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

What are Proportions?

A proportion is a mathematical statement that two ratios are equal. It is often written in the form of a fraction, where the two fractions have the same value. 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.

Identifying Extremes in a Proportion

In a proportion, the extremes are the outer numbers, while the means are the inner numbers. To identify the extremes, we need to look at the two fractions and find the numbers that are not in the middle. In the proportion $\frac{3}{4}=\frac{6}{8}$, the extremes are 3 and 8.

Why are the Extremes Important?

The extremes are important in a proportion because they help us understand the relationship between the two ratios. By identifying the extremes, we can determine the scale factor between the two ratios. In this case, the scale factor is 2, since 6 is twice 3 and 8 is twice 4.

How to Identify Extremes in a Proportion

To identify the extremes in a proportion, follow these steps:

1. Write the proportion as two fractions.
2. Identify the outer numbers in each fraction.
3. The outer numbers are the extremes.

Example: Identifying Extremes in a Proportion

Let's use the proportion $\frac{2}{3}=\frac{4}{6}$ to identify the extremes.

1. Write the proportion as two fractions: $\frac{2}{3}$ and $\frac{4}{6}$.
2. Identify the outer numbers in each fraction: 2 and 6 are the outer numbers in the first fraction, and 3 and 4 are the outer numbers in the second fraction.
3. The outer numbers are the extremes: 2 and 6.

Conclusion

In conclusion, the extremes in a proportion are the outer numbers, while the means are the inner numbers. By identifying the extremes, we can understand the relationship between the two ratios and determine the scale factor between them. In the proportion $\frac{3}{4}=\frac{6}{8}$, the extremes are 3 and 8.

Answer

The correct answer is B. 3 and 8.

Additional Tips and Examples

• To check if two ratios are proportional, we can cross-multiply and see if the resulting equation is true.

• To find the scale factor between two ratios, we can divide the larger ratio by the smaller ratio.

• To identify the extremes in a proportion, we can use the following steps:

  1. Write the proportion as two fractions.
  2. Identify the outer numbers in each fraction.
  3. The outer numbers are the extremes.

Common Mistakes to Avoid

• Don't confuse the extremes with the means. The extremes are the outer numbers, while the means are the inner numbers.
• Don't forget to check if the resulting equation is true when cross-multiplying to check if two ratios are proportional.
• Don't divide the larger ratio by the smaller ratio to find the scale factor between two ratios. Instead, divide the larger ratio by the smaller ratio.

Real-World Applications

Proportions are used in many real-world applications, such as:

• Scaling up or down a recipe
• Finding the scale factor between two similar figures
• Determining the ratio of two quantities

Practice Problems

1. Identify the extremes in the proportion $\frac{5}{6}=\frac{10}{12}$.
2. Find the scale factor between the two ratios in the proportion $\frac{3}{4}=\frac{9}{12}$.
3. Check if the two ratios in the proportion $\frac{2}{3}=\frac{4}{6}$ are proportional.

Answer Key

1. The extremes are 5 and 12.
2. The scale factor is 3.
3. Yes, the two ratios are proportional.
   Proportions Q&A ==================

Q: What is a proportion?

A: A proportion is a mathematical statement that two ratios are equal. It is often written in the form of a fraction, where the two fractions have the same value.

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

A: To identify the extremes in a proportion, follow these steps:

1. Write the proportion as two fractions.
2. Identify the outer numbers in each fraction.
3. The outer numbers are the extremes.

Q: What are the means in a proportion?

A: The means in a proportion are the inner numbers. They are the numbers that are not on the outside of the fractions.

Q: How do I check if two ratios are proportional?

A: To check if two ratios are proportional, you can cross-multiply and see if the resulting equation is true. If the equation is true, then the two ratios are proportional.

Q: What is the scale factor between two ratios?

A: The scale factor between two ratios is the number that you multiply one ratio by to get the other ratio. It is also the number that you divide one ratio by to get the other ratio.

Q: How do I find the scale factor between two ratios?

A: To find the scale factor between two ratios, you can divide the larger ratio by the smaller ratio.

Q: What are some real-world applications of proportions?

A: Proportions are used in many real-world applications, such as:

• Scaling up or down a recipe
• Finding the scale factor between two similar figures
• Determining the ratio of two quantities

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

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

• Confusing the extremes with the means
• Forgetting to check if the resulting equation is true when cross-multiplying
• Dividing the larger ratio by the smaller ratio to find the scale factor between two ratios

Q: How do I practice working with proportions?

A: You can practice working with proportions by:

• Solving practice problems
• Working with real-world applications
• Creating your own proportions and solving them

Q: What are some additional tips for working with proportions?

A: Some additional tips for working with proportions include:

• Using a calculator to check your work
• Drawing diagrams to help you visualize the proportions
• Checking your work multiple times to make sure it is correct

Q: What are some common types of proportions?

A: Some common types of proportions include:

• Simple proportions: These are proportions where the two ratios are equal.
• Complex proportions: These are proportions where the two ratios are not equal.
• Similar proportions: These are proportions where the two ratios are equal and the figures are similar.

Q: How do I determine if two figures are similar?

A: To determine if two figures are similar, you can use the following steps:

1. Check if the two figures have the same shape.
2. Check if the two figures have the same size.
3. Check if the two figures have the same orientation.

Q: What are some real-world applications of similar proportions?

A: Similar proportions are used in many real-world applications, such as:

• Architecture: Architects use similar proportions to design buildings and other structures.
• Engineering: Engineers use similar proportions to design machines and other devices.
• Art: Artists use similar proportions to create realistic and proportional drawings and paintings.

Q: How do I find the scale factor between two similar figures?

A: To find the scale factor between two similar figures, you can use the following steps:

1. Measure the lengths of corresponding sides of the two figures.
2. Divide the length of one side by the length of the corresponding side on the other figure.
3. The result is the scale factor between the two figures.

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

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

• Confusing the scale factor with the ratio of the two figures.
• Forgetting to check if the two figures are similar before finding the scale factor.
• Dividing the length of one side by the length of the corresponding side on the other figure without checking if the two figures are similar.