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Calculator: Compound Rule of Three

Calculate the compound rule of three quickly, easily, and for free

Calculator: Compound Rule of Three

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Simple Rule of Three
Compound Rule of Three

Compound Rule of Three Calculator – Online, Fast, and Free

Need to solve Compound Rule of Three problems quickly?

Fastools offers a free online Compound Rule of Three calculator that delivers instant results, detailed step-by-step explanations, and practical examples—directly in your browser, with no sign-up or downloads required.

Simply enter the known values from your problem, click 'Calculate', and instantly receive the result with clear explanations.

Our Compound Rule of Three tool helps students, teachers, and professionals grasp the logic behind the calculations, making learning more efficient and reliable.

How to use the Compound Rule of Three calculator?

  • 1️⃣ Enter all known values from the problem involving more than two quantities.
  • 2️⃣ Click 'Calculate' to see the result instantly.
  • 3️⃣ Review the detailed step-by-step and understand the solution.

Why use the Fastools calculator?

  • ✅ Completely free and online
  • ✅ Fast and accurate results—even for complex problems
  • ✅ Detailed step-by-step guidance for complete learning
  • ✅ Ideal for students, teachers, and professionals
  • ✅ Works directly in your browser—no downloads or sign-up required

Benefits of using our Compound Rule of Three calculator

  • 📚 Learn and review the Compound Rule of Three with clear examples
  • ⚡ Save time with instant calculations
  • 🎯 Avoid common manual calculation errors
  • 💻 Access from any device: computer, tablet, or smartphone

Can I use the calculator for school exercises?

Yes! The tool is perfect for elementary, high school, and technical education students, helping them solve exercises quickly, accurately, and understandably.

Start calculating the Compound Rule of Three online, for free, and reliably—right now with Fastools!

What is the Compound Rule of Three?

The Compound Rule of Three is a mathematical tool used to solve problems involving more than two related quantities. Unlike the Simple Rule of Three, which handles only two quantities, the compound version can involve three or more—simultaneously.

What is the Compound Rule of Three used for?

It is essential for solving problems involving multiple, mutually influencing variables. Common examples include:

  • Factory production: workers, time, and product quantity.
  • Civil construction: number of workers, days, and projects.
  • Transportation: number of vehicles, speed, and load.

How does the Compound Rule of Three work?

The principle is the same as the Simple Rule of Three: analyze the proportional relationships among quantities and solve using a proportion. However, in the compound case, each quantity must be analyzed relative to the final result to determine whether it is directly or inversely proportional.

Steps to Solve:

  1. List all quantities involved.
  2. Determine whether each quantity is directly or inversely proportional to the result.
  3. Set up the proportion, accounting for proportional relationships.
  4. Multiply the values and solve the equation.

General Formula for the Compound Rule of Three

For a problem with *n* quantities, the solution structure is:

\[ x = \frac{(v_1^{\pm 1}) \times (v_2^{\pm 1}) \times \ldots \times (v_n^{\pm 1}) \times R}{1} \]

Where:

  • \( v_i \): valor da grandeza i
  • O expoente "+1" indica relação direta e "-1" relação inversa.
  • \( R \): resultado ou valor final a ser determinado

Cross Multiplication

In general, multiply the values of quantities that are directly proportional and divide by those that are inversely proportional:

\[ x = \frac{\text{Produto das grandezas diretas}}{\text{Produto das grandezas inversas}} \]

Practical Example

Problem: If 4 machines produce 200 parts in 5 hours, how many parts will 6 machines produce in 3 hours?

Solution:

  • Machines → output: direct relationship (more machines, more output).
  • Time → output: direct relationship (more time, more output).

We set up the proportion:

\[ \frac{x}{200} = \frac{6}{4} \times \frac{3}{5} \]

We multiply:

\[ \frac{x}{200} = \frac{6 \times 3}{4 \times 5} = \frac{18}{20} = \frac{9}{10} \]

Thus:

\[ x = 200 \times \frac{9}{10} \]

\[ x = 180 \text{ peças} \]

Important Tips

  • Always verify whether the relationship between quantities is direct or inverse.
  • Organize the data in a table to improve clarity.
  • Simplify fractions where possible.

Interesting Facts About the Compound Rule of Three

  • The Compound Rule of Three is widely used in fields such as engineering, management, and logistics, where multiple variables must be considered simultaneously.
  • Although it may seem complex, it is simply a logical extension of the Simple Rule of Three—requiring only an understanding of proportional relationships.
  • It is often applied subconsciously—such as when calculating trip time considering the number of vehicles and their speed.

Conclusion

The Compound Rule of Three is a powerful tool that enables solving complex problems in a structured and logical way. Mastering it is essential for various professions and everyday situations involving multiple variables.