Solve For R R R In The Proportion. 8 20 = R + 2 15 \frac{8}{20} = \frac{r+2}{15} 20 8 ​ = 15 R + 2 ​ R = R = R =

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Understanding Proportions

A proportion is a statement that two ratios are equal. It is often written in the form $\frac{a}{b} = \frac{c}{d}$, where $a$, $b$, $c$, and $d$ are numbers. In this article, we will focus on solving for $r$ in the proportion $\frac{8}{20} = \frac{r+2}{15}$.

The Importance of Solving Proportions

Solving proportions is a crucial skill in mathematics, as it allows us to set up and solve equations that involve ratios. This skill is essential in various fields, such as science, engineering, and finance. In this article, we will provide a step-by-step guide on how to solve for $r$ in the proportion $\frac{8}{20} = \frac{r+2}{15}$.

Step 1: Cross-Multiply

To solve for $r$, we need to cross-multiply the two ratios. This means that we multiply the numerator of the first ratio by the denominator of the second ratio, and vice versa. In this case, we have:

$\frac{8}{20} = \frac{r+2}{15}$

Cross-multiplying, we get:

$8 \cdot 15 = 20 \cdot (r+2)$

Step 2: Simplify the Equation

Now that we have cross-multiplied, we can simplify the equation by multiplying the numbers. We get:

$120 = 20r + 40$

Step 3: Isolate $r$

To isolate $r$, we need to get rid of the constant term on the right-hand side of the equation. We can do this by subtracting 40 from both sides of the equation. We get:

$120 - 40 = 20r$

Simplifying, we get:

$80 = 20r$

Step 4: Solve for $r$

Finally, we can solve for $r$ by dividing both sides of the equation by 20. We get:

$r = \frac{80}{20}$

Simplifying, we get:

$r = 4$

Conclusion

In this article, we have provided a step-by-step guide on how to solve for $r$ in the proportion $\frac{8}{20} = \frac{r+2}{15}$. We have shown that the solution to this proportion is $r = 4$. We hope that this article has been helpful in understanding how to solve proportions and has provided a valuable resource for students and teachers alike.

Additional Tips and Resources

• To solve proportions, it is essential to cross-multiply and simplify the equation.
• To isolate $r$, subtract the constant term from both sides of the equation.
• To solve for $r$, divide both sides of the equation by the coefficient of $r$.
• For more practice problems and resources, visit the following websites:
  • Khan Academy: www.khanacademy.org
  • Mathway: www.mathway.com
  • IXL: www.ixl.com

Frequently Asked Questions

• Q: What is a proportion? A: A proportion is a statement that two ratios are equal.
• Q: How do I solve for $r$ in a proportion? A: To solve for $r$, cross-multiply and simplify the equation, then isolate $r$ by subtracting the constant term from both sides of the equation.
• Q: What is the solution to the proportion $\frac{8}{20} = \frac{r+2}{15}$? A: The solution to this proportion is $r = 4$.
  Solving for $r$ in a Proportion: A Q&A Guide =====================================================

Understanding Proportions

A proportion is a statement that two ratios are equal. It is often written in the form $\frac{a}{b} = \frac{c}{d}$, where $a$, $b$, $c$, and $d$ are numbers. In this article, we will provide a Q&A guide on how to solve for $r$ in a proportion.

Q: What is a proportion?

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

Q: How do I solve for $r$ in a proportion?

A: To solve for $r$, you need to cross-multiply and simplify the equation, then isolate $r$ by subtracting the constant term from both sides of the equation.

Q: What is cross-multiplication?

A: Cross-multiplication is the process of multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa. This is done to eliminate the fractions and simplify the equation.

Q: How do I simplify the equation after cross-multiplication?

A: After cross-multiplication, you need to simplify the equation by multiplying the numbers. This will give you a new equation that is easier to work with.

Q: How do I isolate $r$?

A: To isolate $r$, you need to get rid of the constant term on the right-hand side of the equation. This can be done by subtracting the constant term from both sides of the equation.

Q: What is the solution to the proportion $\frac{8}{20} = \frac{r+2}{15}$?

A: The solution to this proportion is $r = 4$.

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

A: Some common mistakes to avoid when solving proportions include:

• Not cross-multiplying
• Not simplifying the equation after cross-multiplication
• Not isolating $r$
• Not checking the solution to make sure it is correct

Q: How can I practice solving proportions?

A: There are many resources available to help you practice solving proportions, including:

• Online practice problems and quizzes
• Math textbooks and workbooks
• Online math tutors and mentors
• Math apps and games

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

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

• Science: Proportions are used to calculate the concentration of a solution.
• Engineering: Proportions are used to design and build structures.
• Finance: Proportions are used to calculate interest rates and investment returns.
• Cooking: Proportions are used to measure ingredients and calculate cooking times.

Conclusion

In this article, we have provided a Q&A guide on how to solve for $r$ in a proportion. We have covered the basics of proportions, including what a proportion is, how to solve for $r$, and common mistakes to avoid. We have also provided some real-world applications of proportions and resources for practicing and learning more.

Additional Tips and Resources

• To solve proportions, it is essential to cross-multiply and simplify the equation.
• To isolate $r$, subtract the constant term from both sides of the equation.
• To solve for $r$, divide both sides of the equation by the coefficient of $r$.
• For more practice problems and resources, visit the following websites:
  • Khan Academy: www.khanacademy.org
  • Mathway: www.mathway.com
  • IXL: www.ixl.com

Frequently Asked Questions

• Q: What is a proportion? A: A proportion is a statement that two ratios are equal.
• Q: How do I solve for $r$ in a proportion? A: To solve for $r$, cross-multiply and simplify the equation, then isolate $r$ by subtracting the constant term from both sides of the equation.
• Q: What is the solution to the proportion $\frac{8}{20} = \frac{r+2}{15}$? A: The solution to this proportion is $r = 4$.