Question 3What Percent Of 20 Is $2 \frac{3}{5}$?

Mar 8, 2025 by ADMIN 51 views

$What Percent of 20 is $2 \frac{3}{5}$?$

Introduction

When dealing with mixed numbers and percentages, it's essential to understand how to convert between these two concepts. In this article, we will explore how to find the percentage of a given number, specifically what percent of 20 is $2 \frac{3}{5}$.

Understanding Mixed Numbers

Before we dive into the problem, let's take a moment to understand what a mixed number is. A mixed number is a combination of a whole number and a fraction. In the case of $2 \frac{3}{5}$, the whole number part is 2, and the fraction part is $\frac{3}{5}$.

Converting Mixed Numbers to Improper Fractions

To make calculations easier, we can convert the mixed number to an improper fraction. To do this, we multiply the whole number part by the denominator and then add the numerator. In this case, we have:

2 \frac{3}{5} = \frac{(2 \times 5) + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5}

Finding the Percentage

Now that we have the mixed number in improper fraction form, we can find the percentage of 20 that it represents. To do this, we need to divide the improper fraction by 20 and multiply by 100.

\frac{\frac{13}{5}}{20} \times 100 = \frac{13}{5} \times \frac{1}{20} \times 100 = \frac{13}{5} \times 5 = 13

Conclusion

In conclusion, to find the percentage of 20 that $2 \frac{3}{5}$ represents, we first converted the mixed number to an improper fraction. Then, we divided the improper fraction by 20 and multiplied by 100. The result is 13%.

Real-World Applications

Understanding how to find the percentage of a given number is essential in many real-world applications. For example, in business, you may need to calculate the percentage of a product that is sold or the percentage of a budget that is allocated to a particular department. In finance, you may need to calculate the percentage return on investment or the percentage increase in stock prices.

Tips and Tricks

Here are a few tips and tricks to keep in mind when working with mixed numbers and percentages:

Always convert mixed numbers to improper fractions before performing calculations.
When dividing by a fraction, multiply by its reciprocal instead.
When multiplying by a fraction, multiply the numerators and denominators separately.
When adding or subtracting fractions, find a common denominator and add or subtract the numerators.

Common Mistakes to Avoid

Here are a few common mistakes to avoid when working with mixed numbers and percentages:

Not converting mixed numbers to improper fractions before performing calculations.
Not multiplying by the reciprocal when dividing by a fraction.
Not finding a common denominator when adding or subtracting fractions.
Not rounding to the nearest whole number when necessary.

Final Thoughts

In conclusion, finding the percentage of a given number is a simple process that requires converting mixed numbers to improper fractions and performing calculations. By following the tips and tricks outlined in this article, you can avoid common mistakes and ensure accurate results. Whether you're working in business, finance, or another field, understanding how to find the percentage of a given number is essential for making informed decisions and achieving success.

Additional Resources

For more information on mixed numbers and percentages, check out the following resources:

Khan Academy: Mixed Numbers and Fractions
Mathway: Mixed Numbers and Percentages
Wolfram Alpha: Mixed Numbers and Percentages

Frequently Asked Questions

Here are a few frequently asked questions about mixed numbers and percentages:

Q: What is a mixed number? A: A mixed number is a combination of a whole number and a fraction.
Q: How do I convert a mixed number to an improper fraction? A: Multiply the whole number part by the denominator and add the numerator.
Q: How do I find the percentage of a given number? A: Divide the improper fraction by the given number and multiply by 100.

Conclusion

Introduction

In our previous article, we explored how to find the percentage of a given number, specifically what percent of 20 is $2 \frac{3}{5}$. In this article, we will continue to delve deeper into the world of mixed numbers and percentages, answering some of the most frequently asked questions about this topic.

Q&A Guide

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. For example, $2 \frac{3}{5}$ is a mixed number where 2 is the whole number part and $\frac{3}{5}$ is the fraction part.

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

A: To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and add the numerator. For example, to convert $2 \frac{3}{5}$ to an improper fraction, we would multiply 2 by 5 and add 3, resulting in $\frac{13}{5}$.

Q: How do I find the percentage of a given number?

A: To find the percentage of a given number, divide the improper fraction by the given number and multiply by 100. For example, to find the percentage of 20 that $2 \frac{3}{5}$ represents, we would divide $\frac{13}{5}$ by 20 and multiply by 100, resulting in 13%.

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

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a single fraction that is greater than 1. For example, $2 \frac{3}{5}$ is a mixed number, while $\frac{13}{5}$ is an improper fraction.

Q: How do I add or subtract mixed numbers?

A: To add or subtract mixed numbers, find a common denominator and add or subtract the numerators. For example, to add $2 \frac{3}{5}$ and $1 \frac{2}{5}$, we would find a common denominator of 5 and add the numerators, resulting in $3 \frac{5}{5}$ or simply 4.

Q: How do I multiply mixed numbers?

A: To multiply mixed numbers, multiply the whole number parts and multiply the fractions. For example, to multiply $2 \frac{3}{5}$ and $3 \frac{2}{5}$, we would multiply the whole number parts (2 and 3) and multiply the fractions ($\frac{3}{5}$ and $\frac{2}{5}$), resulting in $6 \frac{6}{25}$.

Q: How do I divide mixed numbers?

A: To divide mixed numbers, convert the mixed numbers to improper fractions and divide. For example, to divide $2 \frac{3}{5}$ by $3 \frac{2}{5}$, we would convert the mixed numbers to improper fractions ($\frac{13}{5}$ and $\frac{17}{5}$) and divide, resulting in $\frac{13}{17}$.