Answer :
To solve this problem, we need to start with the basic ratio provided in the question: 6 eggs to 1 tablespoon of butter. This can be written as the ratio [tex]\( \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].
Now, let's examine the given options to determine which are equivalent to this ratio:
1. Option 1: [tex]\( \frac{12 \text{ eggs}}{2 \text{ tbsp}} \)[/tex]
- Simplify this ratio by dividing both the numerator and the denominator by 2:
[tex]\[
\frac{12 \div 2}{2 \div 2} = \frac{6 \text{ eggs}}{1 \text{ tbsp}}
\][/tex]
- This is identical to the given ratio of 6 eggs to 1 tablespoon, so it is equivalent.
2. Option 2: [tex]\( \frac{15 \text{ eggs}}{3 \text{ tbsp}} \)[/tex]
- Simplify this ratio by dividing both the numerator and the denominator by 3:
[tex]\[
\frac{15 \div 3}{3 \div 3} = \frac{5 \text{ eggs}}{1 \text{ tbsp}}
\][/tex]
- This is not equivalent to the ratio of 6 eggs to 1 tablespoon.
3. Option 3: [tex]\( \frac{24 \text{ eggs}}{4 \text{ tbsp}} \)[/tex]
- Simplify this ratio by dividing both the numerator and the denominator by 4:
[tex]\[
\frac{24 \div 4}{4 \div 4} = \frac{6 \text{ eggs}}{1 \text{ tbsp}}
\][/tex]
- This is also identical to the given ratio of 6 eggs to 1 tablespoon, so it is equivalent.
4. Option 4: [tex]\( \frac{9 \text{ eggs}}{15 \text{ tbsp}} \)[/tex]
- Simplify this ratio by dividing both the numerator and the denominator by 3:
[tex]\[
\frac{9 \div 3}{15 \div 3} = \frac{3 \text{ eggs}}{5 \text{ tbsp}}
\][/tex]
- This is not equivalent to the ratio of 6 eggs to 1 tablespoon.
From this analysis, the equivalent ratios to [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]
Now, let's examine the given options to determine which are equivalent to this ratio:
1. Option 1: [tex]\( \frac{12 \text{ eggs}}{2 \text{ tbsp}} \)[/tex]
- Simplify this ratio by dividing both the numerator and the denominator by 2:
[tex]\[
\frac{12 \div 2}{2 \div 2} = \frac{6 \text{ eggs}}{1 \text{ tbsp}}
\][/tex]
- This is identical to the given ratio of 6 eggs to 1 tablespoon, so it is equivalent.
2. Option 2: [tex]\( \frac{15 \text{ eggs}}{3 \text{ tbsp}} \)[/tex]
- Simplify this ratio by dividing both the numerator and the denominator by 3:
[tex]\[
\frac{15 \div 3}{3 \div 3} = \frac{5 \text{ eggs}}{1 \text{ tbsp}}
\][/tex]
- This is not equivalent to the ratio of 6 eggs to 1 tablespoon.
3. Option 3: [tex]\( \frac{24 \text{ eggs}}{4 \text{ tbsp}} \)[/tex]
- Simplify this ratio by dividing both the numerator and the denominator by 4:
[tex]\[
\frac{24 \div 4}{4 \div 4} = \frac{6 \text{ eggs}}{1 \text{ tbsp}}
\][/tex]
- This is also identical to the given ratio of 6 eggs to 1 tablespoon, so it is equivalent.
4. Option 4: [tex]\( \frac{9 \text{ eggs}}{15 \text{ tbsp}} \)[/tex]
- Simplify this ratio by dividing both the numerator and the denominator by 3:
[tex]\[
\frac{9 \div 3}{15 \div 3} = \frac{3 \text{ eggs}}{5 \text{ tbsp}}
\][/tex]
- This is not equivalent to the ratio of 6 eggs to 1 tablespoon.
From this analysis, the equivalent ratios to [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]
