1. ZEssential Question How can you use ratios to convert customary and metric units of measure?

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1. **Identify the conversion factor**  
   Determine the relationship between the two units. For example, if you know that  
   $$
   1 \text{ mile} = 1.60934 \text{ kilometers},
   $$  
   then the conversion factor is set up as a ratio, such as  
   $$
   \frac{1.60934 \text{ km}}{1 \text{ mile}}.
   $$

2. **Set up the ratio as a fraction equal to one**  
   Since the conversion factor represents an equality, it is essentially an expression of one. This means you can multiply any measure by this fraction without changing its value. In general, if  
   $$
   1 \text{ unit}_A = c \text{ unit}_B,
   $$  
   then  
   $$
   \frac{c \text{ unit}_B}{1 \text{ unit}_A} = 1.
   $$

3. **Multiply the original quantity by the conversion ratio**  
   If you have a measurement in $$\text{unit}_A$$ that you wish to convert into $$\text{unit}_B$$, multiply the measurement by the conversion factor:
   $$
   \text{Measurement in } \text{unit}_A \times \frac{c \text{ unit}_B}{1 \text{ unit}_A} = \text{Measurement in } \text{unit}_B.
   $$

4. **Apply the same idea for any conversion**  
   - For **customary units**, such as converting inches to feet where  
     $$
     12 \text{ inches} = 1 \text{ foot},
     $$
     you use the ratio  
     $$
     \frac{1 \text{ foot}}{12 \text{ inches}}.
     $$
   - For **metric units**, such as converting centimeters to meters where  
     $$
     100 \text{ cm} = 1 \text{ m},
     $$
     you use the ratio  
     $$
     \frac{1 \text{ m}}{100 \text{ cm}}.
     $$

5. **Cancel units appropriately**  
   When you set up the fractions, ensure the units you want to eliminate (cancel) appear in the numerator of one fraction and the denominator of another. This systematic cancellation leaves you with the desired unit.

In summary, you use ratios to convert customary and metric units of measure by employing conversion factors that are equivalent to one. Multiplying by these ratios allows you to change the units of a measurement without changing its value.
To convert between customary and metric units using ratios, follow these steps: 1. **Find the Conversion Factor**: Identify the relationship between the two units. For example, $$1 \text{ mile} = 1.60934 \text{ kilometers}$$. 2. **Set Up the Ratio**: Use the conversion factor as a fraction equal to one, like $$\frac{1.60934 \text{ km}}{1 \text{ mile}}$$. 3. **Multiply by the Conversion Ratio**: Multiply your original measurement by this fraction to change the units, e.g., $$ \text{Measurement in miles} \times \frac{1.60934 \text{ km}}{1 \text{ mile}} = \text{Measurement in kilometers}$$. 4. **Apply to Any Unit Conversion**: Use similar ratios for other units, such as $$12 \text{ inches} = 1 \text{ foot}$$ or $$100 \text{ cm} = 1 \text{ m}$$. 5. **Cancel Units**: Ensure the units you want to eliminate cancel out, leaving you with the desired unit. By using these ratios, you can easily convert between different measurement systems without changing the value of the measurement.

1. ZEssential Question How can you use ratios to convert customary and metric units of measure?

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