Which pair of fractions are equivalent to 29

?(1 point)
Responses

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
Start Fraction 5 over 27 End Fraction comma Start Fraction 12 over 54 End Fraction

627, 1245

1 answer

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 \( \frac{2}{9} \).

  1. 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 \( \frac{2}{9} \).

  2. 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.

  3. 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.

  4. 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 \( \frac{2}{9} \).