Answer :
To solve this problem, we need to compare the given ratio of eggs to tablespoons of butter and determine which of the provided ratios are equivalent to that ratio.
1. Identify the Original Ratio:
- The original ratio is 6 eggs to 1 tablespoon of butter. This can be expressed as the ratio [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
2. Find Equivalent Ratios:
- A ratio is equivalent to another if they represent the same ratio when simplified. In this case, we can simplify by dividing both parts of the ratio by the same number or multiplying both parts.
3. Check Each Given Ratio:
- First Ratio: [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]
- Simplify: [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 indeed equivalent to the original ratio.
- Second Ratio: [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]
- Simplify: [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 because it simplifies to a different ratio.
- Third Ratio: [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]
- Simplify: [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.
- Fourth Ratio: [tex]\(\frac{9 \text{ eggs}}{15 \text{ tbsp}}\)[/tex]
- Simplify: This ratio does not simplify to the original ratio of [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
4. Conclusion:
- The ratios that are equivalent to the original [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex] ratio are [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex] and [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex].
1. Identify the Original Ratio:
- The original ratio is 6 eggs to 1 tablespoon of butter. This can be expressed as the ratio [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
2. Find Equivalent Ratios:
- A ratio is equivalent to another if they represent the same ratio when simplified. In this case, we can simplify by dividing both parts of the ratio by the same number or multiplying both parts.
3. Check Each Given Ratio:
- First Ratio: [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]
- Simplify: [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 indeed equivalent to the original ratio.
- Second Ratio: [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]
- Simplify: [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 because it simplifies to a different ratio.
- Third Ratio: [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]
- Simplify: [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.
- Fourth Ratio: [tex]\(\frac{9 \text{ eggs}}{15 \text{ tbsp}}\)[/tex]
- Simplify: This ratio does not simplify to the original ratio of [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
4. Conclusion:
- The ratios that are equivalent to the original [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex] ratio are [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex] and [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex].
