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Answer :
To solve the problem of determining which ratios are equivalent to the given ratio of 6 eggs to 1 tablespoon of butter, follow these steps:
1. Understand the Original Ratio:
- The given ratio is 6 eggs for every 1 tablespoon of butter. We can express this ratio as [tex]\( \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].
2. Compare the Ratios:
- We need to find out which of the given ratios are equivalent to this original ratio. An equivalent ratio will have the same relationship between the number of eggs and tablespoons of butter as [tex]\( \frac{6}{1} \)[/tex].
3. Check Each Option:
- Option 1: [tex]\( \frac{12 \text{ eggs}}{2 \text{ tbsp}} \)[/tex]
- Simplify: [tex]\( \frac{12 \div 2}{2 \div 2} = \frac{6}{1} \)[/tex].
- This is equivalent to [tex]\( \frac{6}{1} \)[/tex]. So it's correct.
- Option 2: [tex]\( \frac{15 \text{ eggs}}{3 \text{ tbsp}} \)[/tex]
- Simplify: [tex]\( \frac{15 \div 3}{3 \div 3} = \frac{5}{1} \)[/tex].
- This is not equivalent to [tex]\( \frac{6}{1} \)[/tex].
- Option 3: [tex]\( \frac{24 \text{ eggs}}{4 \text{ tbsp}} \)[/tex]
- Simplify: [tex]\( \frac{24 \div 4}{4 \div 4} = \frac{6}{1} \)[/tex].
- This is equivalent to [tex]\( \frac{6}{1} \)[/tex]. So it's correct.
- Option 4: [tex]\( \frac{9 \text{ eggs}}{1.5 \text{ tbsp}} \)[/tex]
- Simplify: [tex]\( \frac{9 \div 1.5}{1.5 \div 1.5} = \frac{6}{1} \)[/tex].
- This is equivalent to [tex]\( \frac{6}{1} \)[/tex]. So it's correct.
4. Conclusion:
- The ratios that are equivalent to the original ratio of 6 eggs to 1 tablespoon of butter are [tex]\( \frac{12 \text{ eggs}}{2 \text{ tbsp}} \)[/tex], [tex]\( \frac{24 \text{ eggs}}{4 \text{ tbsp}} \)[/tex], and [tex]\( \frac{9 \text{ eggs}}{1.5 \text{ tbsp}} \)[/tex].
1. Understand the Original Ratio:
- The given ratio is 6 eggs for every 1 tablespoon of butter. We can express this ratio as [tex]\( \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].
2. Compare the Ratios:
- We need to find out which of the given ratios are equivalent to this original ratio. An equivalent ratio will have the same relationship between the number of eggs and tablespoons of butter as [tex]\( \frac{6}{1} \)[/tex].
3. Check Each Option:
- Option 1: [tex]\( \frac{12 \text{ eggs}}{2 \text{ tbsp}} \)[/tex]
- Simplify: [tex]\( \frac{12 \div 2}{2 \div 2} = \frac{6}{1} \)[/tex].
- This is equivalent to [tex]\( \frac{6}{1} \)[/tex]. So it's correct.
- Option 2: [tex]\( \frac{15 \text{ eggs}}{3 \text{ tbsp}} \)[/tex]
- Simplify: [tex]\( \frac{15 \div 3}{3 \div 3} = \frac{5}{1} \)[/tex].
- This is not equivalent to [tex]\( \frac{6}{1} \)[/tex].
- Option 3: [tex]\( \frac{24 \text{ eggs}}{4 \text{ tbsp}} \)[/tex]
- Simplify: [tex]\( \frac{24 \div 4}{4 \div 4} = \frac{6}{1} \)[/tex].
- This is equivalent to [tex]\( \frac{6}{1} \)[/tex]. So it's correct.
- Option 4: [tex]\( \frac{9 \text{ eggs}}{1.5 \text{ tbsp}} \)[/tex]
- Simplify: [tex]\( \frac{9 \div 1.5}{1.5 \div 1.5} = \frac{6}{1} \)[/tex].
- This is equivalent to [tex]\( \frac{6}{1} \)[/tex]. So it's correct.
4. Conclusion:
- The ratios that are equivalent to the original ratio of 6 eggs to 1 tablespoon of butter are [tex]\( \frac{12 \text{ eggs}}{2 \text{ tbsp}} \)[/tex], [tex]\( \frac{24 \text{ eggs}}{4 \text{ tbsp}} \)[/tex], and [tex]\( \frac{9 \text{ eggs}}{1.5 \text{ tbsp}} \)[/tex].
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