To compare the ratios \( 7:9 \) and \( 4:6 \), we can convert each ratio to a decimal.
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For the ratio \( 7:9 \):
- Divide \( 7 \) by \( 9 \): \[ 7 \div 9 \approx 0.7777\ldots \text{ (repeating)} \]
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For the ratio \( 4:6 \):
- First, simplify the ratio \( 4:6 \) by dividing both numbers by their greatest common divisor (which is \( 2 \)): \[ \frac{4}{6} = \frac{2}{3} \]
- Now divide \( 2 \) by \( 3 \): \[ 2 \div 3 \approx 0.6666\ldots \text{ (repeating)} \]
Now we can compare the two decimal values:
- \( 7:9 \approx 0.7777\ldots \)
- \( 4:6 \approx 0.6666\ldots \)
Since \( 0.7777\ldots \) is greater than \( 0.6666\ldots \), we can conclude that:
\[ 7:9 > 4:6 \]
In summary, the ratio \( 7:9 \) is greater than the ratio \( 4:6 \).