Solve The Proportion Below.$\[ \frac{55}{x}=\frac{5}{6} \\]x = ?A. 66 B. 50 C. 60 D. 56

What is a Proportion?

A proportion is a statement that two ratios are equal. It is often written in the form of a fraction, where the numerator and denominator of the first fraction are equal to the numerator and denominator of the second fraction, respectively. Proportions are used to solve problems involving ratios and percentages.

The Given Proportion

The given proportion is $\frac{55}{x}=\frac{5}{6}$. We are asked to solve for $x$.

Step 1: Cross-Multiply

To solve the proportion, we need to cross-multiply. This means that we multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa.

$\frac{55}{x}=\frac{5}{6}$

$55 \times 6 = 5 \times x$

$330 = 5x$

Step 2: Divide Both Sides by 5

To solve for $x$, we need to divide both sides of the equation by 5.

$\frac{330}{5} = \frac{5x}{5}$

$66 = x$

Conclusion

Therefore, the value of $x$ is 66.

Why is this the Correct Answer?

To verify that our answer is correct, we can plug it back into the original proportion.

$\frac{55}{x}=\frac{5}{6}$

$\frac{55}{66}=\frac{5}{6}$

Since the two fractions are equal, we can conclude that our answer is correct.

Real-World Applications of Proportions

Proportions have many real-world applications. For example, they can be used to calculate interest rates, convert between units of measurement, and solve problems involving ratios and percentages.

Example 1: Calculating Interest Rates

Suppose we want to calculate the interest rate on a loan. The interest rate is 5% per year, and the loan is for $10,000. We can use a proportion to calculate the interest rate.

$\frac{interest}{principal}=\frac{rate}{100}$

$\frac{interest}{10,000}=\frac{5}{100}$

$interest = \frac{10,000 \times 5}{100}$

$interest = 500$

Example 2: Converting between Units of Measurement

Suppose we want to convert 5 feet to inches. We can use a proportion to make the conversion.

$\frac{feet}{inches}=\frac{1}{12}$

$\frac{5}{inches}=\frac{1}{12}$

$inches = 5 \times 12$

$inches = 60$

Conclusion

In conclusion, proportions are an important concept in mathematics that have many real-world applications. By following the steps outlined in this article, we can solve proportions and apply them to solve problems involving ratios and percentages.

Frequently Asked Questions

Q: What is a proportion?

A: A proportion is a statement that two ratios are equal.

Q: How do I solve a proportion?

A: To solve a proportion, you need to cross-multiply and then divide both sides of the equation by the denominator.

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

A: Proportions have many real-world applications, including calculating interest rates, converting between units of measurement, and solving problems involving ratios and percentages.

Q: Why is it important to understand proportions?

A: Understanding proportions is important because it allows us to solve problems involving ratios and percentages, which are used in many real-world applications.

References

• [1] "Algebra and Trigonometry" by Michael Sullivan
• [2] "Mathematics for the Nonmathematician" by Morris Kline
• [3] "Proportions and Ratios" by Math Open Reference

Additional Resources

• Khan Academy: Proportions
• Mathway: Proportions
• Wolfram Alpha: Proportions
  Proportions Q&A: Frequently Asked Questions and Answers ===========================================================

Q: What is a proportion?

A: A proportion is a statement that two ratios are equal. It is often written in the form of a fraction, where the numerator and denominator of the first fraction are equal to the numerator and denominator of the second fraction, respectively.

Q: How do I solve a proportion?

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

1. Cross-multiply: Multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa.
2. Divide both sides of the equation by the denominator: This will give you the value of the variable.

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

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

• Not cross-multiplying correctly
• Not dividing both sides of the equation by the denominator
• Not checking the units of measurement
• Not using the correct order of operations

Q: How do I check if my answer is correct?

A: To check if your answer is correct, you can plug it back into the original proportion. If the two fractions are equal, then your answer is correct.

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

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

• Calculating interest rates
• Converting between units of measurement
• Solving problems involving ratios and percentages
• Designing buildings and bridges
• Creating art and music

Q: Why is it important to understand proportions?

A: Understanding proportions is important because it allows us to solve problems involving ratios and percentages, which are used in many real-world applications. It also helps us to understand the relationships between different quantities and to make informed decisions.

Q: Can I use proportions to solve problems involving fractions?

A: Yes, you can use proportions to solve problems involving fractions. For example, if you have a fraction and you want to find the equivalent fraction with a different denominator, you can use a proportion to make the conversion.

Q: Can I use proportions to solve problems involving decimals?

A: Yes, you can use proportions to solve problems involving decimals. For example, if you have a decimal and you want to find the equivalent decimal with a different number of decimal places, you can use a proportion to make the conversion.

Q: Can I use proportions to solve problems involving percentages?

A: Yes, you can use proportions to solve problems involving percentages. For example, if you have a percentage and you want to find the equivalent percentage with a different base, you can use a proportion to make the conversion.

Q: Can I use proportions to solve problems involving geometry?

A: Yes, you can use proportions to solve problems involving geometry. For example, if you have a triangle and you want to find the length of a side, you can use a proportion to make the calculation.

Q: Can I use proportions to solve problems involving algebra?

A: Yes, you can use proportions to solve problems involving algebra. For example, if you have an equation and you want to solve for a variable, you can use a proportion to make the calculation.

Conclusion

In conclusion, proportions are an important concept in mathematics that have many real-world applications. By understanding proportions, you can solve problems involving ratios and percentages, and make informed decisions in a variety of fields.

Frequently Asked Questions

Q: What is a proportion?

A: A proportion is a statement that two ratios are equal.

Q: How do I solve a proportion?

A: To solve a proportion, you need to cross-multiply and then divide both sides of the equation by the denominator.

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

A: Proportions have many real-world applications, including calculating interest rates, converting between units of measurement, and solving problems involving ratios and percentages.

Q: Why is it important to understand proportions?

A: Understanding proportions is important because it allows us to solve problems involving ratios and percentages, which are used in many real-world applications.

References

• [1] "Algebra and Trigonometry" by Michael Sullivan
• [2] "Mathematics for the Nonmathematician" by Morris Kline
• [3] "Proportions and Ratios" by Math Open Reference

Additional Resources

• Khan Academy: Proportions
• Mathway: Proportions
• Wolfram Alpha: Proportions