Answer :
To solve the problem of identifying which ratios are equivalent to the given ratio of 6 eggs to 1 tablespoon of butter, let's look at each option and compare it to the original ratio.
The goal is to see if these options have the same relationship between eggs and tablespoons of butter as 6 eggs for every 1 tablespoon.
Original ratio:
- 6 eggs to 1 tablespoon
Let's analyze each choice:
1. Option A: [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]
Comparing this ratio:
- If we simplify [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex], we divide both the number of eggs and tablespoons by 2, resulting in [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
- This matches the original ratio of 6 eggs to 1 tablespoon. So, this option is equivalent.
2. Option B: [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]
Simplifying this ratio:
- If we divide both the number of eggs and tablespoons by 3, we get [tex]\(\frac{5 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
- Since 5 is not equal to the 6 eggs in the original ratio, this option is not equivalent.
3. Option C: [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]
Simplifying this ratio:
- Divide both sides by 4 to get [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
- This is exactly the same as the original ratio, making this option equivalent.
4. Option D: [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]
Simplifying this ratio:
- Divide both sides by 1.5 to get [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
- This matches the original ratio of 6 eggs to 1 tablespoon, so this option is equivalent.
Conclusion:
The ratios that are equivalent to the original ratio of 6 eggs to 1 tablespoon 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]
Therefore, Options A, C, and D are equivalent to the original ratio.
The goal is to see if these options have the same relationship between eggs and tablespoons of butter as 6 eggs for every 1 tablespoon.
Original ratio:
- 6 eggs to 1 tablespoon
Let's analyze each choice:
1. Option A: [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]
Comparing this ratio:
- If we simplify [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex], we divide both the number of eggs and tablespoons by 2, resulting in [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
- This matches the original ratio of 6 eggs to 1 tablespoon. So, this option is equivalent.
2. Option B: [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]
Simplifying this ratio:
- If we divide both the number of eggs and tablespoons by 3, we get [tex]\(\frac{5 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
- Since 5 is not equal to the 6 eggs in the original ratio, this option is not equivalent.
3. Option C: [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]
Simplifying this ratio:
- Divide both sides by 4 to get [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
- This is exactly the same as the original ratio, making this option equivalent.
4. Option D: [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]
Simplifying this ratio:
- Divide both sides by 1.5 to get [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
- This matches the original ratio of 6 eggs to 1 tablespoon, so this option is equivalent.
Conclusion:
The ratios that are equivalent to the original ratio of 6 eggs to 1 tablespoon 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]
Therefore, Options A, C, and D are equivalent to the original ratio.
