Solving Fractional Equations: An SEO-Optimized Guide

Mathematics often involves solving complex equations to uncover hidden truths. One such problem involves fractional equations, which are equations containing fractions. In this guide, we will delve into a specific problem involving fractions and explore the step-by-step process to solve it. This guide is optimized for SEO to ensure it ranks well on search engines like Google, providing a valuable resource for students, teachers, and math enthusiasts.

Problem Statement

Consider the following problem: The numerator of a fraction is 1 less than the denominator. When the numerator is decreased by 2 and the denominator is increased by 3, the fraction becomes 1/4. What is the original fraction?

Step-by-Step Solution

Let's denote the denominator of the fraction as x. According to the problem, the numerator is 1 less than the denominator, so we can express the numerator as x - 1.

The original fraction can be written as:

[ frac{x - 1}{x} ]

Now, according to the problem, if the numerator is decreased by 2 and the denominator is increased by 3, the new fraction becomes 1/4. We can write this as:

[ frac{x - 1 - 2}{x 3} frac{1}{4} ]

This simplifies to:

[ frac{x - 3}{x 3} frac{1}{4} ]

Now, we can cross-multiply to solve for x:

[ 4(x - 3) (x 3) ]

Expanding both sides gives:

[ 4x - 12 x 3 ]

Now we can isolate x by moving x to the left side and the constants to the right side:

[ 4x - x 3 12 ]

This simplifies to:

[ 3x 15 ]

Dividing both sides by 3 yields:

[ x 5 ]

Now that we have the value of x, we can find the numerator:

[ text{Numerator} x - 1 5 - 1 4 ]

Thus, the original fraction is:

[ frac{4}{5} ]

Final Answer

The fraction is 4/5.

Conclusion

This solution process is a clear demonstration of how to solve fractional equations step-by-step. Understanding and mastering this method is crucial for anyone looking to improve their math skills. Whether you are a student, a teacher, or a math enthusiast, practicing such problems will enhance your analytical and problem-solving abilities.

Extra Resources

To further explore fractional equations, you might find the following resources helpful:

Interactive online math tools that allow you to practice solving fractional equations. Mathematical textbooks that cover the topic in depth. Online forums and communities where you can ask questions and engage with other math learners.

By consistently practicing and learning from these resources, you can become more proficient in solving fractional equations.