Question

which fractions are equivalent to \\(\frac{4}{6}\\)?
hint: there may be more than one.
\\(\frac{4}{7}\\) \\(\frac{12}{17}\\) \\(\frac{1}{2}\\) \\(\frac{6}{9}\\)

Explanation:

Step1: Simplify the given fraction

Simplify \(\frac{4}{6}\) by dividing numerator and denominator by their greatest common divisor, which is 2. So \(\frac{4\div2}{6\div2}=\frac{2}{3}\).

Step2: Check each option

• For \(\frac{4}{7}\): Cross - multiply \(4\times3 = 12\) and \(7\times2=14\). Since \(12

eq14\), \(\frac{4}{7}\) is not equivalent to \(\frac{4}{6}\).

• For \(\frac{12}{17}\): Cross - multiply \(12\times6 = 72\) and \(17\times4 = 68\). Since \(72

eq68\), \(\frac{12}{17}\) is not equivalent to \(\frac{4}{6}\).

• For \(\frac{1}{2}\): Cross - multiply \(1\times6 = 6\) and \(2\times4 = 8\). Since \(6

eq8\), \(\frac{1}{2}\) is not equivalent to \(\frac{4}{6}\).

• For \(\frac{6}{9}\): Simplify \(\frac{6}{9}\) by dividing numerator and denominator by 3, we get \(\frac{6\div3}{9\div3}=\frac{2}{3}\), which is the same as the simplified form of \(\frac{4}{6}\) (\(\frac{2}{3}\)). So \(\frac{6}{9}\) is equivalent to \(\frac{4}{6}\).

Answer:

The fraction equivalent to \(\frac{4}{6}\) is \(\frac{6}{9}\) (among the given options).