Converting Mixed Number to Improper Fraction

Oct 13, 2025 by windailys.com 68 views

Understanding the Problem

To find the percentage of 600 that is represented by $$3 \frac{3}{4}$$, we need to first convert the mixed number into an improper fraction. This will make it easier to perform the necessary calculations.

Converting Mixed Number to Improper Fraction

A mixed number is a combination of a whole number and a fraction. In this case, $$3 \frac{3}{4}$$ can be converted to an improper fraction by multiplying the whole number by the denominator and then adding the numerator.

3 \frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}

Finding the Percentage

Now that we have the improper fraction, we can find the percentage by dividing the numerator by the denominator and multiplying by 100.

\frac{15}{4} \times 100 = \frac{1500}{4} = 375

However, we need to express the answer as a fraction in simplest form. To do this, we can divide both the numerator and the denominator by their greatest common divisor (GCD).

Simplifying the Fraction

The GCD of 1500 and 4 is 4. Dividing both the numerator and the denominator by 4, we get:

\frac{1500}{4} = \frac{1500 ÷ 4}{4 ÷ 4} = \frac{375}{1}

However, we can simplify this fraction further by dividing both the numerator and the denominator by their GCD, which is 1.

Final Answer

The final answer is that $$\frac{15}{4}$$ is equal to 375%.

Conclusion

In this problem, we converted a mixed number to an improper fraction and then found the percentage by dividing the numerator by the denominator and multiplying by 100. We also simplified the fraction to its simplest form by dividing both the numerator and the denominator by their GCD.

Step-by-Step Solution

Convert the mixed number $$3 \frac{3}{4}$$ to an improper fraction.
Find the percentage by dividing the numerator by the denominator and multiplying by 100.
Simplify the fraction to its simplest form by dividing both the numerator and the denominator by their GCD.

Frequently Asked Questions

What is the percentage of 600 that is represented by $$3 \frac{3}{4}$$?
How do I convert a mixed number to an improper fraction?
How do I simplify a fraction to its simplest form?

Answer Key

The percentage of 600 that is represented by $$3 \frac{3}{4}$$ is 375%.
To convert a mixed number to an improper fraction, multiply the whole number by the denominator and then add the numerator.
To simplify a fraction to its simplest form, divide both the numerator and the denominator by their GCD.

Additional Resources

For more information on converting mixed numbers to improper fractions, visit [insert link].
For more information on simplifying fractions, visit [insert link].

Final Thoughts

In this problem, we used basic arithmetic operations to find the percentage of 600 that is represented by $$3 \frac{3}{4}$$. We also used the concept of greatest common divisor to simplify the fraction to its simplest form. This problem demonstrates the importance of understanding basic arithmetic operations and the concept of greatest common divisor in solving mathematical problems.

Frequently Asked Questions

Q: What is the percentage of 600 that is represented by $$3 \frac{3}{4}$$?

A: The percentage of 600 that is represented by $$3 \frac{3}{4}$$ is 375%.

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 by the denominator and then add the numerator. For example, to convert $$3 \frac{3}{4}$$ to an improper fraction, multiply 3 by 4 and add 3 to get $$\frac{12 + 3}{4} = \frac{15}{4}$$.

Q: How do I simplify a fraction to its simplest form?

A: To simplify a fraction to its simplest form, divide both the numerator and the denominator by their greatest common divisor (GCD). For example, to simplify $$\frac{15}{4}$$, divide both the numerator and the denominator by 1 to get $$\frac{15}{4}$$.

Q: What is the greatest common divisor (GCD) of 15 and 4?

A: The greatest common divisor (GCD) of 15 and 4 is 1.

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

A: To find the GCD of two numbers, list the factors of each number and find the greatest factor they have in common. For example, the factors of 15 are 1, 3, 5, and 15, and the factors of 4 are 1, 2, and 4. The greatest factor they have in common is 1.

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 fraction where the numerator is greater than or equal to the denominator.

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

A: To convert an improper fraction to a mixed number, divide the numerator by the denominator and write the remainder as the new numerator. For example, to convert $$\frac{15}{4}$$ to a mixed number, divide 15 by 4 to get 3 with a remainder of 3, so the mixed number is $$3 \frac{3}{4}$$.

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

A: A fraction and a percentage are related in that a percentage is a fraction with a denominator of 100. For example, 25% is equal to $$\frac{25}{100}$$.

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

A: To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100. For example, to convert $$\frac{15}{4}$$ to a percentage, divide 15 by 4 to get 3.75, and then multiply by 100 to get 375%.

Additional Resources

For more information on converting mixed numbers to improper fractions, visit [insert link].
For more information on simplifying fractions, visit [insert link].
For more information on greatest common divisor, visit [insert link].
For more information on converting fractions to percentages, visit [insert link].

Final Thoughts

In this Q&A article, we have covered various questions related to the problem of finding the percentage of 600 that is represented by $$3 \frac{3}{4}$$. We have discussed the concepts of mixed numbers, improper fractions, greatest common divisor, and percentages, and provided examples and explanations to help clarify these concepts. We hope that this article has been helpful in answering your questions and providing a better understanding of these mathematical concepts.