To compare the ratios 16:18 and 5:6, we can simplify each ratio:
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For 16:18, we can divide both numbers by their greatest common divisor, which is 2: \[ \frac{16}{18} = \frac{16 \div 2}{18 \div 2} = \frac{8}{9} \]
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For 5:6, there are no common factors to simplify, so it remains: \[ \frac{5}{6} \]
Next, we can compare the simplified ratios \(\frac{8}{9}\) and \(\frac{5}{6}\) by cross-multiplying:
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For \(\frac{8}{9}\):
- Cross-multiply to compare with \(\frac{5}{6}\): \[ 8 \times 6 = 48 \]
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For \(\frac{5}{6}\):
- Cross-multiply with \(\frac{8}{9}\): \[ 5 \times 9 = 45 \]
Since \(48 > 45\), we conclude that \(\frac{8}{9} > \frac{5}{6}\).
Therefore, the ratio 16:18 is greater than 5:6.
So, the correct response is: 16:18 is greater.
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