Which pair of fractions are equivalent to 29

?(1 point)
Responses

627, 1245
Start Fraction 6 over 27 End Fraction comma Start Fraction 12 over 45 End Fraction

627, 1254
Start Fraction 6 over 27 End Fraction comma Start Fraction 12 over 54 End Fraction

2027, 1219
Start Fraction 20 over 27 End Fraction comma Start Fraction 12 over 19 End Fraction

527, 1254

1 answer

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:

  1. \( \frac{6}{27} \) 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.
  2. \( \frac{6}{27} \) and \( \frac{12}{54} \):

    • \( \frac{6}{27} = \frac{2}{9} \)
    • \( \frac{12}{54} = \frac{2}{9} \) (12 ÷ 6 = 2; 54 ÷ 6 = 9)
    • Equivalent!
  3. \( \frac{20}{27} \) and \( \frac{12}{19} \):

    • \( \frac{20}{27} \) cannot be simplified further.
    • \( \frac{12}{19} \) cannot be simplified either.
    • Not equivalent.
  4. \( \frac{5}{27} \) 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.