To determine which fraction is equivalent to [tex]\(\frac{1}{6}\)[/tex], we need to compare each given fraction to [tex]\(\frac{1}{6}\)[/tex] by simplifying them to their simplest form or by comparing their decimal values.
1. Compare [tex]\(\frac{3}{8}\)[/tex] to [tex]\(\frac{1}{6}\)[/tex]:
- Convert each fraction to decimal form:
[tex]\[
\frac{1}{6} = 0.1667 \quad (\text{approximately})
\][/tex]
[tex]\[
\frac{3}{8} = 0.375
\][/tex]
- Clearly, [tex]\(0.375 \neq 0.1667\)[/tex], so [tex]\(\frac{3}{8}\)[/tex] is not equivalent to [tex]\(\frac{1}{6}\)[/tex].
2. Compare [tex]\(\frac{2}{8}\)[/tex] to [tex]\(\frac{1}{6}\)[/tex]:
- Simplify [tex]\(\frac{2}{8}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[
\frac{2}{8} = \frac{1}{4}
\][/tex]
- Convert each fraction to decimal form:
[tex]\[
\frac{1}{4} = 0.25
\][/tex]
[tex]\[
\frac{1}{6} = 0.1667
\][/tex]
- Clearly, [tex]\(0.25 \neq 0.1667\)[/tex], so [tex]\(\frac{2}{8}\)[/tex] is not equivalent to [tex]\(\frac{1}{6}\)[/tex].
3. Compare [tex]\(\frac{3}{24}\)[/tex] to [tex]\(\frac{1}{6}\)[/tex]:
- Simplify [tex]\(\frac{3}{24}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
[tex]\[
\frac{3}{24} = \frac{1}{8}
\][/tex]
- Convert each fraction to decimal form:
[tex]\[
\frac{1}{8} = 0.125
\][/tex]
[tex]\[
\frac{1}{6} = 0.1667
\][/tex]
- Clearly, [tex]\(0.125 \neq 0.1667\)[/tex], so [tex]\(\frac{3}{24}\)[/tex] is not equivalent to [tex]\(\frac{1}{6}\)[/tex].
4. Compare [tex]\(\frac{4}{24}\)[/tex] to [tex]\(\frac{1}{6}\)[/tex]:
- Simplify [tex]\(\frac{4}{24}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
[tex]\[
\frac{4}{24} = \frac{1}{6}
\][/tex]
- Since [tex]\(\frac{4}{24}\)[/tex] simplifies exactly to [tex]\(\frac{1}{6}\)[/tex], these fractions are equivalent.
Therefore, the fraction that is equivalent to [tex]\(\frac{1}{6}\)[/tex] is [tex]\(\frac{4}{24}\)[/tex].
