Solve For $w$ In The Proportion:$\[ \frac{2}{3.4} = \frac{w}{13.6} \\]$w =$

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Understanding the Problem

In this article, we will focus on solving for the variable w in a given proportion. A proportion is a mathematical statement that two ratios are equal. It is often represented as a fraction or a decimal. In this case, we have the proportion 23.4=w13.6\frac{2}{3.4} = \frac{w}{13.6}, and we need to solve for the value of w.

What is a Proportion?

A proportion is a mathematical statement that two ratios are equal. It is often represented as a fraction or a decimal. For example, the proportion 23.4=w13.6\frac{2}{3.4} = \frac{w}{13.6} means that the ratio of 2 to 3.4 is equal to the ratio of w to 13.6.

How to Solve for w in a Proportion

To solve for w in a proportion, we can use the following steps:

  1. Cross-multiply: Cross-multiplying is a technique used to eliminate the fractions in a proportion. To cross-multiply, we multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa. In this case, we multiply 2 by 13.6 and 3.4 by w.
  2. Simplify the equation: After cross-multiplying, we simplify the equation by combining like terms. In this case, we have the equation 2(13.6) = 3.4w.
  3. Solve for w: To solve for w, we divide both sides of the equation by 3.4. This will give us the value of w.

Step-by-Step Solution

Now that we have the steps to solve for w in a proportion, let's apply them to the given proportion 23.4=w13.6\frac{2}{3.4} = \frac{w}{13.6}.

Step 1: Cross-multiply

To cross-multiply, we multiply 2 by 13.6 and 3.4 by w.

2(13.6)=3.4w2(13.6) = 3.4w

Step 2: Simplify the equation

After cross-multiplying, we simplify the equation by combining like terms.

27.2=3.4w27.2 = 3.4w

Step 3: Solve for w

To solve for w, we divide both sides of the equation by 3.4.

w=27.23.4w = \frac{27.2}{3.4}

Step 4: Calculate the value of w

Now that we have the equation, we can calculate the value of w.

w=8w = 8

Conclusion

In this article, we have learned how to solve for w in a proportion. We have applied the steps of cross-multiplying, simplifying the equation, and solving for w to find the value of w. The final answer is w = 8.

Example Use Cases

Solving for w in a proportion has many practical applications in real-life situations. Here are a few examples:

  • Finance: In finance, proportions are used to calculate interest rates, investment returns, and other financial metrics.
  • Science: In science, proportions are used to calculate the concentration of a substance, the rate of a chemical reaction, and other scientific metrics.
  • Engineering: In engineering, proportions are used to calculate the stress and strain on a material, the efficiency of a machine, and other engineering metrics.

Tips and Tricks

Here are a few tips and tricks to help you solve for w in a proportion:

  • Use a calculator: When solving for w, it's often helpful to use a calculator to simplify the equation and calculate the value of w.
  • Check your units: When solving for w, make sure to check your units to ensure that they are consistent.
  • Use a proportion table: When solving for w, it's often helpful to use a proportion table to visualize the relationship between the two ratios.

Conclusion

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about solving for w in a proportion.

Q: What is a proportion?

A: A proportion is a mathematical statement that two ratios are equal. It is often represented as a fraction or a decimal.

Q: How do I solve for w in a proportion?

A: To solve for w in a proportion, you can use the following steps:

  1. Cross-multiply: Cross-multiplying is a technique used to eliminate the fractions in a proportion. To cross-multiply, you multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa.
  2. Simplify the equation: After cross-multiplying, you simplify the equation by combining like terms.
  3. Solve for w: To solve for w, you divide both sides of the equation by the denominator of the second fraction.

Q: What is cross-multiplication?

A: Cross-multiplication is a technique used to eliminate the fractions in a proportion. To cross-multiply, you multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa.

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

A: To simplify the equation after cross-multiplying, you combine like terms. This means that you add or subtract the same terms on both sides of the equation.

Q: What is the final step in solving for w in a proportion?

A: The final step in solving for w in a proportion is to divide both sides of the equation by the denominator of the second fraction.

Q: Can I use a calculator to solve for w in a proportion?

A: Yes, you can use a calculator to solve for w in a proportion. In fact, it's often helpful to use a calculator to simplify the equation and calculate the value of w.

Q: What are some common mistakes to avoid when solving for w in a proportion?

A: Some common mistakes to avoid when solving for w in a proportion include:

  • Not cross-multiplying: Failing to cross-multiply can lead to incorrect solutions.
  • Not simplifying the equation: Failing to simplify the equation can lead to incorrect solutions.
  • Not checking units: Failing to check units can lead to incorrect solutions.

Q: Can I use a proportion table to solve for w in a proportion?

A: Yes, you can use a proportion table to solve for w in a proportion. A proportion table is a visual representation of the relationship between the two ratios.

Q: What are some real-life applications of solving for w in a proportion?

A: Solving for w in a proportion has many real-life applications, including:

  • Finance: In finance, proportions are used to calculate interest rates, investment returns, and other financial metrics.
  • Science: In science, proportions are used to calculate the concentration of a substance, the rate of a chemical reaction, and other scientific metrics.
  • Engineering: In engineering, proportions are used to calculate the stress and strain on a material, the efficiency of a machine, and other engineering metrics.

Conclusion

In conclusion, solving for w in a proportion is a simple yet powerful technique that has many practical applications in real-life situations. By following the steps of cross-multiplying, simplifying the equation, and solving for w, we can find the value of w and apply it to a variety of problems.