Which Numbers Are The Extremes Of The Proportion Shown Below?$\frac{3}{4} = \frac{6}{8}$A. 3 And 6 B. 3 And 8 C. 4 And 6 D. 4 And 8

Feb 27, 2025 by ADMIN 137 views

**Understanding Proportions and Identifying Extremes**

In mathematics, proportions are used to compare two ratios. 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. In this article, we will explore the concept of proportions and identify the extremes of a given proportion.

What are Proportions?

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. For example, the proportion $\frac{3}{4} = \frac{6}{8}$ states that the ratio of 3 to 4 is equal to the ratio of 6 to 8.

Understanding the Components of a Proportion

A proportion consists of four components: two numbers on the top (numerator) and two numbers on the bottom (denominator). In the proportion $\frac{3}{4} = \frac{6}{8}$ , the two numbers on the top are 3 and 6, and the two numbers on the bottom are 4 and 8.

Identifying the Extremes of a Proportion

The extremes of a proportion are the two numbers that are not equal. In the proportion $\frac{3}{4} = \frac{6}{8}$ , the two numbers that are not equal are 3 and 8. The extremes of a proportion are also known as the "outer numbers" or the "outer terms".

Why are the Extremes Important?

The extremes of a proportion are important because they help us understand the relationship between the two ratios. By identifying the extremes, we can determine which numbers are being compared and which numbers are being equated.

How to Identify the Extremes of a Proportion

To identify the extremes of a proportion, we need to look at the two numbers that are not equal. In the proportion $\frac{3}{4} = \frac{6}{8}$ , the two numbers that are not equal are 3 and 8. Therefore, the extremes of this proportion are 3 and 8.

Example 1: Identifying the Extremes of a Proportion

Let's consider the proportion $\frac{2}{3} = \frac{4}{6}$ . To identify the extremes of this proportion, we need to look at the two numbers that are not equal. In this case, the two numbers that are not equal are 2 and 6. Therefore, the extremes of this proportion are 2 and 6.

Example 2: Identifying the Extremes of a Proportion

Let's consider the proportion $\frac{5}{6} = \frac{10}{12}$ . To identify the extremes of this proportion, we need to look at the two numbers that are not equal. In this case, the two numbers that are not equal are 5 and 12. Therefore, the extremes of this proportion are 5 and 12.

Conclusion

In conclusion, the extremes of a proportion are the two numbers that are not equal. By identifying the extremes, we can understand the relationship between the two ratios and determine which numbers are being compared and which numbers are being equated. In the proportion $\frac{3}{4} = \frac{6}{8}$ , the extremes are 3 and 8.

Answer

The correct answer is B. 3 and 8.

Final Thoughts

In this article, we will answer some frequently asked questions about proportions and extremes.

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: What are the components of a proportion?

A: A proportion consists of four components: two numbers on the top (numerator) and two numbers on the bottom (denominator).

Q: What are the extremes of a proportion?

A: The extremes of a proportion are the two numbers that are not equal. They are also known as the "outer numbers" or the "outer terms".

Q: How do I identify the extremes of a proportion?

A: To identify the extremes of a proportion, you need to look at the two numbers that are not equal. In the proportion $\frac{3}{4} = \frac{6}{8}$ , the two numbers that are not equal are 3 and 8. Therefore, the extremes of this proportion are 3 and 8.

Q: Why are the extremes of a proportion important?

A: The extremes of a proportion are important because they help us understand the relationship between the two ratios. By identifying the extremes, we can determine which numbers are being compared and which numbers are being equated.

Q: Can you give me an example of how to identify the extremes of a proportion?

A: Let's consider the proportion $\frac{2}{3} = \frac{4}{6}$ . To identify the extremes of this proportion, we need to look at the two numbers that are not equal. In this case, the two numbers that are not equal are 2 and 6. Therefore, the extremes of this proportion are 2 and 6.

Q: How do I know which numbers are the extremes of a proportion?

A: To determine which numbers are the extremes of a proportion, you need to look at the two numbers that are not equal. In the proportion $\frac{3}{4} = \frac{6}{8}$ , the two numbers that are not equal are 3 and 8. Therefore, the extremes of this proportion are 3 and 8.

Q: Can you give me another example of how to identify the extremes of a proportion?

A: Let's consider the proportion $\frac{5}{6} = \frac{10}{12}$ . To identify the extremes of this proportion, we need to look at the two numbers that are not equal. In this case, the two numbers that are not equal are 5 and 12. Therefore, the extremes of this proportion are 5 and 12.

Q: What is the difference between the extremes and the means of a proportion?

A: The extremes of a proportion are the two numbers that are not equal, while the means of a proportion are the two numbers that are equal. In the proportion $\frac{3}{4} = \frac{6}{8}$ , the means are 3 and 6, while the extremes are 3 and 8.

Q: Can you give me a real-world example of how proportions are used?

A: Proportions are used in a wide range of real-world applications, including architecture, engineering, and finance. For example, a builder may use proportions to determine the ratio of the length of a wall to the height of a building. A financial analyst may use proportions to determine the ratio of the price of a stock to the price of a bond.

Q: How do I solve a proportion problem?

A: To solve a proportion problem, you need to follow these steps:

Write the proportion as an equation.
Cross-multiply the two ratios.
Solve for the unknown variable.
Check your answer by plugging it back into the original equation.

Q: Can you give me a step-by-step example of how to solve a proportion problem?

A: Let's consider the proportion $\frac{2}{3} = \frac{4}{6}$ . To solve this problem, we need to follow these steps:

Write the proportion as an equation: $\frac{2}{3} = \frac{4}{6}$ .
Cross-multiply the two ratios: $2 \times 6 = 3 \times 4$ .
Solve for the unknown variable: $12 = 12$ .
Check your answer by plugging it back into the original equation: $\frac{2}{3} = \frac{4}{6}$ .

Conclusion

In conclusion, proportions and extremes are important concepts in mathematics. By understanding how to identify the extremes of a proportion, you can solve a wide range of problems and make informed decisions in various fields.