18 Reason If you multiply by a factor of 16 to convert a la unit of measurement to a smaller unit, by what factor would you multiply to convert the smaller unit of measurement to larger unit? Explain your reasoning. Open Ended Write a word problem that involves converti between pints and fluid ounces, and give the answer.

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### Converting Between Units: Understanding the Conversion Factor

**Problem 1:**  
*If you multiply by a factor of 16 to convert a larger unit of measurement to a smaller unit, by what factor would you multiply to convert the smaller unit of measurement to the larger unit? Explain your reasoning.*

**Answer:**  
When converting from a larger unit to a smaller unit, you multiply by the conversion factor to increase the quantity appropriately. In this case, multiplying by 16 converts the larger unit to a smaller unit.

To convert **back** from the smaller unit to the larger unit, you need to reverse the process. This means you should multiply by the reciprocal of the original conversion factor. Therefore, you would multiply by **1/16** (which is the same as dividing by 16) to convert from the smaller unit back to the larger unit.

**Reasoning:**  
- **Larger to Smaller:** Multiply by 16  
- **Smaller to Larger:** Multiply by 1/16

This ensures that both conversions are inverse operations of each other, maintaining consistency and accuracy in measurements.

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### Word Problem Involving Pints and Fluid Ounces

**Problem 2:**  
*Sarah has a recipe that requires 3 pints of milk. However, her measuring jug only has measurements in fluid ounces. Knowing that 1 pint equals 16 fluid ounces, how many fluid ounces of milk does Sarah need to use for the recipe?*

**Answer:**  
To find out how many fluid ounces Sarah needs, multiply the number of pints by the conversion factor:

$$ \text{Fluid Ounces} = \text{Pints} \times \text{Conversion Factor} $$

$$ \text{Fluid Ounces} = 3 \, \text{pints} \times 16 \, \text{fluid ounces per pint} $$

$$ \text{Fluid Ounces} = 48 \, \text{fluid ounces} $$

**Solution:**  
Sarah needs **48 fluid ounces** of milk for her recipe.
To convert from a larger unit to a smaller unit, multiply by 16. To convert from a smaller unit back to a larger unit, multiply by 1/16. For example, 3 pints is equal to 48 fluid ounces (3 × 16).

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