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To make a quiche, you need 1 tablespoon of butter for every 6 eggs. Write a ratio that compares these two quantities. Which ratios are equivalent to this ratio? Check all that apply.

- [tex]\(\frac{12 \text{ eggs }}{2 \text{ tbsp }}\)[/tex]
- [tex]\(\frac{15 \text{ eggs }}{3 \text{ tbsp }}\)[/tex]
- [tex]\(\frac{24 \text{ eggs }}{4 \text{ tbsp }}\)[/tex]
- [tex]\(\frac{9 \text{ eggs }}{1.5 \text{ tbsp }}\)[/tex]

Answer :

To determine which ratios are equivalent to the given ratio of 6 eggs per 1 tablespoon of butter, let's follow these steps to compare each option:

1. Understand the given ratio:
The ratio is 6 eggs to 1 tablespoon of butter. This can be written as a fraction: [tex]\(\frac{6\text{ eggs}}{1\text{ tbsp}}\)[/tex].

2. Check each ratio provided to see if they're equivalent:

- [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 matches the given ratio, so it is equivalent.

- [tex]\(\frac{15\text{ eggs}}{3\text{ tbsp}}\)[/tex]:
- Simplify by dividing both by 3: [tex]\(\frac{15 \div 3}{3 \div 3} = \frac{5\text{ eggs}}{1\text{ tbsp}}\)[/tex].
- This does not match the given ratio, so it is not equivalent.

- [tex]\(\frac{24\text{ eggs}}{4\text{ tbsp}}\)[/tex]:
- Simplify by dividing both by 4: [tex]\(\frac{24 \div 4}{4 \div 4} = \frac{6\text{ eggs}}{1\text{ tbsp}}\)[/tex].
- This matches the given ratio, so it is equivalent.

- [tex]\(\frac{9\text{ eggs}}{1.5\text{ tbsp}}\)[/tex]:
- Simplify by dividing both by 1.5: [tex]\(\frac{9 \div 1.5}{1.5 \div 1.5} = \frac{6\text{ eggs}}{1\text{ tbsp}}\)[/tex].
- This matches the given ratio, so it is equivalent.

Based on this analysis, the ratios that are equivalent to the original ratio of 6 eggs per 1 tablespoon of butter 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]

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Rewritten by : Barada