Solving Fraction Problems: A Step-by-Step Guide

Mathematics is a playground for logical thinking and problem-solving. One common type of problem involves manipulating fractions. In this article, we will delve into a specific fraction problem and discuss how to solve it step-by-step.

Understanding the Problem Statement

The problem statement is as follows: If the numerator of a fraction is decreased by 15 and the denominator remains the same, the value of the fraction is 9/5. We need to find the original fraction.

Step-by-Step Solution

To solve this, we need to establish a relationship between the original fraction and the modified fraction. Let's denote the original numerator as x and the original denominator as y.

Given:

The modified fraction is (frac{x - 15}{y} frac{9}{5}) The denominator remains the same, so (y 5)

Substituting (y 5) into the equation:

[frac{x - 15}{5} frac{9}{5}]

Multiplying both sides by 5:

[frac{x - 15}{5} times 5 frac{9}{5} times 5]

Simplifying the right-hand side:

[x - 15 9]

Add 15 to both sides:

[x 24]

So, the original fraction is (frac{x}{y} frac{24}{5}).

The original fraction was obtained by solving the given conditions. The key steps were:

Identifying the modified fraction equation. Equating the denominators. Solving the resulting equation to find the original numerator. Substituting back to find the original fraction.

Practical Applications

Fractions are widely used in real-world scenarios, including:

Cooking and baking where recipes often need to be adjusted for different portion sizes. Engineering and construction where measurements and proportions are crucial. Finance where fractions are used in interest calculations and ratio analysis.

Mastering the manipulation of fractions is essential for understanding these applications effectively.

Conclusion

In conclusion, solving the fraction problem where a numerator is decreased and the denominator remains constant showcases the importance of algebraic manipulation in problem-solving. By following a step-by-step approach, we can systematically and accurately determine the original fraction.

For those looking to improve their skills in fraction problem-solving or who want to explore similar mathematical concepts, practicing with a variety of problems and engaging in online tutorials and resources can significantly enhance their understanding!