To compare the ratios 7:9 and 4:6, we can simplify them and express them as decimals for easier comparison.
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Simplifying the Ratios:
- The ratio \( \frac{7}{9} \) is already in its simplest form.
- The ratio \( \frac{4}{6} \) can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2: \[ \frac{4}{6} = \frac{2}{3} \]
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Finding Decimal Values:
- The decimal value for \( \frac{7}{9} \): \[ 7 \div 9 \approx 0.7777\ldots \]
- The decimal value for \( \frac{2}{3} \): \[ 2 \div 3 \approx 0.6666\ldots \]
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Comparing the Values:
- \( 0.7777\ldots > 0.6666\ldots \)
Thus, we can conclude that the ratio \( 7:9 \) is greater than the ratio \( 4:6 \).
To double-check using the provided tables:
- The pairs in the first table represent multiples of 7 and 9.
- The pairs in the second table (corresponding to the ratio \( 4:6 \)) represent multiples of 4 and 6.
When we compare their values from the tables directly, notice that:
- For each pair corresponding to the ratios:
- \( 7 \) to \( 9 \): \( 14 \) to \( 18 \), \( 21 \) to \( 27 \), etc.
- \( 4 \) to \( 6 \): \( 8 \) to \( 12 \), \( 12 \) to \( 18 \), etc. (derived from the ratio)
In every case, the value pairs for \( \frac{7}{9} \) (or \( 7, 9, \ldots \)) will yield greater results than those for \( \frac{4}{6} \) when stated in similar fractions or ratios.
Therefore, the conclusion remains that the ratio \( 7:9 \) is greater than the ratio \( 4:6 \).