Question

Which pair of fractions are equivalent to 2/9 5/27 and 12/54, 6/27 or 12/54, 6/20 712/45, 20/27 or 12/19

Answer 1

To determine which pair of fractions is equivalent to \( \frac{2}{9} \), we will simplify each fraction and compare it to \( \frac{2}{9} \).

1. **Check \( \frac{5}{27} \):**
- \( \frac{2}{9} = \frac{2 \times 3}{9 \times 3} = \frac{6}{27} \)
- Since \( \frac{5}{27} \) is not equal to \( \frac{6}{27} \), it is not equivalent.

2. **Check \( \frac{12}{54} \):**
- Simplify \( \frac{12}{54} \) by dividing both the numerator and denominator by 6:
\[
\frac{12 \div 6}{54 \div 6} = \frac{2}{9}
\]
- \( \frac{12}{54} \) is equivalent to \( \frac{2}{9} \).

3. **Check \( \frac{6}{27} \):**
- Simplify \( \frac{6}{27} \) by dividing both by 3:
\[
\frac{6 \div 3}{27 \div 3} = \frac{2}{9}
\]
- \( \frac{6}{27} \) is also equivalent to \( \frac{2}{9} \).

4. **Check \( \frac{12}{54} \) and \( \frac{6}{20} \):**
- As we found earlier, \( \frac{12}{54} \) is equivalent.
- Simplify \( \frac{6}{20} \) by dividing both by 2:
\[
\frac{6 \div 2}{20 \div 2} = \frac{3}{10}
\]
- \( \frac{6}{20} \) is not equivalent.

5. **Check \( \frac{712}{45} \):**
- This fraction is much larger than \( \frac{2}{9} \) and clearly does not simplify to it.

6. **Check \( \frac{20}{27} \):**
- This fraction is not equivalent as the denominator does not match either.

7. **Check \( \frac{12}{19} \):**
- This fraction is not equivalent as the denominator does not match either.

Thus, the pairs of fractions that are equivalent to \( \frac{2}{9} \) are \( \frac{12}{54} \) and \( \frac{6}{27} \).

So the answer is: **\( \frac{12}{54} \) and \( \frac{6}{27} \)**.