To simplify the ratios in the table, we start by expressing each quantity clearly. We'll take each of the given ratios and simplify them.
Given Ratios
- Bottle ratio: \( 2 \)
- Case ratio: \( 10 \)
- Other quantities: \( 6, 30, 50, 60, 10, 12 \)
From the table, we appear to have the following ratios (in regards to how many bottles per cases and other combinations).
Let’s assume we have ratios of bottles and cases:
- For \( 2 \) bottles to \( 10 \) cases, the ratio can be expressed as \( \frac{2}{10} \).
- For \( 6 \) bottles to \( 30 \) cases, the ratio is \( \frac{6}{30} \).
- For \( 10 \) bottles to \( 50 \) cases, the ratio is \( \frac{10}{50} \).
- For \( 12 \) bottles to \( 60 \) cases, the ratio is \( \frac{12}{60} \).
Simplifying Each Ratio
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For \( \frac{2}{10} \): \[ \frac{2}{10} = \frac{1}{5} \]
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For \( \frac{6}{30} \): \[ \frac{6}{30} = \frac{1}{5} \]
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For \( \frac{10}{50} \): \[ \frac{10}{50} = \frac{1}{5} \]
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For \( \frac{12}{60} \): \[ \frac{12}{60} = \frac{1}{5} \]
Conclusion
All the simplified ratios are equivalent:
- \( \frac{2}{10} = \frac{1}{5} \)
- \( \frac{6}{30} = \frac{1}{5} \)
- \( \frac{10}{50} = \frac{1}{5} \)
- \( \frac{12}{60} = \frac{1}{5} \)
So, each of the ratios simplifies to \( \frac{1}{5} \), proving that they are equivalent.
To complete your request format:
- \( 210 = \frac{1}{5} \)
- \( 630 = \frac{1}{5} \)
- \( 1050 = \frac{1}{5} \)
- \( 1260 = \frac{1}{5} \)
Note: The numbers \( 210, 630, 1050, \) and \( 1260 \) seem to be part of this exercise, but we need context to see how they relate to the ratios you displayed or if they should also be simplified accordingly. But based on the ratios directly provided and confirmed, all are equivalently simplified to \( \frac{1}{5} \).
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