Question

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

Explanation:

Step1: Recall equivalent fractions

Equivalent fractions are obtained by multiplying or dividing both numerator and denominator by the same non - zero number. For a fraction \(\frac{a}{b}\), an equivalent fraction can be found as \(\frac{a\times k}{b\times k}\) or \(\frac{a\div k}{b\div k}\) where \(k
eq0\).

Step2: Check each option

• For option \(\frac{1}{2}\): The numerator of \(\frac{1}{3}\) is 1 and denominator is 3. To get from 3 to 2, we can't multiply or divide 3 by a non - zero integer to get 2. And \(\frac{1}{2}

eq\frac{1}{3}\).

• For option \(\frac{2}{6}\): We know that if we multiply the numerator and denominator of \(\frac{1}{3}\) by 2, we have \(\frac{1\times2}{3\times2}=\frac{2}{6}\). So \(\frac{2}{6}\) is equivalent to \(\frac{1}{3}\).
• For option \(\frac{1}{6}\): If we try to get from \(\frac{1}{3}\) to \(\frac{1}{6}\), we would have to divide the numerator by 1 and the denominator by \(\frac{3}{6} = 0.5\), but we need to multiply or divide by the same non - zero number. \(\frac{1}{3}=\frac{2}{6}

eq\frac{1}{6}\).

• For option \(\frac{1}{8}\): The denominator 3 can't be transformed into 8 by multiplying or dividing by a non - zero integer to get an equivalent fraction with numerator 1. So \(\frac{1}{8}

eq\frac{1}{3}\).

Answer:

\(\frac{2}{6}\) (the second option)