Professor Robson Linhas explains the rule of three, an ancient concept of proportionality used to compare two or more quantities like distance, time, value, etc. There are two types: simple (comparing two quantities) and compound (three or more quantities). Simple rule of three is direct if quantities are directly proportional and inverse if they're inversely proportional. He demonstrates with examples: calculating travel time based on distance, determining the number of pens one can buy with a certain amount of money, and more complex scenarios involving multiple variables like constructing a wall or paving a road. The lesson includes tips for setting up proportions correctly and solving them using the fundamental property of proportions.
Here are the key facts extracted from the text:
1. There are two types of rule of three: simple rule of three and compound rule of three.
2. The simple rule of three compares only two quantities.
3. The compound rule of three performs a comparison of three or more quantities.
4. Directly proportional quantities increase or decrease together.
5. Inversely proportional quantities increase as the other decreases.
6. The rule of three can be used to solve problems involving proportions.
7. To solve a problem using the rule of three, organize the quantities in columns and identify which quantities are direct and which are inverse.
8. The fundamental property of proportion is that the product of the extremes is equal to the product of the means.
9. To solve a proportion, cross-multiply and solve for the unknown quantity.
10. In the compound rule of three, there can be both directly and inversely proportional quantities.
11. To analyze which quantities are direct and which are inverse, cover the other quantities and analyze each quantity in relation to the quantity that is in the column.
12. The trick to remembering which quantities are direct and which are inverse is to think of "God" being up and "hell" being down.
13. The proportion should be set up with the quantity that has the unknown value (x) first.
14. The quantities should be multiplied together and simplified to solve the proportion.
Note: These facts are based on the provided text and may not be a comprehensive list of all the facts related to the rule of three.