What Are The Extremes Of The Proportion 9.8 11.5 = 4.9 5.75 \frac{9.8}{11.5} = \frac{4.9}{5.75} 11.5 9.8 ​ = 5.75 4.9 ​ ?A. 9.8 And 11.5 B. 9.8 And 4.9 C. 9.8 And 5.75 D. 11.5 And 4.9

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Introduction

In mathematics, proportions are used to compare the ratios of two or more quantities. A proportion is a statement that two ratios are equal, and it can be written in the form $\frac{a}{b} = \frac{c}{d}$. In this article, we will explore the extremes of the proportion $\frac{9.8}{11.5} = \frac{4.9}{5.75}$.

Understanding Proportions

A proportion is a mathematical statement that two ratios are equal. It can be written in the form $\frac{a}{b} = \frac{c}{d}$, where $a$, $b$, $c$, and $d$ are numbers. The proportion $\frac{9.8}{11.5} = \frac{4.9}{5.75}$ is an example of a proportion where the two ratios are equal.

Cross-Multiplication

To find the extremes of the proportion, we can use cross-multiplication. Cross-multiplication is a technique used to solve proportions by multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa. In this case, we can cross-multiply the proportion $\frac{9.8}{11.5} = \frac{4.9}{5.75}$ by multiplying $9.8$ by $5.75$ and $4.9$ by $11.5$.

Calculating the Extremes

Using cross-multiplication, we can calculate the extremes of the proportion as follows:

$9.8 \times 5.75 = 56.45$

$4.9 \times 11.5 = 56.45$

As we can see, the two products are equal, which means that the proportion $\frac{9.8}{11.5} = \frac{4.9}{5.75}$ is true.

Finding the Extremes

Now that we have confirmed the proportion, we can find the extremes of the proportion. The extremes of a proportion are the largest and smallest values in the proportion. In this case, the extremes are $9.8$ and $5.75$.

Conclusion

In conclusion, the extremes of the proportion $\frac{9.8}{11.5} = \frac{4.9}{5.75}$ are $9.8$ and $5.75$. This means that the largest value in the proportion is $9.8$ and the smallest value is $5.75$.

Final Answer

The final answer to the question is:

C. 9.8 and 5.75

Discussion

The discussion of this problem involves understanding the concept of proportions and how to use cross-multiplication to solve them. It also involves finding the extremes of a proportion, which is an important concept in mathematics.

Related Problems

Some related problems to this one include:

• Finding the extremes of the proportion $\frac{3.2}{4.8} = \frac{2.1}{3.2}$
• Solving the proportion $\frac{7.9}{9.5} = \frac{5.6}{7.9}$
• Finding the extremes of the proportion $\frac{1.9}{2.5} = \frac{1.4}{1.9}$

References

• [1] "Proportions" by Math Open Reference. Retrieved from https://www.mathopenref.com/proportions.html
• [2] "Cross-Multiplication" by Khan Academy. Retrieved from https://www.khanacademy.org/math/algebra/x2f-proportions/x2f-proportions-cross-multiplication/v/cross-multiplication
• [3] "Extremes of a Proportion" by Math Is Fun. Retrieved from https://www.mathisfun.com/proportions/extremes.html
  

Introduction

In our previous article, we explored the concept of proportions and how to find the extremes of a proportion. In this article, we will answer some frequently asked questions about proportions and extremes.

Q: What is a proportion?

A: A proportion is a mathematical statement that two ratios are equal. It can be written in the form $\frac{a}{b} = \frac{c}{d}$, where $a$, $b$, $c$, and $d$ are numbers.

Q: How do I solve a proportion?

A: To solve a proportion, you can use cross-multiplication. Cross-multiplication is a technique used to solve proportions by multiplying 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 by multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa. For example, in the proportion $\frac{9.8}{11.5} = \frac{4.9}{5.75}$, you can cross-multiply by multiplying $9.8$ by $5.75$ and $4.9$ by $11.5$.

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

A: To find the extremes of a proportion, you can use cross-multiplication and then compare the products. The extremes of a proportion are the largest and smallest values in the proportion.

Q: What are the extremes of the proportion $\frac{3.2}{4.8} = \frac{2.1}{3.2}$?

A: To find the extremes of the proportion $\frac{3.2}{4.8} = \frac{2.1}{3.2}$, you can use cross-multiplication and then compare the products. The extremes of the proportion are $3.2$ and $2.1$.

Q: How do I solve the proportion $\frac{7.9}{9.5} = \frac{5.6}{7.9}$?

A: To solve the proportion $\frac{7.9}{9.5} = \frac{5.6}{7.9}$, you can use cross-multiplication. Cross-multiplying the proportion gives $7.9 \times 7.9 = 62.61$ and $5.6 \times 9.5 = 53.2$. Since the two products are not equal, the proportion is not true.

Q: What are the extremes of the proportion $\frac{1.9}{2.5} = \frac{1.4}{1.9}$?

A: To find the extremes of the proportion $\frac{1.9}{2.5} = \frac{1.4}{1.9}$, you can use cross-multiplication and then compare the products. The extremes of the proportion are $1.9$ and $1.4$.

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 know the ratio of the length of a rectangle to its width, you can use proportions to find the length or width of the rectangle.

Q: What are some common applications of proportions?

A: Some common applications of proportions include:

• Finding the area of a rectangle
• Finding the perimeter of a rectangle
• Finding the volume of a rectangular prism
• Finding the surface area of a rectangular prism

Conclusion

In conclusion, proportions are an important concept in mathematics that can be used to solve a wide range of problems. By understanding how to solve proportions and find the extremes of a proportion, you can apply this knowledge to real-world problems and make informed decisions.

Final Answer

The final answer to the question is:

• The extremes of the proportion $\frac{3.2}{4.8} = \frac{2.1}{3.2}$ are $3.2$ and $2.1$.
• The proportion $\frac{7.9}{9.5} = \frac{5.6}{7.9}$ is not true.
• The extremes of the proportion $\frac{1.9}{2.5} = \frac{1.4}{1.9}$ are $1.9$ and $1.4$.

Discussion

The discussion of this problem involves understanding the concept of proportions and how to use cross-multiplication to solve them. It also involves finding the extremes of a proportion, which is an important concept in mathematics.

Related Problems

Some related problems to this one include:

• Finding the extremes of the proportion $\frac{4.5}{6.2} = \frac{3.1}{4.5}$
• Solving the proportion $\frac{9.1}{11.8} = \frac{6.3}{9.1}$
• Finding the extremes of the proportion $\frac{2.3}{3.1} = \frac{1.7}{2.3}$

References

• [1] "Proportions" by Math Open Reference. Retrieved from https://www.mathopenref.com/proportions.html
• [2] "Cross-Multiplication" by Khan Academy. Retrieved from https://www.khanacademy.org/math/algebra/x2f-proportions/x2f-proportions-cross-multiplication/v/cross-multiplication
• [3] "Extremes of a Proportion" by Math Is Fun. Retrieved from https://www.mathisfun.com/proportions/extremes.html