To determine which statement about the given fractions is true, we first convert all the fractions to decimal form or analyze them by cross-multiplication.
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StartFraction 9 Over 14 EndFraction:
- Decimal: \( \frac{9}{14} \approx 0.642857 \)
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StartFraction 22 Over 28 EndFraction:
- Simplifies to \( \frac{11}{14} \) (both numerator and denominator divided by 2)
- Thus, Decimal: \( \frac{11}{14} \approx 0.785714 \)
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StartFraction 5 Over 7 EndFraction:
- Decimal: \( \frac{5}{7} \approx 0.714286 \)
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StartFraction 12 Over 14 EndFraction:
- Simplifies to \( \frac{6}{7} \) (both numerator and denominator divided by 2)
- Thus, Decimal: \( \frac{6}{7} \approx 0.857143 \)
Now we can compare the fractions:
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Comparing \( \frac{9}{14} \) and \( \frac{5}{7} \):
- \( 0.642857 < 0.714286 \)
- Thus, \( \frac{9}{14} < \frac{5}{7} \)
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Comparing \( \frac{5}{7} \) and \( \frac{11}{14} \) (or \( \frac{22}{28} \)):
- \( 0.714286 < 0.785714 \)
- Thus, \( \frac{5}{7} < \frac{22}{28} \)
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Comparing \( \frac{12}{14} \) and \( \frac{22}{28} \):
- \( 0.857143 > 0.785714 \)
- Thus, \( \frac{12}{14} > \frac{22}{28} \)
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Comparing \( \frac{9}{14} \) and \( \frac{12}{14} \):
- \( 0.642857 < 0.857143 \)
- Thus, \( \frac{9}{14} < \frac{12}{14} \)
Putting it all together, the true statements are:
- \( \frac{12}{14} > \frac{22}{28} \)
So, the correct statement from the list provided is:
- StartFraction 12 Over 14 EndFraction greater-than StartFraction 22 Over 28 EndFraction.
1 answer