Converting Mixed Numbers to Equivalent Fractions

Oct 13, 2025 by recoveryshake.com 83 views

Robyn's Running Distance: A Math Problem

In this article, we will explore a simple yet interesting math problem involving fractions. Robyn, a keen runner, has been tracking her progress over the past two weeks. We will use equivalent fractions to determine how many more miles she ran last week compared to this week.

Robyn ran $$5 \frac{3}{4}$$ miles last week and $$4 \frac{1}{4}$$ miles this week. To find out how many more miles she ran last week, we need to subtract the distance she ran this week from the distance she ran last week.

Converting Mixed Numbers to Equivalent Fractions

Before we can perform the subtraction, we need to convert the mixed numbers to equivalent fractions. A mixed number is a combination of a whole number and a fraction. To convert a mixed number to an equivalent fraction, we multiply the whole number by the denominator and add the numerator.

For the mixed number $$5 \frac{3}{4}$$, we can convert it to an equivalent fraction as follows:

5 \frac{3}{4} = \frac{(5 \times 4) + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4}

Similarly, for the mixed number $$4 \frac{1}{4}$$, we can convert it to an equivalent fraction as follows:

4 \frac{1}{4} = \frac{(4 \times 4) + 1}{4} = \frac{16 + 1}{4} = \frac{17}{4}

Subtracting Equivalent Fractions

Now that we have converted the mixed numbers to equivalent fractions, we can perform the subtraction. To subtract equivalent fractions, we subtract the numerators while keeping the denominator the same.

\frac{23}{4} - \frac{17}{4} = \frac{23 - 17}{4} = \frac{6}{4}

Simplifying the Result

The result of the subtraction is $$\frac{6}{4}$$. However, we can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

\frac{6}{4} = \frac{6 ÷ 2}{4 ÷ 2} = \frac{3}{2}

Converting the Result to a Mixed Number

To make the result more understandable, we can convert the improper fraction $$\frac{3}{2}$$ to a mixed number.

\frac{3}{2} = 1 \frac{1}{2}

In conclusion, Robyn ran $$1 \frac{1}{2}$$ miles more last week compared to this week. We used equivalent fractions to solve the problem, which involved converting mixed numbers to equivalent fractions and then subtracting the fractions.

The correct answer is:

1 \frac{1}{2}

This problem is a great example of how fractions can be used to solve real-world problems. By converting mixed numbers to equivalent fractions and then subtracting the fractions, we can determine how many more miles Robyn ran last week compared to this week.

When working with fractions, it's essential to convert mixed numbers to equivalent fractions before performing operations.
To subtract equivalent fractions, subtract the numerators while keeping the denominator the same.
To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor.
To convert an improper fraction to a mixed number, divide the numerator by the denominator and write the remainder as the new numerator.
Robyn's Running Distance: A Math Problem - Q&A

In our previous article, we explored a simple yet interesting math problem involving fractions. Robyn, a keen runner, has been tracking her progress over the past two weeks. We used equivalent fractions to determine how many more miles she ran last week compared to this week. In this article, we will answer some frequently asked questions related to the problem.

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 a mixed number to an equivalent fraction?

A: To convert a mixed number to an equivalent fraction, multiply the whole number by the denominator and add the numerator. Then, write the result as a fraction with the denominator.

Q: What is the greatest common divisor (GCD) and why is it important?

A: The GCD is the largest number that divides two or more numbers without leaving a remainder. It is essential to find the GCD when simplifying fractions, as it helps to reduce the fraction to its simplest form.

Q: How do I subtract equivalent fractions?

A: To subtract equivalent fractions, subtract the numerators while keeping the denominator the same.

Q: Can I simplify a fraction by dividing both the numerator and the denominator by any number?

A: No, you can only simplify a fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

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.

Q: What is the final answer to the problem?

A: The final answer is $$1 \frac{1}{2}$$ miles.

Not converting mixed numbers to equivalent fractions before performing operations.
Not finding the greatest common divisor (GCD) when simplifying fractions.
Subtracting fractions without keeping the denominator the same.
Dividing both the numerator and the denominator by any number instead of the GCD.

Always convert mixed numbers to equivalent fractions before performing operations.
Use the greatest common divisor (GCD) to simplify fractions.
Keep the denominator the same when subtracting equivalent fractions.
Practice, practice, practice! The more you practice, the more comfortable you will become with working with fractions.

In conclusion, we have answered some frequently asked questions related to the problem of determining how many more miles Robyn ran last week compared to this week. We hope that this article has helped to clarify any confusion and provide a better understanding of fractions and how to work with them.

For more information on fractions, visit the Khan Academy website.
For practice problems and exercises, visit the Mathway website.
For a comprehensive guide to fractions, visit the Purplemath website.

Working with fractions can be challenging, but with practice and patience, it becomes easier. Remember to always convert mixed numbers to equivalent fractions, find the greatest common divisor (GCD), and keep the denominator the same when subtracting equivalent fractions. With these tips and tricks, you will become a pro at working with fractions in no time!