In The Proportion $\frac{5}{7} = \frac{35}{49}$, Find The Means And Extremes.Calculate 80 7 + 2 ⋅ 49 80^7 + 2 \cdot 49 8 0 7 + 2 ⋅ 49 .Consider 7 And 35 7 \text{ And } 35 7 And 35 As The Means And 5 And 49 5 \text{ And } 49 5 And 49 As The Extremes.

by ADMIN 252 views

Introduction

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 proportion $\frac{5}{7} = \frac{35}{49}$ and find the means and extremes.

Understanding the Proportion

The proportion $\frac{5}{7} = \frac{35}{49}$ can be rewritten as $\frac{5}{7} \times \frac{7}{7} = \frac{35}{49}$, which simplifies to $\frac{5 \times 7}{7 \times 7} = \frac{35}{49}$. This shows that the proportion is true, as the two ratios are equal.

Finding the Means and Extremes

In a proportion, the means are the two middle numbers, while the extremes are the two outer numbers. In this case, 77 and 3535 are the means, while 55 and 4949 are the extremes.

Calculating the Means and Extremes

To calculate the means and extremes, we can use the following formulas:

  • Means: extreme1+extreme22\frac{extreme_1 + extreme_2}{2}
  • Extremes: mean1+mean22\frac{mean_1 + mean_2}{2}

Using these formulas, we can calculate the means and extremes as follows:

  • Means: 7+352=422=21\frac{7 + 35}{2} = \frac{42}{2} = 21
  • Extremes: 5+492=542=27\frac{5 + 49}{2} = \frac{54}{2} = 27

Calculating 807+2⋅4980^7 + 2 \cdot 49

Now, let's calculate 807+2⋅4980^7 + 2 \cdot 49. To do this, we need to follow the order of operations (PEMDAS):

  1. Calculate 80780^7: 807=268,435,45680^7 = 268,435,456
  2. Calculate 2⋅492 \cdot 49: 2⋅49=982 \cdot 49 = 98
  3. Add the two results: 268,435,456+98=268,435,554268,435,456 + 98 = 268,435,554

Therefore, 807+2⋅49=268,435,55480^7 + 2 \cdot 49 = 268,435,554.

Conclusion

In this article, we explored the proportion $\frac{5}{7} = \frac{35}{49}$ and found the means and extremes. We also calculated 807+2⋅4980^7 + 2 \cdot 49. The means and extremes are 2121 and 2727, respectively, and the result of the calculation is 268,435,554268,435,554.

References

Further Reading

Related Topics

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 identify the means and extremes in a proportion?

A: In a proportion, the means are the two middle numbers, while the extremes are the two outer numbers. To identify the means and extremes, look for the two numbers that are multiplied together to get the first ratio, and the two numbers that are multiplied together to get the second ratio.

Q: How do I calculate the means and extremes in a proportion?

A: To calculate the means and extremes, use the following formulas:

  • Means: extreme1+extreme22\frac{extreme_1 + extreme_2}{2}
  • Extremes: mean1+mean22\frac{mean_1 + mean_2}{2}

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when you have multiple operations in an expression. The acronym PEMDAS stands for:

  • Parentheses: Evaluate expressions inside parentheses first.
  • Exponents: Evaluate any exponential expressions next (e.g., 2^3).
  • Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  • Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I calculate 807+2⋅4980^7 + 2 \cdot 49?

A: To calculate 807+2⋅4980^7 + 2 \cdot 49, follow the order of operations (PEMDAS):

  1. Calculate 80780^7: 807=268,435,45680^7 = 268,435,456
  2. Calculate 2⋅492 \cdot 49: 2⋅49=982 \cdot 49 = 98
  3. Add the two results: 268,435,456+98=268,435,554268,435,456 + 98 = 268,435,554

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

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

  • Not following the order of operations (PEMDAS)
  • Not identifying the means and extremes correctly
  • Not using the correct formulas to calculate the means and extremes
  • Not checking your work for errors

Q: How can I practice working with proportions and calculations?

A: You can practice working with proportions and calculations by:

  • Working through examples and exercises in a math textbook or online resource
  • Using online calculators or software to check your work
  • Practicing with real-world applications, such as finance or science
  • Joining a study group or working with a tutor to get help and feedback

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

A: Proportions and calculations have many real-world applications, including:

  • Finance: Calculating interest rates, investment returns, and loan payments
  • Science: Measuring quantities, calculating rates, and analyzing data
  • Engineering: Designing and building structures, calculating stresses and strains
  • Business: Calculating costs, revenues, and profits

Conclusion

In this article, we answered some frequently asked questions about proportions and calculations. We covered topics such as identifying the means and extremes, calculating the means and extremes, and following the order of operations (PEMDAS). We also discussed some common mistakes to avoid and provided some tips for practicing and applying proportions and calculations in real-world situations.