The **rule of three** (" **rule****of three**") is an operation that helps us to quickly solve both direct and inverse proportionality problems. To use the rule of three, we need three values (two that are proportional to each other and a third). From this we will determine the fourth value.

## Rule of three: example and formula

Let's take a look at an example:

Yesterday, 2 trucks transported goods from the harbor to the warehouse. Today, 3 trucks of the same size have to make 6 trips to transport the same amount of goods from the warehouse to the shopping center. How many trips did the trucks make yesterday?

We put the values in a table and apply the formula for the rule of three:

3 --> 6

2 --> X

X = 3 * 6/2 = 9

Answer: Yesterday 2 trucks made 9 trips each.

## Example 1

There are 3 gardeners at the Hilton Hotel in winter. Together they water and take care of all the gardens in the hotel in 6 hours. If there are 3 more gardeners in the summer, how long will it take to water and take care of all the gardens in the hotel?

To solve this problem, we first need to add the 3 new gardeners to the existing 3. If the 3 gardeners need 6 hours in winter, then 6 gardeners need x hours in summer.

3 --> 6

6 --> X

Once we have put together our formula, we just have to solve it.

X = 3 * 6/6

X = 18/6

X = 3

Solution: if 3 gardeners need 6 hours, then 6 gardeners need 3 hours.

## Example 2

The motorcycle rally team has 15 mechanics who are able to change all parts on a car in 60 seconds. How many seconds would it take 5 mechanics to do the same job?

To solve this problem, we need to look at the situation as follows: If 15 mechanics change parts on a car in 60 seconds, then it takes 5 mechanics x seconds.

15 --> 60

5 --> X

Once we have put together our formula, all we have to do is solve it.

X = 15 * 60/5

X = 900/5

X = 180

Solution: If 15 mechanics need 60 seconds, 5 mechanics need 180 seconds.

## Example 3

Last month, it took 3 gardeners 12 hours to renovate the gardens in the town's main square. This month, the city has a larger budget and can hire 6 gardeners. Knowing that it took 12 hours to get the job done with 3 gardeners, how much time will it take 6 gardeners to beautify the gardens?

The first step is to determine whether the problem requires the direct rule of three or the inverse proportion:

- If the city hired more gardeners, will it take more or less time to finish the job?
- Having more gardeners will reduce the total time it takes to do the job.

So if one quantity increases, the other decreases in the same proportion: we solve a problem with the inverse proportion.

3 gardeners --> 12 hours

6 gardeners --> X

X = 3 * 12/6

X = 6

With 6 gardeners, the gardens are completed in 6 hours.

## Mathematics

- Angle
- Ball
- Binomial formula
- Circle
- Cone
- Cube
- Cuboid
- Cylinder
- Derivation rules
- Difference
- Dragon square
- Fractions
- Integral
- Midnight formula
- Parallelogram
- Percent
- Polynomial division
- PQ formula
- Pyramid
- Rectangle
- Rhombus
- Rule of three
- Square
- Standard deviation
- Sum of digits
- Surface area
- Trapezoid
- Triangle
- Volume
- Zeros

## Mathematics

- Angle
- Ball
- Binomial formula
- Circle
- Cone
- Cube
- Cuboid
- Cylinder
- Derivation rules
- Difference
- Dragon square
- Fractions
- Integral
- Midnight formula
- Parallelogram
- Percent
- Polynomial division
- PQ formula
- Pyramid
- Rectangle
- Rhombus
- Rule of three
- Square
- Standard deviation
- Sum of digits
- Surface area
- Trapezoid
- Triangle
- Volume
- Zeros