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:
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Start with the ratio 3:4:
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To find an equivalent ratio by multiplication, multiply both numbers by 2:
- \(3 \times 2 : 4 \times 2 = 6:8\)
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To find an equivalent ratio by division, divide both numbers by 1 (though this doesn't change the ratio, it's a demonstration):
- \(3 \div 1 : 4 \div 1 = 3:4\)
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Using the ratio 5:10:
- To find an equivalent ratio by division, divide both numbers by 5:
- \(5 \div 5 : 10 \div 5 = 1:2\)
- To find an equivalent ratio by division, divide both numbers by 5:
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.
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