To determine which fractions are equivalent to [tex]\(\frac{2}{4}\)[/tex], we need to follow these steps:
1. Understand equivalent fractions: Two fractions [tex]\(\frac{a}{b}\)[/tex] and [tex]\(\frac{c}{d}\)[/tex] are equivalent if the cross-multiplication of terms gives the same result. This means [tex]\(a \cdot d = b \cdot c\)[/tex].
2. Check each given fraction:
- For [tex]\(\frac{6}{8}\)[/tex]:
[tex]\[
2 \times 8 = 16 \quad \text{and} \quad 4 \times 6 = 24
\][/tex]
Since [tex]\(16 \neq 24\)[/tex], [tex]\(\frac{6}{8}\)[/tex] is not equivalent to [tex]\(\frac{2}{4}\)[/tex].
- For [tex]\(\frac{6}{12}\)[/tex]:
[tex]\[
2 \times 12 = 24 \quad \text{and} \quad 4 \times 6 = 24
\][/tex]
Since [tex]\(24 = 24\)[/tex], [tex]\(\frac{6}{12}\)[/tex] is equivalent to [tex]\(\frac{2}{4}\)[/tex].
- For [tex]\(\frac{4}{6}\)[/tex]:
[tex]\[
2 \times 6 = 12 \quad \text{and} \quad 4 \times 4 = 16
\][/tex]
Since [tex]\(12 \neq 16\)[/tex], [tex]\(\frac{4}{6}\)[/tex] is not equivalent to [tex]\(\frac{2}{4}\)[/tex].
- For [tex]\(\frac{4}{8}\)[/tex]:
[tex]\[
2 \times 8 = 16 \quad \text{and} \quad 4 \times 4 = 16
\][/tex]
Since [tex]\(16 = 16\)[/tex], [tex]\(\frac{4}{8}\)[/tex] is equivalent to [tex]\(\frac{2}{4}\)[/tex].
- For [tex]\(\frac{5}{7}\)[/tex]:
[tex]\[
2 \times 7 = 14 \quad \text{and} \quad 4 \times 5 = 20
\][/tex]
Since [tex]\(14 \neq 20\)[/tex], [tex]\(\frac{5}{7}\)[/tex] is not equivalent to [tex]\(\frac{2}{4}\)[/tex].
3. Conclude the results: Based on these calculations, the fractions that are equivalent to [tex]\(\frac{2}{4}\)[/tex] are:
[tex]\[
\boxed{\frac{6}{12} \text{ and } \frac{4}{8}}
\][/tex]
