Complex Ratios and Advanced Simplification
This page delves into more advanced topics related to combining and expanding complex ratios.
The page starts with an example of expanding and simplifying ratios involving squares and triangles. It demonstrates how to manipulate ratios with different geometric shapes.
Example: A ratio of squares to triangles 3:4 can be expanded to 15:20:4 when considering rectangles as well
Complex ratios involving square roots are introduced. These ratios require more sophisticated simplification techniques.
Vocabulary: LCM (Least Common Multiple) is often used in simplifying complex ratios
The page provides step-by-step guidance on simplifying complex ratios involving square roots. It shows how to expand, factorize, and simplify these ratios.
Highlight: When working with square roots in ratios, it's often helpful to simplify the square roots first before combining terms
The final example demonstrates how to combine three complex ratios (a:b, b:c, and a:c) into a single simplified ratio. This process involves careful manipulation of square roots and fractions.
These advanced ratio techniques are particularly useful in higher-level mathematics, physics, and engineering applications where precise proportions involving complex numbers are required.
