Question

which fractions are equivalent to \\(\frac{2}{8}\\)?
hint: there may be more than one.
\\(\frac{3}{12}\\) \\(\frac{1}{4}\\) \\(\frac{7}{14}\\) \\(\frac{5}{20}\\)

Explanation:

Step1: Simplify the given fraction

Simplify \(\frac{2}{8}\) by dividing numerator and denominator by their greatest common divisor (GCD), which is 2. So \(\frac{2\div2}{8\div2}=\frac{1}{4}\).

Step2: Check each fraction

• For \(\frac{3}{12}\): Divide numerator and denominator by GCD 3. \(\frac{3\div3}{12\div3}=\frac{1}{4}\), so it is equivalent.
• For \(\frac{1}{4}\): It is the simplified form of \(\frac{2}{8}\), so equivalent.
• For \(\frac{7}{14}\): Divide numerator and denominator by GCD 7. \(\frac{7\div7}{14\div7}=\frac{1}{2}

eq\frac{1}{4}\), so not equivalent (this was a mistake in the original check). Wait, no, wait: Wait, \(\frac{2}{8}=\frac{1}{4}\), \(\frac{7}{14}=\frac{1}{2}\), so actually \(\frac{7}{14}\) is not equivalent. Wait, maybe the original problem's fraction was \(\frac{2}{8}\) or maybe I misread. Wait, the original fraction is \(\frac{2}{8}\)? Wait, no, maybe the original fraction was \(\frac{2}{8}\) or maybe \(\frac{2}{8}\) is \(\frac{1}{4}\), and \(\frac{7}{14}\) is \(\frac{1}{2}\), so that's not equivalent. Wait, maybe the original fraction was \(\frac{2}{8}\) (which is \(\frac{1}{4}\)) and the other fractions: \(\frac{3}{12}=\frac{1}{4}\), \(\frac{1}{4}\) is same, \(\frac{7}{14}=\frac{1}{2}\) (not same), \(\frac{5}{20}=\frac{1}{4}\) (since \(5\div5 = 1\), \(20\div5=4\)). So let's recalculate:

Wait, \(\frac{2}{8}=\frac{1}{4}\) (divide numerator and denominator by 2). Now check each:

• \(\frac{3}{12}\): divide numerator and denominator by 3: \(\frac{1}{4}\) → equivalent.
• \(\frac{1}{4}\): same as simplified \(\frac{2}{8}\) → equivalent.
• \(\frac{7}{14}\): divide by 7: \(\frac{1}{2}\) → not equivalent.
• \(\frac{5}{20}\): divide by 5: \(\frac{1}{4}\) → equivalent.

So the correct equivalent fractions are \(\frac{3}{12}\), \(\frac{1}{4}\), \(\frac{5}{20}\). The \(\frac{7}{14}\) is not equivalent (it's \(\frac{1}{2}\)).

Answer:

The equivalent fractions to \(\frac{2}{8}\) (which simplifies to \(\frac{1}{4}\)) are \(\frac{3}{12}\), \(\frac{1}{4}\), and \(\frac{5}{20}\). So the correct options (assuming the boxes are labeled with these fractions) are the ones with \(\frac{3}{12}\), \(\frac{1}{4}\), and \(\frac{5}{20}\).