Question

which fractions are equivalent to \\(\frac{14}{18}\\)?
hint: there may be more than one.
\\(\frac{2}{5}\\) \\(\frac{10}{15}\\) \\(\frac{7}{9}\\) \\(\frac{3}{7}\\)

Explanation:

Step1: Simplify the given fraction

Simplify \(\frac{14}{18}\) by dividing numerator and denominator by their greatest common divisor, which is 2. So \(\frac{14\div2}{18\div2}=\frac{7}{9}\).

Step2: Check each option

• For \(\frac{2}{5}\): Cross - multiply \(14\times5 = 70\) and \(18\times2=36\). Since \(70

eq36\), \(\frac{2}{5}\) is not equivalent to \(\frac{14}{18}\).

• For \(\frac{10}{15}\): Simplify \(\frac{10}{15}=\frac{2}{3}\), and \(\frac{14}{18}=\frac{7}{9}\). Cross - multiply \(7\times3 = 21\) and \(9\times2 = 18\). Since \(21

eq18\), \(\frac{10}{15}\) is not equivalent to \(\frac{14}{18}\).

• For \(\frac{7}{9}\): As we saw in Step 1, \(\frac{14}{18}\) simplifies to \(\frac{7}{9}\), so \(\frac{7}{9}\) is equivalent.
• For \(\frac{3}{7}\): Cross - multiply \(14\times7=98\) and \(18\times3 = 54\). Since \(98

eq54\), \(\frac{3}{7}\) is not equivalent to \(\frac{14}{18}\).

Answer:

The fraction equivalent to \(\frac{14}{18}\) is \(\frac{7}{9}\) (the third option: \(\frac{7}{9}\)). The other options (\(\frac{2}{5}\), \(\frac{10}{15}\), \(\frac{3}{7}\)) are not equivalent. So the correct one is the third option: \(\frac{7}{9}\)