Solve.${ 3 \frac{1}{3} - 1 \frac{1}{5} = , }$(Use Scrap Paper If Necessary.)

Mar 13, 2025 by ADMIN 78 views

Solve: 3 1/3 - 1 1/5

Introduction

When dealing with fractions, it's essential to understand the concept of equivalent ratios and how to perform operations with them. In this article, we will explore the solution to the equation 3 1/3 - 1 1/5 using scrap paper and mathematical techniques.

Understanding the Problem

The given equation involves two mixed numbers: 3 1/3 and 1 1/5. To solve this equation, we need to find a common denominator for the two fractions and then perform the subtraction operation.

Finding a Common Denominator

To find a common denominator, we need to identify the least common multiple (LCM) of the denominators 3 and 5. The LCM of 3 and 5 is 15.

Converting Mixed Numbers to Improper Fractions

To convert the mixed numbers to improper fractions, we need to multiply the whole number part by the denominator and then add the numerator.

For 3 1/3, we multiply 3 by 3 to get 9, and then add 1 to get 10. So, 3 1/3 = 10/3.
For 1 1/5, we multiply 1 by 5 to get 5, and then add 1 to get 6. So, 1 1/5 = 6/5.

Finding a Common Denominator for the Improper Fractions

Now that we have the improper fractions, we need to find a common denominator for 10/3 and 6/5. The LCM of 3 and 5 is 15, so we can multiply the numerator and denominator of each fraction by 5 and 3, respectively, to get a common denominator.

For 10/3, we multiply the numerator and denominator by 5 to get 50/15.
For 6/5, we multiply the numerator and denominator by 3 to get 18/15.

Subtracting the Improper Fractions

Now that we have the improper fractions with a common denominator, we can subtract them.

50/15 - 18/15 = (50 - 18)/15 = 32/15

Converting the Improper Fraction to a Mixed Number

To convert the improper fraction to a mixed number, we need to divide the numerator by the denominator.

32 ÷ 15 = 2 with a remainder of 4

So, 32/15 = 2 4/15.

Conclusion

In conclusion, the solution to the equation 3 1/3 - 1 1/5 is 2 4/15. This solution was obtained by finding a common denominator for the two mixed numbers, converting them to improper fractions, finding a common denominator for the improper fractions, subtracting them, and then converting the result back to a mixed number.

Tips and Tricks

When dealing with fractions, it's essential to find a common denominator to perform operations with them.
To find a common denominator, identify the least common multiple (LCM) of the denominators.
To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and then add the numerator.
To subtract improper fractions, find a common denominator and then subtract the numerators.

Real-World Applications

Understanding how to solve equations involving fractions is essential in various real-world applications, such as:

Cooking: When a recipe calls for a specific amount of an ingredient, it's essential to understand how to perform operations with fractions to ensure the correct amount is used.
Building: When building a structure, it's essential to understand how to perform operations with fractions to ensure the correct measurements are used.
Finance: When dealing with financial transactions, it's essential to understand how to perform operations with fractions to ensure the correct amounts are used.

Common Mistakes to Avoid

Not finding a common denominator when performing operations with fractions.
Not converting mixed numbers to improper fractions before performing operations.
Not subtracting the numerators when subtracting improper fractions.

Final Thoughts

Solving equations involving fractions requires a strong understanding of mathematical concepts and techniques. By following the steps outlined in this article, you can confidently solve equations involving fractions and apply your knowledge to real-world applications.

Introduction

In our previous article, we explored the solution to the equation 3 1/3 - 1 1/5 using scrap paper and mathematical techniques. In this article, we will answer some frequently asked questions related to the solution of this equation.

Q&A

Q: What is the least common multiple (LCM) of 3 and 5?

A: The LCM of 3 and 5 is 15.

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 then add the numerator.

Q: What is the common denominator for 10/3 and 6/5?

A: The common denominator for 10/3 and 6/5 is 15.

Q: How do I subtract improper fractions?

A: To subtract improper fractions, find a common denominator and then subtract the numerators.

Q: What is the solution to the equation 3 1/3 - 1 1/5?

A: The solution to the equation 3 1/3 - 1 1/5 is 2 4/15.

Q: Why is it essential to find a common denominator when performing operations with fractions?

A: It's essential to find a common denominator when performing operations with fractions because it allows us to perform the operation accurately and ensures that the result is a valid fraction.

Q: What are some real-world applications of understanding how to solve equations involving fractions?

A: Understanding how to solve equations involving fractions is essential in various real-world applications, such as cooking, building, and finance.

Q: What are some common mistakes to avoid when solving equations involving fractions?

A: Some common mistakes to avoid when solving equations involving fractions include not finding a common denominator, not converting mixed numbers to improper fractions, and not subtracting the numerators when subtracting improper fractions.

Q: How can I practice solving equations involving fractions?

A: You can practice solving equations involving fractions by working through examples and exercises, such as the one we solved in our previous article.