Question

Which fraction is equivalent to StartFraction 2 Over 6 EndFraction?
StartFraction 3 Over 7 EndFraction, because StartFraction 2 Over 6 EndFraction = StartFraction 2 + 1 Over 6 + 1 EndFraction = StartFraction 3 Over 7 EndFraction
StartFraction 3 Over 9 EndFraction, because StartFraction 2 Over 6 EndFraction = one-third and One-third = StartFraction 3 Over 9 EndFraction
StartFraction 3 Over 12 EndFraction, because StartFraction 2 Over 6 EndFraction = one-third and One-third = StartFraction 3 Over 12 EndFraction
StartFraction 3 Over 8 EndFraction, because StartFraction 2 Over 6 EndFraction = one-half = StartFraction 2 + 1 Over 6 + 2 EndFraction = StartFraction 3 Over 8 EndFraction

Answer 1

To find a fraction equivalent to \( \frac{2}{6} \), we should first simplify \( \frac{2}{6} \).

1. Simplifying \( \frac{2}{6} \):
\[
\frac{2}{6} = \frac{2 \div 2}{6 \div 2} = \frac{1}{3}
\]

Next, we need to check which of the given fractions is also equal to \( \frac{1}{3} \):

- **For \( \frac{3}{7} \):**
This does not equal \( \frac{1}{3} \).

- **For \( \frac{3}{9} \):**
Simplifying \( \frac{3}{9} \):
\[
\frac{3}{9} = \frac{3 \div 3}{9 \div 3} = \frac{1}{3}
\]
This is equivalent to \( \frac{2}{6} \).

- **For \( \frac{3}{12} \):**
Simplifying \( \frac{3}{12} \):
\[
\frac{3}{12} = \frac{3 \div 3}{12 \div 3} = \frac{1}{4}
\]
This does not equal \( \frac{1}{3} \).

- **For \( \frac{3}{8} \):**
This does not equal \( \frac{1}{3} \).

Thus, the correct equivalent fraction to \( \frac{2}{6} \) is \( \frac{3}{9} \), because \( \frac{2}{6} = \frac{1}{3} \) and \( \frac{3}{9} = \frac{1}{3} \).

Therefore, the answer is:
**StartFraction 3 Over 9 EndFraction, because StartFraction 2 Over 6 EndFraction = one-third and One-third = StartFraction 3 Over 9 EndFraction.**