Question

which fraction is equivalent to \\(\frac{1}{2}\\)? \\(\frac{2}{3}\\) \\(\frac{3}{8}\\) \\(\frac{2}{4}\\) \\(\frac{4}{6}\\)

Explanation:

Step1: Recall equivalent fraction rule

To find an equivalent fraction, we can multiply or divide both the numerator and the denominator of a fraction by the same non - zero number. The rule is that for a fraction \(\frac{a}{b}\), an equivalent fraction is \(\frac{a\times k}{b\times k}\) or \(\frac{a\div k}{b\div k}\) where \(k
eq0\).

Step2: Check each option

• For \(\frac{2}{3}\): If we try to get from \(\frac{1}{2}\) to \(\frac{2}{3}\), \(\frac{1\times2}{2\times2}=\frac{2}{4}

eq\frac{2}{3}\), so \(\frac{2}{3}\) is not equivalent to \(\frac{1}{2}\).

• For \(\frac{3}{8}\): \(\frac{1\times3}{2\times3}=\frac{3}{6}

eq\frac{3}{8}\), so \(\frac{3}{8}\) is not equivalent to \(\frac{1}{2}\).

• For \(\frac{2}{4}\): We can divide the numerator and denominator of \(\frac{2}{4}\) by 2. \(\frac{2\div2}{4\div2}=\frac{1}{2}\), so \(\frac{2}{4}\) is equivalent to \(\frac{1}{2}\).
• For \(\frac{4}{6}\): \(\frac{1\times4}{2\times4}=\frac{4}{8}

eq\frac{4}{6}\), so \(\frac{4}{6}\) is not equivalent to \(\frac{1}{2}\).

Answer:

\(\frac{2}{4}\) (the third option)