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Answer :
To solve the problem of finding which ratios are equivalent to the ratio of 1 tablespoon of butter for every 6 eggs, let's break it down step by step:
1. Understanding the original ratio:
- The quiche recipe uses 1 tablespoon of butter for every 6 eggs.
- This ratio can be expressed as [tex]\( \frac{6\, \text{eggs}}{1\, \text{tbsp}} \)[/tex].
2. Equivalent ratios:
- Two ratios are equivalent if they represent the same relationship when simplified.
3. List of given ratios:
- [tex]\( \frac{12\, \text{eggs}}{2\, \text{tbsp}} \)[/tex]
- [tex]\( \frac{15\, \text{eggs}}{3\, \text{tbsp}} \)[/tex]
- [tex]\( \frac{24\, \text{eggs}}{4\, \text{tbsp}} \)[/tex]
- [tex]\( \frac{9\, \text{eggs}}{1.5\, \text{tbsp}} \)[/tex]
4. Checking the equivalency:
- A ratio is equivalent to [tex]\( \frac{6\, \text{eggs}}{1\, \text{tbsp}} \)[/tex] if when simplified, it equals 6 eggs for every 1 tablespoon of butter.
5. Simplifying each ratio:
- [tex]\( \frac{12\, \text{eggs}}{2\, \text{tbsp}} = \frac{6}{1} \)[/tex] (equivalent)
- [tex]\( \frac{15\, \text{eggs}}{3\, \text{tbsp}} = \frac{5}{1} \)[/tex] (not equivalent)
- [tex]\( \frac{24\, \text{eggs}}{4\, \text{tbsp}} = \frac{6}{1} \)[/tex] (equivalent)
- [tex]\( \frac{9\, \text{eggs}}{1.5\, \text{tbsp}} = \frac{6}{1} \)[/tex] (equivalent)
6. Conclusion:
- The ratios that are equivalent to the original ratio [tex]\( \frac{6\, \text{eggs}}{1\, \text{tbsp}} \)[/tex] are:
- [tex]\( \frac{12\, \text{eggs}}{2\, \text{tbsp}} \)[/tex]
- [tex]\( \frac{24\, \text{eggs}}{4\, \text{tbsp}} \)[/tex]
- [tex]\( \frac{9\, \text{eggs}}{1.5\, \text{tbsp}} \)[/tex]
These are the ratios that maintain the same proportional relationship as the original recipe requirement!
1. Understanding the original ratio:
- The quiche recipe uses 1 tablespoon of butter for every 6 eggs.
- This ratio can be expressed as [tex]\( \frac{6\, \text{eggs}}{1\, \text{tbsp}} \)[/tex].
2. Equivalent ratios:
- Two ratios are equivalent if they represent the same relationship when simplified.
3. List of given ratios:
- [tex]\( \frac{12\, \text{eggs}}{2\, \text{tbsp}} \)[/tex]
- [tex]\( \frac{15\, \text{eggs}}{3\, \text{tbsp}} \)[/tex]
- [tex]\( \frac{24\, \text{eggs}}{4\, \text{tbsp}} \)[/tex]
- [tex]\( \frac{9\, \text{eggs}}{1.5\, \text{tbsp}} \)[/tex]
4. Checking the equivalency:
- A ratio is equivalent to [tex]\( \frac{6\, \text{eggs}}{1\, \text{tbsp}} \)[/tex] if when simplified, it equals 6 eggs for every 1 tablespoon of butter.
5. Simplifying each ratio:
- [tex]\( \frac{12\, \text{eggs}}{2\, \text{tbsp}} = \frac{6}{1} \)[/tex] (equivalent)
- [tex]\( \frac{15\, \text{eggs}}{3\, \text{tbsp}} = \frac{5}{1} \)[/tex] (not equivalent)
- [tex]\( \frac{24\, \text{eggs}}{4\, \text{tbsp}} = \frac{6}{1} \)[/tex] (equivalent)
- [tex]\( \frac{9\, \text{eggs}}{1.5\, \text{tbsp}} = \frac{6}{1} \)[/tex] (equivalent)
6. Conclusion:
- The ratios that are equivalent to the original ratio [tex]\( \frac{6\, \text{eggs}}{1\, \text{tbsp}} \)[/tex] are:
- [tex]\( \frac{12\, \text{eggs}}{2\, \text{tbsp}} \)[/tex]
- [tex]\( \frac{24\, \text{eggs}}{4\, \text{tbsp}} \)[/tex]
- [tex]\( \frac{9\, \text{eggs}}{1.5\, \text{tbsp}} \)[/tex]
These are the ratios that maintain the same proportional relationship as the original recipe requirement!
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