Convert $54 \frac{2}{7} \%$ To A Fraction In Lowest Terms. Provide Your Answer Below:

Introduction

Percentages are a common way to express a value as a fraction of 100. However, in many mathematical operations, it's more convenient to work with fractions. In this article, we'll show you how to convert a percentage to a fraction in lowest terms.

Understanding Percentages

A percentage is a number that represents a value as a fraction of 100. It's denoted by the symbol "%". For example, 25% means 25 out of 100. To convert a percentage to a fraction, we need to divide the percentage value by 100.

Converting $54 \frac{2}{7} \%$ to a Fraction

To convert $54 \frac{2}{7} \%$ to a fraction, we need to follow these steps:

1. Convert the mixed number to an improper fraction: The mixed number $54 \frac{2}{7}$ can be converted to an improper fraction by multiplying the whole number part by the denominator and then adding the numerator.

   $54 \frac{2}{7} = \frac{(54 \times 7) + 2}{7} = \frac{378 + 2}{7} = \frac{380}{7}$

2. Divide the numerator by the denominator: To convert the improper fraction to a decimal, we need to divide the numerator by the denominator.

   $\frac{380}{7} = 54.2857142857$

3. Convert the decimal to a percentage: To convert the decimal to a percentage, we need to multiply it by 100.

   $54.2857142857 \times 100 = 5428.57142857 \%$

4. Simplify the fraction: To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.

   The GCD of 380 and 7 is 1. Therefore, the fraction $\frac{380}{7}$ is already in its simplest form.

Conclusion

Converting a percentage to a fraction in lowest terms involves several steps, including converting the mixed number to an improper fraction, dividing the numerator by the denominator, converting the decimal to a percentage, and simplifying the fraction. By following these steps, we can convert $54 \frac{2}{7} \%$ to a fraction in lowest terms.

Example Use Cases

Converting percentages to fractions is useful in various mathematical operations, such as:

• Finance: When working with interest rates, it's often more convenient to work with fractions rather than percentages.
• Science: In scientific calculations, fractions are often more accurate and easier to work with than percentages.
• Engineering: In engineering applications, fractions are often used to represent proportions and ratios.

Tips and Tricks

• Use a calculator: When working with large numbers, it's often easier to use a calculator to perform calculations.
• Simplify fractions: To simplify fractions, find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.
• Use online tools: There are many online tools available that can help you convert percentages to fractions, such as online calculators and conversion tools.

Conclusion

Introduction

Converting percentages to fractions is a common task in mathematics, but it can be confusing, especially for beginners. In this article, we'll answer some frequently asked questions about converting percentages to fractions.

Q: What is the difference between a percentage and a fraction?

A: A percentage is a number that represents a value as a fraction of 100, while a fraction is a way of expressing a part of a whole as a ratio of two numbers.

Q: How do I convert a percentage to a fraction?

A: To convert a percentage to a fraction, you need to divide the percentage value by 100 and then simplify the resulting fraction.

Q: What is the formula for converting a percentage to a fraction?

A: The formula for converting a percentage to a fraction is:

$\frac{percentage}{100} = \frac{numerator}{denominator}$

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator of a fraction without leaving a remainder.

Q: How do I find the GCD of two numbers?

A: There are several ways to find the GCD of two numbers, including:

• Listing the factors: List the factors of each number and find the greatest common factor.
• Using the Euclidean algorithm: Use the Euclidean algorithm to find the GCD of two numbers.
• Using a calculator: Use a calculator to find the GCD of two numbers.

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a way of expressing a fraction as a combination of a whole number and a fraction, while an improper fraction is a way of expressing a fraction as a ratio of two numbers.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you need to multiply the whole number part by the denominator and then add the numerator.

Q: What are some common mistakes to avoid when converting percentages to fractions?

A: Some common mistakes to avoid when converting percentages to fractions include:

• Forgetting to divide by 100: Make sure to divide the percentage value by 100 when converting it to a fraction.
• Not simplifying the fraction: Make sure to simplify the fraction by finding the GCD of the numerator and the denominator.
• Using the wrong formula: Make sure to use the correct formula for converting a percentage to a fraction.

Conclusion

Converting percentages to fractions is a useful skill to have in mathematics. By following the steps outlined in this article and avoiding common mistakes, you can confidently convert percentages to fractions. Remember to use a calculator when working with large numbers, simplify fractions by finding the greatest common divisor, and use online tools to help you with conversions.

Example Use Cases

Converting percentages to fractions is useful in various mathematical operations, such as:

• Finance: When working with interest rates, it's often more convenient to work with fractions rather than percentages.
• Science: In scientific calculations, fractions are often more accurate and easier to work with than percentages.
• Engineering: In engineering applications, fractions are often used to represent proportions and ratios.

Tips and Tricks

• Use a calculator: When working with large numbers, it's often easier to use a calculator to perform calculations.
• Simplify fractions: To simplify fractions, find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.
• Use online tools: There are many online tools available that can help you convert percentages to fractions, such as online calculators and conversion tools.