Question

which fractions are equivalent to \\(\frac{9}{10}\\)?
hint: there may be more than one.
\\(\frac{18}{20}\\) \\(\frac{9}{11}\\) \\(\frac{15}{17}\\) \\(\frac{10}{13}\\)

Explanation:

Step1: Recall equivalent fraction rule

To find equivalent fractions, we multiply or divide the 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 \(\frac{18}{20}\)

For the fraction \(\frac{9}{10}\), if we multiply the numerator and denominator by 2, we get \(\frac{9\times2}{10\times2}=\frac{18}{20}\). So \(\frac{18}{20}\) is equivalent to \(\frac{9}{10}\).

Step3: Check \(\frac{9}{11}\)

To check if \(\frac{9}{11}\) is equivalent to \(\frac{9}{10}\), we can use cross - multiplication. If \(\frac{9}{10}=\frac{9}{11}\), then \(9\times11 = 9\times10\). But \(99
eq90\), so \(\frac{9}{11}\) is not equivalent to \(\frac{9}{10}\).

Step4: Check \(\frac{15}{17}\)

Using cross - multiplication for \(\frac{9}{10}\) and \(\frac{15}{17}\), we have \(9\times17=153\) and \(10\times15 = 150\). Since \(153
eq150\), \(\frac{15}{17}\) is not equivalent to \(\frac{9}{10}\).

Step5: Check \(\frac{10}{13}\)

Using cross - multiplication for \(\frac{9}{10}\) and \(\frac{10}{13}\), we get \(9\times13 = 117\) and \(10\times10=100\). Since \(117
eq100\), \(\frac{10}{13}\) is not equivalent to \(\frac{9}{10}\).

Answer:

The fraction equivalent to \(\frac{9}{10}\) is \(\frac{18}{20}\)