Quick Reference Table for Working with Ratios

Here is a helpful reference table focused specifically on the topic of ratios. This table helps students understand and apply ratios effectively.

Action	Steps/Methods	Example
Finding Equivalent Ratios	Multiply or divide both terms by the same number.	For the ratio 3:4, multiplying by 2 gives an equivalent ratio of 6:8.
Simplifying Ratios	Divide both terms by their GCD (greatest common divisor).	For the ratio 14:21, GCD is 7; thus, it simplifies to 2:3.
Writing Ratios as Fractions	Express ratios as fractions for easier calculations.	The ratio 5:10 can be written as $\frac{5}{10}$​ which simplifies to $\frac{1}{2}$​.
Using Ratios in Proportions	Set up proportions to solve for unknowns using cross-multiplication.	If $\frac{x}{6}$​ = $\frac{4}{12}$​, cross-multiply to find 𝑥 =$\frac{4 \times 6}{12}$​ = 2
Converting Percentages to Ratios	Convert percentages to fractions and then simplify if needed.	A percentage of 25% can be expressed as $\frac{25}{100}$​ which simplifies to $\frac{1}{4}$​ or the ratio of 1:4.
Real-Life Applications of Ratios	Use ratios in cooking (ingredient proportions), finance (interest rates), and construction (scale models).	A recipe calls for a ratio of flour to sugar as 3:1; for every 3 cups of flour, use 1 cup of sugar.

This table serves as a quick reference for students studying ratios, providing essential concepts and practical methods for solving aptitude exams and application in problem-solving scenarios. To deepen your understanding, delve into the topic of ratios in detail by exploring Ratio and Proportion.