Simplifying Complex Fractions: A Step-by-Step Guide

When dealing with complex fractions, it's essential to break down the problem into smaller, manageable parts. In this article, we will guide you through the process of simplifying the fraction 3/4 - 1 1/4 - 3/5. This step-by-step approach will help you understand the underlying mathematical concepts and provide you with a clear solution.

Introduction to Complex Fractions

Complex fractions are fractions that contain fractions within them. They might appear intimidating at first glance, but by breaking them down, they can be practically solved using basic arithmetic operations and the concept of the least common denominator (LCD).

Solving the Problem

Method 1: Traditional Fraction Subtraction

1. Convert the mixed number 1 1/4 to an improper fraction. 2. Find a common denominator for the fractions to be added and subtracted. 3. Perform the subtraction step-by-step.

Let's tackle the problem step by step:

Convert the mixed number to an improper fraction: 1 1/4 (4/4 * 1) 1/4 4/4 1/4 5/4 Set up the subtraction problem: 3/4 - 5/4 - 3/5 Find the least common denominator (LCD) for 4 and 5, which is 20. Convert each fraction to an equivalent fraction with the LCD as the denominator: 3/4 15/20 5/4 25/20 3/5 12/20 Perform the subtraction: 15/20 - 25/20 - 12/20 -22/20 Reduce the fraction if possible: -22/20 -11/10

The answer is -11/10 or -1 1/10.

Method 2: Simplifying Step-by-Step

1. Begin by simplifying each fraction to its lowest form. 2. Subtract step-by-step using the proper method.

Here's a detailed breakdown:

Simplify each fraction: 3/4 remains as 3/4 1 1/4 5/4 3/5 remains as 3/5 Perform the subtraction in two steps: 3/4 - 5/4 -2/4 -2/4 - 3/5 -1/2 - 3/5 Convert -1/2 to an equivalent fraction with a denominator of 10: -1/2 -5/10 Convert -3/5 to an equivalent fraction with a denominator of 10: -3/5 -6/10 Subtract the fractions: -5/10 - 6/10 -11/10 or -1 1/10

The final answer is still -11/10 or -1 1/10.

Conclusion

By understanding the steps involved in simplifying complex fractions, you can solve even the most challenging problems with ease. The key is to find the LCD and convert all fractions to equivalent forms before performing the subtraction.

Resources

To help you further, here are some additional resources:

Fractions Subtraction - Math is Fun Khan Academy: Subtract Fractions

Keywords

Simplifying fractions, complex fractions, least common denominator (LCD)