dollars

Increasing the magnitude from 4 to 7 pallets also increases the magnitude of the cost from 20 to 35 dollars, therefore, it has to be a simple direct rule of three.

Pallets Dollars
4 20
7 35

### Inverse simple three rule

It is considered to be inverse when one magnitude increases and the other decreases.
Below is an example to know the unknown using the rule of three
Assuming that 2 workpeople finish painting in 10 hours. How long will it take 5 workers?

Note: It is a problem of inverse proportion, for logical reasoning more workers less time will take to paint.

For this case the simplest way to relate is to multiply the different variables, in this case (workpeople) (hours), therefore, the following equation would be obtained:

(2 workpeople)(10 hours) = (5 workpeople)(X)

Making the corresponding clearance:

X = (
2 workpeople /
5 workpeople
) (10 hours) = 4 hours

As the magnitude increases from 2 to 5 workpeople, the time decreases from 10 to 4 hours of work, therefore, it has to be a rule of three simple inverse.

workpeople Time
2 10
5 4

### How to know if it is a direct or inverse rule of three?

To know what method to use, you have to make a logical reasoning of the problem, by reasoning or imagining the problem, you can easily know the procedure to be used.

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