Question

which fractions are equivalent to \\(\frac{8}{9}\\)?
hint: there may be more than one.
\\(\frac{7}{11}\\) \\(\frac{11}{20}\\) \\(\frac{8}{12}\\) \\(\frac{16}{18}\\)

Explanation:

Step1: Recall equivalent fraction rule

Equivalent fractions are found by multiplying or dividing numerator and denominator by the same non - zero number. 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 \(\frac{7}{11}\)

Simplify \(\frac{7}{11}\) and \(\frac{8}{9}\). Cross - multiply: \(7\times9 = 63\) and \(8\times11=88\). Since \(63
eq88\), \(\frac{7}{11}\) is not equivalent to \(\frac{8}{9}\).

Step3: Check \(\frac{11}{20}\)

Cross - multiply: \(11\times9 = 99\) and \(8\times20 = 160\). Since \(99
eq160\), \(\frac{11}{20}\) is not equivalent to \(\frac{8}{9}\).

Step4: Check \(\frac{8}{12}\)

Simplify \(\frac{8}{12}=\frac{8\div4}{12\div4}=\frac{2}{3}\). Cross - multiply \(\frac{2}{3}\) and \(\frac{8}{9}\): \(2\times9 = 18\) and \(3\times8 = 24\). Since \(18
eq24\), \(\frac{8}{12}\) is not equivalent to \(\frac{8}{9}\).

Step5: Check \(\frac{16}{18}\)

Simplify \(\frac{16}{18}=\frac{16\div2}{18\div2}=\frac{8}{9}\). So \(\frac{16}{18}\) is equivalent to \(\frac{8}{9}\).

Answer:

The fraction equivalent to \(\frac{8}{9}\) is \(\frac{16}{18}\) (among the given options, only \(\frac{16}{18}\) is equivalent to \(\frac{8}{9}\) as \(\frac{16\div2}{18\div2}=\frac{8}{9}\), while \(\frac{7}{11}\), \(\frac{11}{20}\), and \(\frac{8}{12}\) are not equivalent when checked via cross - multiplication or simplification).