Question

Which pair of fractions are equivalent to 2/9 ? Responses 5/27, 12/54 - no response given 6/27, 12/45 - no response given 20/27, 12/19 - no response given 6/27, 1/254 - no response given

Answer 1

To determine which pairs of fractions are equivalent to \( \frac{2}{9} \), we can cross-multiply and check if the fractions are indeed equal.

1. For the pair \( \frac{5}{27} \) and \( \frac{2}{9} \):
\[
2 \times 27 = 54 \quad \text{and} \quad 5 \times 9 = 45 \quad (\text{not equal})
\]

2. For the pair \( \frac{12}{54} \) and \( \frac{2}{9} \):
\[
2 \times 54 = 108 \quad \text{and} \quad 12 \times 9 = 108 \quad (\text{equal})
\]

3. For the pair \( \frac{6}{27} \) and \( \frac{2}{9} \):
\[
2 \times 27 = 54 \quad \text{and} \quad 6 \times 9 = 54 \quad (\text{equal})
\]

4. For the pair \( \frac{12}{45} \) and \( \frac{2}{9} \):
\[
2 \times 45 = 90 \quad \text{and} \quad 12 \times 9 = 108 \quad (\text{not equal})
\]

5. For the pair \( \frac{20}{27} \) and \( \frac{2}{9} \):
\[
2 \times 27 = 54 \quad \text{and} \quad 20 \times 9 = 180 \quad (\text{not equal})
\]

6. For the pair \( \frac{12}{19} \) and \( \frac{2}{9} \):
\[
2 \times 19 = 38 \quad \text{and} \quad 12 \times 9 = 108 \quad (\text{not equal})
\]

7. For the pair \( \frac{6}{27} \) and \( \frac{2}{9} \):
\[
2 \times 27 = 54 \quad \text{and} \quad 6 \times 9 = 54 \quad (\text{equal})
\]

8. For the pair \( \frac{1}{254} \) and \( \frac{2}{9} \):
\[
2 \times 254 = 508 \quad \text{and} \quad 1 \times 9 = 9 \quad (\text{not equal})
\]

From the evaluations, we find that the pairs of fractions equivalent to \( \frac{2}{9} \) are:

- \( \frac{12}{54} \)
- \( \frac{6}{27} \)

So, the French equivalent fractions are \( \frac{12}{54} \) and \( \frac{6}{27} \).