To compare the fractions \( \frac{4}{7} \) and \( \frac{5}{12} \), we can find a common denominator or convert them to decimals.
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Finding a Common Denominator: The least common multiple (LCM) of 7 and 12 is 84.
Convert \( \frac{4}{7} \) and \( \frac{5}{12} \) to have a denominator of 84:
\[ \frac{4}{7} = \frac{4 \times 12}{7 \times 12} = \frac{48}{84} \]
\[ \frac{5}{12} = \frac{5 \times 7}{12 \times 7} = \frac{35}{84} \]
Now we can compare:
\( \frac{48}{84} \) is greater than \( \frac{35}{84} \).
Therefore, \( \frac{4}{7} > \frac{5}{12} \).
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Converting to Decimals: Alternatively, converting both fractions to decimals:
\[ \frac{4}{7} \approx 0.5714 \] \[ \frac{5}{12} \approx 0.4167 \]
Since \( 0.5714 > 0.4167 \), this further confirms that \( \frac{4}{7} > \frac{5}{12} \).
In conclusion, you can fill in the blank with "greater than":
\( \frac{4}{7} > \frac{5}{12} \)