Rules of Fraction Subtraction

Oct 13, 2025 by talynt.org 112 views

Introduction

When dealing with fractions, one of the most common operations is subtraction. However, when the fractions have the same denominator, it becomes a relatively simple process. In this case, we are given two fractions with the same denominator, and we need to subtract them. The given expression is $\frac{5x-2}{x-1} - \frac{7x-4}{x-1}$ . Our goal is to simplify this expression by subtracting the two fractions.

Understanding the Problem

Before we proceed with the subtraction, let's understand the problem at hand. We have two fractions with the same denominator, which is $x-1$ . The numerators of the fractions are $5x-2$ and $7x-4$ , respectively. To subtract these fractions, we need to follow the rules of fraction subtraction.

Rules of Fraction Subtraction

When subtracting fractions with the same denominator, we simply subtract the numerators while keeping the denominator the same. In other words, we can write the subtraction as:

\frac{5x-2}{x-1} - \frac{7x-4}{x-1} = \frac{(5x-2) - (7x-4)}{x-1}

Simplifying the Expression

Now that we have the expression in the form of a single fraction, we can simplify it further. To do this, we need to combine the like terms in the numerator.

\frac{(5x-2) - (7x-4)}{x-1} = \frac{5x-2-7x+4}{x-1}

Combining Like Terms

When we combine the like terms in the numerator, we get:

\frac{5x-2-7x+4}{x-1} = \frac{-2x+2}{x-1}

Final Answer

The final answer to the given expression is $\frac{-2x+2}{x-1}$ . This is the simplified form of the expression after subtracting the two fractions.

Conclusion

In this article, we learned how to subtract fractions with the same denominator. We started with the given expression $\frac{5x-2}{x-1} - \frac{7x-4}{x-1}$ and simplified it by following the rules of fraction subtraction. We combined the like terms in the numerator and arrived at the final answer of $\frac{-2x+2}{x-1}$ . This process demonstrates the importance of understanding the rules of fraction subtraction and how to apply them to simplify complex expressions.

Additional Tips and Tricks

When dealing with fractions, it's essential to remember the following tips and tricks:

When subtracting fractions with the same denominator, simply subtract the numerators while keeping the denominator the same.
Combine like terms in the numerator to simplify the expression.
Be careful when canceling out common factors in the numerator and denominator.

By following these tips and tricks, you can simplify complex expressions and arrive at the correct answer.

Real-World Applications

The concept of subtracting fractions with the same denominator has numerous real-world applications. For example, in finance, you may need to subtract two fractions to calculate the interest rate on a loan. In science, you may need to subtract two fractions to calculate the concentration of a solution. By understanding the rules of fraction subtraction, you can apply this concept to a wide range of real-world problems.

Common Mistakes to Avoid

When subtracting fractions with the same denominator, there are several common mistakes to avoid:

Don't forget to subtract the numerators while keeping the denominator the same.
Don't forget to combine like terms in the numerator.
Be careful when canceling out common factors in the numerator and denominator.

By avoiding these common mistakes, you can ensure that your calculations are accurate and your answers are correct.

Final Thoughts

In conclusion, subtracting fractions with the same denominator is a fundamental concept in mathematics. By understanding the rules of fraction subtraction and applying them to simplify complex expressions, you can arrive at the correct answer. Remember to combine like terms in the numerator and be careful when canceling out common factors in the numerator and denominator. With practice and patience, you can master the art of subtracting fractions with the same denominator.

Introduction

In our previous article, we discussed how to subtract fractions with the same denominator. However, we understand that there may be some questions and doubts that readers may have. In this article, we will address some of the frequently asked questions (FAQs) on subtracting fractions with the same denominator.

Q: What is the rule for subtracting fractions with the same denominator?

A: The rule for subtracting fractions with the same denominator is to simply subtract the numerators while keeping the denominator the same. In other words, we can write the subtraction as:

\frac{a}{b} - \frac{c}{b} = \frac{a-c}{b}

Q: How do I combine like terms in the numerator?

A: To combine like terms in the numerator, we need to identify the terms that have the same variable and coefficient. For example, in the expression $\frac{5x-2-7x+4}{x-1}$ , we can combine the like terms as follows:

\frac{5x-2-7x+4}{x-1} = \frac{-2x+2}{x-1}

Q: What is the difference between subtracting fractions with the same denominator and subtracting fractions with different denominators?

A: When subtracting fractions with the same denominator, we simply subtract the numerators while keeping the denominator the same. However, when subtracting fractions with different denominators, we need to find the least common multiple (LCM) of the denominators and then subtract the fractions.

Q: Can I cancel out common factors in the numerator and denominator?

A: Yes, you can cancel out common factors in the numerator and denominator. However, be careful not to cancel out any factors that are not common to both the numerator and denominator.

Q: What is the final answer to the expression $\frac{5x-2}{x-1} - \frac{7x-4}{x-1}$ ?

A: The final answer to the expression $\frac{5x-2}{x-1} - \frac{7x-4}{x-1}$ is $\frac{-2x+2}{x-1}$ .

Q: How do I apply the concept of subtracting fractions with the same denominator to real-world problems?

A: The concept of subtracting fractions with the same denominator has numerous real-world applications. For example, in finance, you may need to subtract two fractions to calculate the interest rate on a loan. In science, you may need to subtract two fractions to calculate the concentration of a solution. By understanding the rules of fraction subtraction, you can apply this concept to a wide range of real-world problems.

Q: What are some common mistakes to avoid when subtracting fractions with the same denominator?

A: Some common mistakes to avoid when subtracting fractions with the same denominator include:

Forgetting to subtract the numerators while keeping the denominator the same.
Forgetting to combine like terms in the numerator.
Canceling out common factors in the numerator and denominator that are not common to both the numerator and denominator.

Q: How can I practice subtracting fractions with the same denominator?

A: You can practice subtracting fractions with the same denominator by working through a series of examples and exercises. You can also try applying the concept to real-world problems to see how it is used in different contexts.

Conclusion

In this article, we have addressed some of the frequently asked questions (FAQs) on subtracting fractions with the same denominator. We hope that this article has provided you with a better understanding of the concept and how to apply it to real-world problems. Remember to practice subtracting fractions with the same denominator to build your confidence and skills.

Additional Resources

If you are looking for additional resources to help you learn about subtracting fractions with the same denominator, we recommend the following:

Khan Academy: Subtracting Fractions with the Same Denominator
Mathway: Subtracting Fractions with the Same Denominator
IXL: Subtracting Fractions with the Same Denominator

We hope that these resources are helpful in your learning journey.