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Sagot :
To determine which ratios are equivalent to the given ratio of 1 tablespoon of butter for every 6 eggs, we first express the given ratio as:
[tex]\[ \frac{6 \text{ eggs}}{1 \text{ tbsp}} \][/tex]
Now, we need to check if the given ratios are equivalent to this ratio.
### Step-by-step Verification
1. Compare [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]:
[tex]\[ \frac{12 \text{ eggs}}{2 \text{ tbsp}} = \frac{12 \div 2}{2 \div 2} = \frac{6 \text{ eggs}}{1 \text{ tbsp}} \][/tex]
This is equivalent to the original ratio [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
[tex]\[ \text{True} \][/tex]
2. Compare [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]:
[tex]\[ \frac{15 \text{ eggs}}{3 \text{ tbsp}} = \frac{15 \div 3}{3 \div 3} = \frac{5 \text{ eggs}}{1 \text{ tbsp}} \][/tex]
This is not equivalent to the original ratio [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
[tex]\[ \text{False} \][/tex]
3. Compare [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]:
[tex]\[ \frac{24 \text{ eggs}}{4 \text{ tbsp}} = \frac{24 \div 4}{4 \div 4} = \frac{6 \text{ eggs}}{1 \text{ tbsp}} \][/tex]
This is equivalent to the original ratio [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
[tex]\[ \text{True} \][/tex]
4. Compare [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]:
[tex]\[ \frac{9 \text{ eggs}}{1.5 \text{ tbsp}} = \frac{9 \div 1.5}{1.5 \div 1.5} = \frac{6 \text{ eggs}}{1 \text{ tbsp}} \][/tex]
This is equivalent to the original ratio [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
[tex]\[ \text{True} \][/tex]
### Summary of Results
The original ratio [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex] is equivalent to the following ratios:
- [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]
The ratio that is not equivalent:
- [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]
The final results are:
[tex]\[ (\text{True}, \text{False}, \text{True}, \text{True}) \][/tex]
[tex]\[ \frac{6 \text{ eggs}}{1 \text{ tbsp}} \][/tex]
Now, we need to check if the given ratios are equivalent to this ratio.
### Step-by-step Verification
1. Compare [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]:
[tex]\[ \frac{12 \text{ eggs}}{2 \text{ tbsp}} = \frac{12 \div 2}{2 \div 2} = \frac{6 \text{ eggs}}{1 \text{ tbsp}} \][/tex]
This is equivalent to the original ratio [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
[tex]\[ \text{True} \][/tex]
2. Compare [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]:
[tex]\[ \frac{15 \text{ eggs}}{3 \text{ tbsp}} = \frac{15 \div 3}{3 \div 3} = \frac{5 \text{ eggs}}{1 \text{ tbsp}} \][/tex]
This is not equivalent to the original ratio [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
[tex]\[ \text{False} \][/tex]
3. Compare [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]:
[tex]\[ \frac{24 \text{ eggs}}{4 \text{ tbsp}} = \frac{24 \div 4}{4 \div 4} = \frac{6 \text{ eggs}}{1 \text{ tbsp}} \][/tex]
This is equivalent to the original ratio [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
[tex]\[ \text{True} \][/tex]
4. Compare [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]:
[tex]\[ \frac{9 \text{ eggs}}{1.5 \text{ tbsp}} = \frac{9 \div 1.5}{1.5 \div 1.5} = \frac{6 \text{ eggs}}{1 \text{ tbsp}} \][/tex]
This is equivalent to the original ratio [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
[tex]\[ \text{True} \][/tex]
### Summary of Results
The original ratio [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex] is equivalent to the following ratios:
- [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]
The ratio that is not equivalent:
- [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]
The final results are:
[tex]\[ (\text{True}, \text{False}, \text{True}, \text{True}) \][/tex]
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