To determine which pair of fractions is equivalent to 29, we can express 29 as a fraction. The simplest way is to write it as \( \frac{29}{1} \).
Now, we can check each set of fractions to see if they can be simplified to the same form.
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\( \frac{6}{27} \) and \( \frac{12}{45} \):
- Simplifying \( \frac{6}{27} \): \( \frac{6 \div 3}{27 \div 3} = \frac{2}{9} \)
- Simplifying \( \frac{12}{45} \): \( \frac{12 \div 3}{45 \div 3} = \frac{4}{15} \)
- These fractions do not match.
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\( \frac{6}{27} \) and \( \frac{12}{54} \):
- We have seen that \( \frac{6}{27} = \frac{2}{9} \).
- Simplifying \( \frac{12}{54} \): \( \frac{12 \div 6}{54 \div 6} = \frac{2}{9} \)
- These fractions are equivalent.
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\( \frac{5}{27} \) and \( \frac{12}{54} \):
- Simplifying \( \frac{12}{54} = \frac{2}{9} \) as calculated already.
- \( \frac{5}{27} \) is already in simplest form and does not equal \( \frac{2}{9} \).
- These fractions are not equivalent.
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\( \frac{20}{27} \) and \( \frac{12}{19} \):
- \( \frac{20}{27} \) is in simplest form.
- \( \frac{12}{19} \) is also in simplest form and does not equal \( \frac{20}{27} \).
- These fractions are not equivalent.
The only pair of fractions that are equivalent to each other are \( \frac{6}{27} \) and \( \frac{12}{54} \). Therefore, the correct answer is:
\( \frac{6}{27} \) and \( \frac{12}{54} \).