To determine which fractions are equivalent to [tex]\(\frac{4}{8}\)[/tex], we follow these steps:
1. Simplify the given fraction [tex]\(\frac{4}{8}\)[/tex]:
The fraction [tex]\(\frac{4}{8}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4.
[tex]\[
\frac{4 \div 4}{8 \div 4} = \frac{1}{2}
\][/tex]
Therefore, [tex]\(\frac{4}{8}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex].
2. Compare each fraction with [tex]\(\frac{1}{2}\)[/tex]:
We need to check which of the given fractions are equivalent to [tex]\(\frac{1}{2}\)[/tex].
- [tex]\(\frac{2}{4}\)[/tex]:
Simplify [tex]\(\frac{2}{4}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
[tex]\[
\frac{2 \div 2}{4 \div 2} = \frac{1}{2}
\][/tex]
Therefore, [tex]\(\frac{2}{4}\)[/tex] is equivalent to [tex]\(\frac{1}{2}\)[/tex].
- [tex]\(\frac{2}{6}\)[/tex]:
Simplify [tex]\(\frac{2}{6}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
[tex]\[
\frac{2 \div 2}{6 \div 2} = \frac{1}{3}
\][/tex]
Therefore, [tex]\(\frac{2}{6}\)[/tex] is not equivalent to [tex]\(\frac{1}{2}\)[/tex].
- [tex]\(\frac{1}{4}\)[/tex]:
The fraction [tex]\(\frac{1}{4}\)[/tex] is already in its simplest form and is not equivalent to [tex]\(\frac{1}{2}\)[/tex].
- [tex]\(\frac{1}{2}\)[/tex]:
The fraction is already [tex]\(\frac{1}{2}\)[/tex], which means it is equivalent to itself.
- [tex]\(\frac{1}{5}\)[/tex]:
The fraction [tex]\(\frac{1}{5}\)[/tex] is already in its simplest form and is not equivalent to [tex]\(\frac{1}{2}\)[/tex].
3. List the equivalent fractions:
From the comparisons above, the fractions that are equivalent to [tex]\(\frac{1}{2}\)[/tex] (and thus to [tex]\(\frac{4}{8}\)[/tex]) are:
[tex]\[
\frac{2}{4} \text{ and } \frac{1}{2}
\][/tex]
Therefore, the correct answers are:
[tex]\[
\frac{2}{4} \quad \text{and} \quad \frac{1}{2}
\][/tex]
