Answer:
To find equivalent ratios using a tape diagram, follow these steps:
1. **Understand the Concept**: A tape diagram, also known as a bar model or strip diagram, is a visual representation that helps you understand and solve mathematical problems involving ratios and proportions.
2. **Set Up the Tape Diagram**: Draw a rectangle to represent the whole or the total amount. Divide the rectangle into segments or parts that correspond to the given ratio. For example, if you have a ratio of 2:3, you would divide the rectangle into two segments and three segments.
3. **Scale the Diagram**: If the given ratio is not in its simplest form, you may need to scale the diagram. For example, if you have a ratio of 4:6, you can scale it down to its simplest form of 2:3.
4. **Find Equivalent Ratios**: To find equivalent ratios, you can adjust the number of segments in the tape diagram while keeping the same overall structure. For instance, if you have a ratio of 2:3 and you want to find an equivalent ratio, you could double both parts to get 4:6.
5. **Check for Simplicity**: Always check if the equivalent ratio is in its simplest form. If not, simplify it by dividing both parts by their greatest common factor.
6. **Example**: Let's say you have a ratio of 2:5. You draw a tape diagram with 2 segments and 5 segments. To find an equivalent ratio, you can double both parts to get 4:10. However, this isn't in its simplest form, so you can simplify it by dividing both parts by 2 to get 2:5 again.
Remember that tape diagrams are a visual tool that help you understand the relationship between ratios and how they can be scaled or adjusted. They are particularly useful for solving problems involving ratios and proportions in a tangible and visual way.