REGRA DE TRÊS COMPOSTA | COMO CALCULAR REGRA DE TRÊS COMPOSTA | \Prof. Gis/

Summary

In this tutorial, Gis introduces the compound rule of three, explaining how to solve problems involving multiple quantities, such as time, workers, and output. The compound rule extends the simple rule of three by involving more than two quantities, teaching users how to identify direct and inverse proportionality in various scenarios. Through examples like seamstresses producing towels and painters painting areas, Gis demonstrates how to set up ratios and solve for unknowns using cross-multiplication. The video serves as an insightful guide for anyone struggling with proportionality problems, offering clear steps for solution.

Takeaways

• 😀 The compound rule of three deals with problems involving more than two quantities, in contrast to the simple rule of three, which involves only two quantities.
• 😀 To solve a compound rule of three problem, you must first identify the magnitudes (quantities) involved in the problem.
• 😀 After identifying the magnitudes, determine if the quantities are directly or inversely proportional to each other.
• 😀 Directly proportional quantities increase or decrease together, while inversely proportional quantities move in opposite directions (one increases, the other decreases).
• 😀 Set up ratios based on the relationships between the quantities, starting with the unknown term and comparing it to known terms.
• 😀 In compound problems, always compare two quantities at a time, making sure to handle their proportionality correctly (direct or inverse).
• 😀 When dealing with directly proportional quantities, the ratio stays the same, whereas for inversely proportional quantities, the ratio is inverted.
• 😀 After setting up the ratios, cross-multiply and divide to solve for the unknown term.
• 😀 For example, if you know the number of seamstresses, time, and towels, you can solve for how many towels will be produced by different numbers of seamstresses or different amounts of time.
• 😀 Understanding the differences between simple and compound rule of three problems is essential for correctly identifying and solving real-world problems involving multiple quantities.
• 😀 Always practice with different examples to ensure a solid grasp of the compound rule of three, and remember to check if you are using the correct proportional relationships.

Q & A

What is the compound rule of three?

The compound rule of three is used to solve problems involving more than two quantities, where the relationships between the quantities can be either directly or inversely proportional. Unlike the simple rule of three, which deals with two quantities, the compound rule requires the identification of multiple magnitudes and their proportionality.

How is the simple rule of three different from the compound rule of three?

The simple rule of three involves only two quantities and compares them directly. In contrast, the compound rule of three involves more than two quantities, requiring the identification of multiple magnitudes and their relationships (direct or inverse proportionality) before solving the problem.

What is the first step in solving a compound rule of three problem?

The first step is to identify the quantities involved in the problem. You must determine what each quantity represents (e.g., time, workers, items produced) and note the values given in the problem.

How do you determine whether quantities are directly or inversely proportional?

To determine proportionality, you need to consider how changes in one quantity affect the others. If increasing one quantity increases the other (e.g., more workers leading to more towels produced), the quantities are directly proportional. If increasing one quantity decreases the other (e.g., more workers leading to less time), the quantities are inversely proportional.

In the given example, what is the proportionality between towels and time?

In the example, the number of towels and time are directly proportional. This means that the more time available, the more towels can be produced.

In the second example involving painters, what is the relationship between the number of painters and the area to be painted?

The number of painters and the area to be painted are directly proportional. More painters can cover more area in the same amount of time.

What is the relationship between the number of painters and the time taken to complete a task?

The number of painters and the time taken are inversely proportional. As the number of painters increases, the time required to complete the task decreases.

How do you set up a proportion for a compound rule of three problem?

To set up a proportion, first identify the known values and the unknown term. Then, arrange the quantities in a ratio, ensuring that the units and their relationships (direct or inverse proportionality) are correctly aligned. Use cross multiplication to solve for the unknown term.

In the second example, what was the result when the area increased to 400 square meters?

When the area increased to 400 square meters, the number of painters needed also increased. This is because more painters are required to meet the new task demand, especially given the decrease in time available.

What is the final answer for the number of painters needed to paint 400 square meters in 1 hour in the second example?

The final answer is that 18 painters are needed to paint 400 square meters in 1 hour, based on the calculations using the compound rule of three.