Question

Learn about equivalent ratios in measurement.
|
Use _ to complete tables of equivalent ratios.
Use _ or _ to find equivalent ratios.

Answer 1

Equivalent ratios are pairs of ratios that express the same relationship between quantities. To understand equivalent ratios in measurement, let’s explore how to create and manipulate them.

### Completing Tables of Equivalent Ratios

To fill in a table of equivalent ratios, consider a known ratio and use multiplication or division to find new values. For example, if we have the ratio 2:3, we can create equivalent ratios by multiplying both terms by the same number:

| Ratio (x:y) | Equivalent Ratio |
|-------------|------------------|
| 2:3 | 4:6 |
| 2:3 | 6:9 |
| 2:3 | 8:12 |

### Finding Equivalent Ratios

When asked to find equivalent ratios, you can either _multiply_ or _divide_ both parts of the ratio to generate new ratios. Here are some examples:

- Start with the ratio **3:4**:
- To find an equivalent ratio by multiplication, multiply both numbers by 2:
- \(3 \times 2 : 4 \times 2 = 6:8\)

- To find an equivalent ratio by division, divide both numbers by 1 (though this doesn't change the ratio, it's a demonstration):
- \(3 \div 1 : 4 \div 1 = 3:4\)

- Using the ratio **5:10**:
- To find an equivalent ratio by division, divide both numbers by 5:
- \(5 \div 5 : 10 \div 5 = 1:2\)

### Summary

- **Use multiplication** or **division** to find equivalent ratios.
- Complete tables by applying the same operation to both components of the ratio.

By mastering these techniques, you can work easily with equivalent ratios in various applications.