Solve The Proportion Below.${ \frac{55}{x} = \frac{5}{6} }${ X =\$} A. 56 B. 60 C. 50 D. 66
What is a Proportion?
A proportion is a statement that two ratios are equal. It is often written in the form of an equation, where the two ratios are set equal to each other. Proportions are used to solve problems involving ratios and percentages, and are a fundamental concept in mathematics.
The Given Proportion
The given proportion is . This means that the ratio of 55 to x is equal to the ratio of 5 to 6.
Step 1: Cross-Multiply
To solve the proportion, we need to cross-multiply. This means that we multiply the numerator of the first ratio by the denominator of the second ratio, and vice versa. In this case, we multiply 55 by 6, and 5 by x.
Step 2: Divide Both Sides by 5
To solve for x, we need to divide both sides of the equation by 5.
Conclusion
Therefore, the value of x is 66.
Why is this Important?
Solving proportions is an important skill in mathematics, as it allows us to solve problems involving ratios and percentages. It is used in a wide range of applications, including finance, science, and engineering.
Real-World Applications
Proportions are used in a wide range of real-world applications, including:
- Finance: Proportions are used to calculate interest rates and investment returns.
- Science: Proportions are used to calculate the concentration of solutions and the amount of a substance present in a sample.
- Engineering: Proportions are used to design and build structures, such as bridges and buildings.
Tips and Tricks
Here are some tips and tricks for solving proportions:
- Use cross-multiplication: Cross-multiplication is a quick and easy way to solve proportions.
- Check your work: Always check your work to make sure that the solution is correct.
- Use a calculator: If you are having trouble solving a proportion, try using a calculator to check your work.
Common Mistakes
Here are some common mistakes to avoid when solving proportions:
- Not cross-multiplying: Failing to cross-multiply is a common mistake when solving proportions.
- Not checking your work: Failing to check your work can lead to incorrect solutions.
- Not using a calculator: Failing to use a calculator can make it difficult to check your work.
Conclusion
Q: What is a proportion?
A: A proportion is a statement that two ratios are equal. It is often written in the form of an equation, where the two ratios are set equal to each other.
Q: How do I solve a proportion?
A: To solve a proportion, you need to cross-multiply and then solve for the variable. This means that you multiply the numerator of the first ratio by the denominator of the second ratio, and vice versa.
Q: What is cross-multiplication?
A: Cross-multiplication is a technique used to solve proportions. It involves multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa.
Q: Why do I need to check my work when solving a proportion?
A: Checking your work is important when solving a proportion because it helps you to ensure that your solution is correct. If you don't check your work, you may end up with an incorrect solution.
Q: Can I use a calculator to solve a proportion?
A: Yes, you can use a calculator to solve a proportion. In fact, using a calculator can be a great way to check your work and ensure that your solution is correct.
Q: What are some common mistakes to avoid when solving a proportion?
A: Some common mistakes to avoid when solving a proportion include:
- Not cross-multiplying
- Not checking your work
- Not using a calculator to check your work
Q: How do I know if a proportion is true or false?
A: To determine if a proportion is true or false, you need to check if the two ratios are equal. If the ratios are equal, then the proportion is true. If the ratios are not equal, then the proportion is false.
Q: Can I use proportions to solve problems involving percentages?
A: Yes, you can use proportions to solve problems involving percentages. In fact, proportions are often used to calculate percentages and interest rates.
Q: What are some real-world applications of proportions?
A: Some real-world applications of proportions include:
- Finance: Proportions are used to calculate interest rates and investment returns.
- Science: Proportions are used to calculate the concentration of solutions and the amount of a substance present in a sample.
- Engineering: Proportions are used to design and build structures, such as bridges and buildings.
Q: How can I practice solving proportions?
A: There are many ways to practice solving proportions, including:
- Using online resources, such as math websites and apps
- Working with a tutor or teacher
- Practicing with sample problems and exercises
Q: What are some tips for solving proportions quickly and accurately?
A: Some tips for solving proportions quickly and accurately include:
- Using cross-multiplication
- Checking your work
- Using a calculator to check your work
- Practicing regularly to build your skills and confidence.
Conclusion
Solving proportions is an important skill in mathematics, and is used in a wide range of applications. By following the steps outlined in this article, you can solve proportions with ease. Remember to use cross-multiplication, check your work, and use a calculator to check your solutions. With practice and patience, you will become a pro at solving proportions in no time.