PROPORTIONAL 7 REASONING-1 | Class 8 Mathematics Notes

Equivalent Ratios

Equivalent ratios are ratios that express the same relationship between quantities, even though the numbers themselves may be different. For example, the ratio 2:3 is equivalent to 4:6 because both represent the same proportional relationship.

This section explains how to generate equivalent ratios by multiplying or dividing both terms of a ratio by the same non-zero number. This process is similar to simplifying or expanding fractions. The concept is crucial because it allows us to compare ratios easily and recognize when two ratios are proportional.

The chapter provides step-by-step methods for finding equivalent ratios. For instance, starting with the ratio 3:5, multiplying both terms by 2 yields 6:10, which is equivalent to the original ratio. Similarly, dividing both terms of 8:12 by 4 gives 2:3, an equivalent ratio in simplest form.

Students learn that equivalent ratios maintain the same relative size or proportion between quantities. This understanding is essential for solving problems involving scaling, resizing, and converting units.

The section also includes examples where students identify equivalent ratios and use them to solve problems, reinforcing the concept through practice.

📊 Diagram: Diagrams illustrate the process of generating equivalent ratios by scaling both terms of a ratio, showing arrows from the original ratio to its multiples and simplified forms.

🧪 Activity: Activity 7.2: Students are given various ratios and asked to find equivalent ratios by multiplying or dividing both terms by different numbers, then verify if the ratios are equivalent using cross multiplication.

🔗 Connection: Understanding equivalent ratios prepares students for the next section on comparing ratios and solving problems involving proportions.