Write The Statement As A Proportion Using Colons: 4 Is To 20 As 2 Is To 10.Select One Of The Following:A. \[$42:2=10:2\$\] B. \[$\frac{4}{20}=\frac{2}{10}\$\] C. \[$4:20=2:10\$\] D. \[$42:21:00\$\]

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Proportions are a fundamental concept in mathematics that help us understand the relationship between different quantities. In this article, we will explore how to write a statement as a proportion using colons and provide examples to illustrate the concept.

What is a Proportion?

A proportion is a statement that two ratios are equal. It is often written in the form of a colon, where the first ratio is equal to the second ratio. For example, "4 is to 20 as 2 is to 10" can be written as a proportion using colons.

Writing a Statement as a Proportion

To write a statement as a proportion, we need to identify the two ratios and write them in the form of a colon. The first ratio is the one that is being compared, and the second ratio is the one that is being equated to it.

Example: 4 is to 20 as 2 is to 10

Let's take the statement "4 is to 20 as 2 is to 10" as an example. To write this statement as a proportion, we need to identify the two ratios and write them in the form of a colon.

The first ratio is 4:20, and the second ratio is 2:10. We can write this statement as a proportion using colons as follows:

4:20 = 2:10

This is an example of a proportion, where the first ratio (4:20) is equal to the second ratio (2:10).

Answer Options

Now that we have understood how to write a statement as a proportion, let's look at the answer options provided.

A. $$422=10:2$$

This option is incorrect because it does not represent the proportion correctly. The correct proportion is 4:20 = 2:10, not 42:2 = 10:2.

B. {\frac{4}{20}=\frac{2}{10}$}$

This option is incorrect because it represents the proportion as a fraction, not as a colon. While the fraction is correct, the colon representation is what we are looking for.

C. $$420=2:10$$

This option is correct because it represents the proportion correctly using colons.

D. $$4221:00$$

This option is incorrect because it does not represent the proportion correctly. The correct proportion is 4:20 = 2:10, not 42:21:00.

Conclusion

In conclusion, a proportion is a statement that two ratios are equal, and it is often written in the form of a colon. To write a statement as a proportion, we need to identify the two ratios and write them in the form of a colon. The correct answer option is C. $$420=2:10$$, which represents the proportion correctly using colons.

Key Takeaways

  • A proportion is a statement that two ratios are equal.
  • To write a statement as a proportion, we need to identify the two ratios and write them in the form of a colon.
  • The correct answer option is C. $$420=2:10$$, which represents the proportion correctly using colons.

Further Reading

If you want to learn more about proportions and how to use them in mathematics, here are some additional resources:

  • Khan Academy: Proportions
  • Mathway: Proportions
  • Wikipedia: Proportion (mathematics)

In this article, we will answer some frequently asked questions about proportions and provide additional examples to help you understand the concept.

Q: What is the difference between a proportion and a ratio?

A: A ratio is a comparison of two numbers, while a proportion is a statement that two ratios are equal. For example, the ratio of 4 to 20 is the same as the ratio of 2 to 10, but the proportion 4:20 = 2:10 states that the two ratios are equal.

Q: How do I write a proportion using colons?

A: To write a proportion using colons, you need to identify the two ratios and write them in the form of a colon. For example, the proportion 4:20 = 2:10 can be written as:

4:20 = 2:10

Q: Can I write a proportion using fractions?

A: Yes, you can write a proportion using fractions. For example, the proportion 4:20 = 2:10 can be written as:

420=210\frac{4}{20} = \frac{2}{10}

However, the colon representation is often preferred because it is more concise and easier to read.

Q: How do I solve a proportion?

A: To solve a proportion, you need to find the missing value that makes the two ratios equal. For example, if you have the proportion 4:20 = x:10, you can solve for x by setting up an equation:

420=x10\frac{4}{20} = \frac{x}{10}

Cross-multiplying, you get:

4 Ă— 10 = 20 Ă— x

40 = 20x

Dividing both sides by 20, you get:

x = 2

Q: Can I use proportions to solve real-world problems?

A: Yes, proportions can be used to solve real-world problems. For example, if you are building a fence and you know that the ratio of the length of the fence to the width of the fence is 4:20, you can use this proportion to find the missing value if you know the length of the fence.

Q: What are some common applications of proportions?

A: Proportions have many common applications in mathematics and real-world problems, including:

  • Scaling: Proportions are used to scale up or down a design or a model.
  • Measurement: Proportions are used to measure the size of objects or the amount of materials needed.
  • Finance: Proportions are used to calculate interest rates and investment returns.
  • Science: Proportions are used to describe the relationships between different variables in scientific experiments.

Q: Can I use proportions to solve algebraic equations?

A: Yes, proportions can be used to solve algebraic equations. For example, if you have the equation 4x = 20, you can use the proportion 4:20 = x:5 to solve for x.

Q: What are some common mistakes to avoid when working with proportions?

A: Some common mistakes to avoid when working with proportions include:

  • Not setting up the proportion correctly
  • Not solving for the missing value
  • Not checking the units of the variables
  • Not using the correct operation (e.g. multiplication instead of division)

Conclusion

In conclusion, proportions are a fundamental concept in mathematics that can be used to solve a wide range of problems. By understanding how to write a proportion using colons and how to solve a proportion, you can improve your math skills and become more confident in your ability to solve problems.

Key Takeaways

  • A proportion is a statement that two ratios are equal.
  • To write a proportion using colons, you need to identify the two ratios and write them in the form of a colon.
  • To solve a proportion, you need to find the missing value that makes the two ratios equal.
  • Proportions have many common applications in mathematics and real-world problems.

Further Reading

If you want to learn more about proportions and how to use them in mathematics, here are some additional resources:

  • Khan Academy: Proportions
  • Mathway: Proportions
  • Wikipedia: Proportion (mathematics)

By understanding proportions and how to use them in mathematics, you can improve your math skills and become more confident in your ability to solve problems.