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.