To compare the ratios 9 to 12 and 4 to 6, we can convert both ratios to their simplest forms.
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For the ratio 9 to 12: \[ \frac{9}{12} = \frac{3}{4} \quad \text{(by dividing both numerator and denominator by 3)} \]
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For the ratio 4 to 6: \[ \frac{4}{6} = \frac{2}{3} \quad \text{(by dividing both numerator and denominator by 2)} \]
Now we will compare \(\frac{3}{4}\) and \(\frac{2}{3}\).
To do this, we can find a common denominator, which is 12:
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Convert \(\frac{3}{4}\) to have a denominator of 12: \[ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \]
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Convert \(\frac{2}{3}\) to have a denominator of 12: \[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \]
Now we can compare:
- \(\frac{9}{12}\) (which is \(\frac{3}{4}\)) and
- \(\frac{8}{12}\) (which is \(\frac{2}{3}\)).
Since \(9 > 8\), we find that: \[ \frac{3}{4} > \frac{2}{3} \]
Thus, the ratio \(9\) to \(12\) is greater than the ratio \(4\) to \(6\).
Therefore, the correct statement is: The ratio 9 to 12 is greater than 4 to 6.
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