To determine which pair of fractions are equivalent to \( \frac{2}{9} \), we will simplify each fraction to see if it can be expressed as \( \frac{2}{9} \).
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First Pair:
- \( \frac{6}{27} \): \( \frac{6 \div 3}{27 \div 3} = \frac{2}{9} \) (This is equivalent)
- \( \frac{12}{54} \): \( \frac{12 \div 6}{54 \div 6} = \frac{2}{9} \) (This is equivalent)
So both fractions in this pair are equivalent to \( \frac{2}{9} \).
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Second Pair:
- \( \frac{20}{27} \) (does not equal \( \frac{2}{9} \))
- \( \frac{12}{19} \) (does not equal \( \frac{2}{9} \))
Neither of these fractions is equivalent.
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Third Pair:
- \( \frac{5}{27} \) (does not equal \( \frac{2}{9} \))
- \( \frac{12}{54} \): \( \frac{12 \div 6}{54 \div 6} = \frac{2}{9} \) (This is equivalent)
This pair only has one fraction that is equivalent.
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Fourth Pair:
- \( \frac{6}{27} \): \( \frac{6 \div 3}{27 \div 3} = \frac{2}{9} \) (This is equivalent)
- \( \frac{6}{45} \): \( \frac{6 \div 3}{45 \div 3} = \frac{2}{15} \) (not equivalent)
This pair also does not consist of two equivalent fractions.
Based on this analysis, the first pair:
\( \frac{6}{27} \) and \( \frac{12}{54} \)
is the correct answer since both fractions are equivalent to \( \frac{2}{9} \).