To determine which pair of fractions are equivalent to \( \frac{29}{1} \), we need to understand that a fraction is equivalent if it can be simplified to the same value.
Let’s analyze the options provided:
-
\( \frac{6}{27} \) and \( \frac{12}{45} \):
- \( \frac{6}{27} = \frac{2}{9} \) (6 ÷ 3 = 2; 27 ÷ 3 = 9)
- \( \frac{12}{45} = \frac{4}{15} \) (12 ÷ 3 = 4; 45 ÷ 3 = 15)
- Not equivalent.
-
\( \frac{6}{27} \) and \( \frac{12}{54} \):
- \( \frac{6}{27} = \frac{2}{9} \)
- \( \frac{12}{54} = \frac{2}{9} \) (12 ÷ 6 = 2; 54 ÷ 6 = 9)
- Equivalent!
-
\( \frac{20}{27} \) and \( \frac{12}{19} \):
- \( \frac{20}{27} \) cannot be simplified further.
- \( \frac{12}{19} \) cannot be simplified either.
- Not equivalent.
-
\( \frac{5}{27} \) and \( \frac{12}{54} \):
- \( \frac{5}{27} \) cannot be simplified further.
- \( \frac{12}{54} = \frac{2}{9} \)
- Not equivalent.
Thus, the pair that is equivalent to \( \frac{29}{1} \) is \( \frac{6}{27} \) and \( \frac{12}{54} \) from the second option.