Answer :
To solve the question of which ratios are equivalent, we start by identifying the initial ratio given in the problem. The original ratio is 6 eggs to 1 tablespoon of butter, which can be written as [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
Now, let's compare each provided ratio to see if they are equivalent to the original ratio:
1. [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]:
- Simplify the ratio by dividing both the numerator and the denominator by 2: [tex]\(\frac{12 \div 2}{2 \div 2} = \frac{6}{1}\)[/tex].
- This ratio simplifies to the original ratio [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex]. So, this is equivalent.
2. [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]:
- Simplify the ratio by dividing both the numerator and the denominator by 3: [tex]\(\frac{15 \div 3}{3 \div 3} = \frac{5}{1}\)[/tex].
- This ratio simplifies to [tex]\(\frac{5 \text{ eggs}}{1 \text{ tbsp}}\)[/tex], which is different from the original ratio. Hence, this is not equivalent.
3. [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]:
- Simplify the ratio by dividing both the numerator and the denominator by 4: [tex]\(\frac{24 \div 4}{4 \div 4} = \frac{6}{1}\)[/tex].
- This ratio simplifies to the original ratio [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex]. So, this is equivalent.
4. [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]:
- Simplify the ratio by dividing both the numerator and the denominator by 1.5: [tex]\(\frac{9 \div 1.5}{1.5 \div 1.5} = \frac{6}{1}\)[/tex].
- This ratio also simplifies to the original ratio [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex]. So, this is equivalent.
Therefore, the equivalent ratios 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].
Now, let's compare each provided ratio to see if they are equivalent to the original ratio:
1. [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]:
- Simplify the ratio by dividing both the numerator and the denominator by 2: [tex]\(\frac{12 \div 2}{2 \div 2} = \frac{6}{1}\)[/tex].
- This ratio simplifies to the original ratio [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex]. So, this is equivalent.
2. [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]:
- Simplify the ratio by dividing both the numerator and the denominator by 3: [tex]\(\frac{15 \div 3}{3 \div 3} = \frac{5}{1}\)[/tex].
- This ratio simplifies to [tex]\(\frac{5 \text{ eggs}}{1 \text{ tbsp}}\)[/tex], which is different from the original ratio. Hence, this is not equivalent.
3. [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]:
- Simplify the ratio by dividing both the numerator and the denominator by 4: [tex]\(\frac{24 \div 4}{4 \div 4} = \frac{6}{1}\)[/tex].
- This ratio simplifies to the original ratio [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex]. So, this is equivalent.
4. [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]:
- Simplify the ratio by dividing both the numerator and the denominator by 1.5: [tex]\(\frac{9 \div 1.5}{1.5 \div 1.5} = \frac{6}{1}\)[/tex].
- This ratio also simplifies to the original ratio [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex]. So, this is equivalent.
Therefore, the equivalent ratios 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].
