Equivalent Ratios

Definition

Equivalent ratios are two or more ratios that represent the same relationship between quantities. They have the same proportional value, even though the individual numbers in the ratios may be different.

5 Must Know Facts For Your Next Test

1. Equivalent ratios can be used to solve problems involving proportions and similar figures.
2. To determine if two ratios are equivalent, you can cross-multiply the numerators and denominators to see if the products are equal.
3. Equivalent ratios can be used to scale measurements, such as increasing or decreasing the size of a figure while maintaining its proportions.
4. Finding equivalent ratios is a key step in solving problems that involve proportional reasoning, such as unit rates and scaling.
5. Equivalent ratios are often used in real-world applications, such as recipe conversions, currency exchange, and mixing solutions.

Review Questions

• Explain how equivalent ratios are used to solve proportion problems.
  • Equivalent ratios are the foundation for solving proportion problems. A proportion is an equation that states that two ratios are equivalent. By setting up a proportion and solving for an unknown value, you can find a missing term in the proportion. This allows you to determine the relationship between quantities and solve for unknown values in applications involving similar figures or other proportional relationships.
• Describe how equivalent ratios can be used to scale measurements in similar figures.
  • When two figures are similar, their corresponding sides are proportional. This means that the ratios of their corresponding sides are equivalent. By finding an equivalent ratio, you can scale the measurements of one figure to determine the measurements of a similar figure. For example, if a small-scale model has a ratio of 1:10 compared to the actual object, you can use equivalent ratios to calculate the actual size of the object based on the measurements of the model.
• Analyze how equivalent ratios are applied in real-world situations to solve problems involving proportional reasoning.
  • Equivalent ratios are widely used in real-world applications that involve proportional relationships. For instance, in recipe conversions, you can use equivalent ratios to scale the quantities of ingredients up or down to adjust the serving size. In currency exchange, equivalent ratios are used to determine the appropriate exchange rate between different currencies. Additionally, in mixing solutions, equivalent ratios can be used to maintain the correct proportions of solute to solvent when adjusting the volume of the solution. Understanding how to work with equivalent ratios is a valuable skill for solving a variety of problems that require proportional reasoning.

Related terms

Ratio: A ratio is a comparison of two quantities expressed as a fraction or using a colon.

Proportion: A proportion is an equation that states that two ratios are equivalent.

Similar Figures: Similar figures are shapes that have the same proportions, even if they differ in size.