Solve The Proportion. If There Is No Solution, Enter DNE. N + 5 11 = 55 − N 2 \frac{n+5}{11}=\frac{55-n}{2} 11 N + 5 ​ = 2 55 − N ​ Solution: N = N = N = □ \square □ If There Is More Than One Solution To The Equation, Use A Comma To Separate Solutions.

Introduction

Proportions are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will explore the process of solving proportions, using the given equation as a case study. We will break down the steps involved in solving the proportion and provide a clear explanation of the solution.

What is a Proportion?

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 given equation $\frac{n+5}{11}=\frac{55-n}{2}$ is a proportion, where the two ratios are $\frac{n+5}{11}$ and $\frac{55-n}{2}$.

Step 1: Cross-Multiply

To solve a proportion, we need to cross-multiply, which involves multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa. This gives us the equation $(n+5)(2) = (55-n)(11)$.

Step 2: Expand and Simplify

Next, we need to expand and simplify the equation. Expanding the equation gives us $2n + 10 = 605 - 11n$. Simplifying the equation gives us $13n = 595$.

Step 3: Solve for n

To solve for n, we need to isolate n on one side of the equation. Dividing both sides of the equation by 13 gives us $n = \frac{595}{13}$.

Step 4: Simplify the Solution

Simplifying the solution gives us $n = 45.76923$. However, since the problem asks for a specific value of n, we can round the solution to the nearest integer.

Conclusion

In conclusion, solving proportions involves cross-multiplying, expanding and simplifying the equation, and solving for the variable. In this case, we found that $n = 45.76923$, which can be rounded to the nearest integer.

Discussion

The given equation is a proportion, where the two ratios are $\frac{n+5}{11}$ and $\frac{55-n}{2}$. To solve the proportion, we need to cross-multiply, expand and simplify the equation, and solve for n. The solution to the equation is $n = 45.76923$, which can be rounded to the nearest integer.

Example Use Cases

Solving proportions has many practical applications in real-life situations. For example, in finance, proportions are used to calculate interest rates and investment returns. In engineering, proportions are used to design and build structures that are proportional to the loads they will bear.

Tips and Tricks

When solving proportions, it is essential to follow the order of operations (PEMDAS) and to simplify the equation as much as possible. Additionally, it is crucial to check the solution to ensure that it satisfies the original equation.

Common Mistakes

One common mistake when solving proportions is to forget to cross-multiply or to simplify the equation. Another common mistake is to round the solution to the nearest integer without checking if it satisfies the original equation.

Conclusion

In conclusion, solving proportions is a crucial skill for students to master. By following the steps outlined in this article, students can solve proportions with ease and confidence. Remember to cross-multiply, expand and simplify the equation, and solve for the variable. With practice and patience, students can become proficient in solving proportions and apply this skill to real-life situations.

Final Answer

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Introduction

In our previous article, we explored the process of solving proportions, using the given equation as a case study. In this article, we will provide a Q&A guide to help students and professionals alike understand the concept of solving proportions and apply it to real-life situations.

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 solve a proportion?

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

1. Cross-multiply, which involves multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa.
2. Expand and simplify the equation.
3. Solve for the variable.

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 gives us the equation $(n+5)(2) = (55-n)(11)$.

Q: Why do I need to expand and simplify the equation?

A: Expanding and simplifying the equation helps us to isolate the variable and solve for it. It also helps us to check if the solution satisfies the original equation.

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

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

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I check if my solution satisfies the original equation?

A: To check if your solution satisfies the original equation, you need to plug the solution back into the original equation and see if it is true. If it is true, then your solution is correct.

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

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

• Forgetting to cross-multiply or simplify the equation.
• Rounding the solution to the nearest integer without checking if it satisfies the original equation.
• Not following the order of operations (PEMDAS).

Q: How do I apply solving proportions to real-life situations?

A: Solving proportions has many practical applications in real-life situations. For example, in finance, proportions are used to calculate interest rates and investment returns. In engineering, proportions are used to design and build structures that are proportional to the loads they will bear.

Q: What are some examples of proportions in real-life situations?

A: Some examples of proportions in real-life situations include:

• Calculating interest rates on loans or investments.
• Designing buildings or bridges that can withstand certain loads.
• Measuring the proportions of a person's body to determine their height or weight.
• Calculating the proportions of a recipe to make a certain amount of food.

Conclusion

In conclusion, solving proportions is a crucial skill for students and professionals alike to master. By following the steps outlined in this article and avoiding common mistakes, you can apply solving proportions to real-life situations and make informed decisions. Remember to cross-multiply, expand and simplify the equation, and solve for the variable. With practice and patience, you can become proficient in solving proportions and apply this skill to a wide range of situations.

Final Answer

The final answer is: Solving proportions is a crucial skill that has many practical applications in real-life situations.