Recall decimal values of common fractions (1/8, 1/3, 1/6, 1/7, 1/9, 1/11) on sight.
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Know these values without thinking. They turn many questions into one-step answers.
For unit fractions, a bigger denominator means a smaller value: \(\frac{1}{5} > \frac{1}{9}\). To find the fraction closest to a decimal, compare the distances: \(0.3\) is about \(0.03\) from \(\frac{1}{3}\) but \(0.05\) from \(\frac{1}{4}\).
Common slip: thinking \(\frac{1}{12}\) is bigger than \(\frac{1}{8}\) because 12 is bigger than 8.
For unit fractions, a smaller denominator means a larger value. From greatest to least: \(\frac{1}{8}\) > \(\frac{1}{9}\) > \(\frac{1}{10}\) > \(\frac{1}{11}\), so \(\frac{1}{11}\) is least. (Choosing the smallest denominator gives \(\frac{1}{8}\), the greatest value. The other choices are not at either end of the list.)
Convert each unit fraction to a decimal and compare to the target: \(\frac{1}{2}\) \(\approx 0.500\), \(\frac{1}{6}\) \(\approx 0.167\), \(\frac{1}{7}\) \(\approx 0.143\), \(\frac{1}{8}\) \(\approx 0.125\). \(\frac{1}{6}\) is closest to 0.27.
\(0.\overline{3} = \frac{1}{3}\) and \(0.\overline{6} = \frac{2}{3}\), so the sum is \(\frac{3}{3} = 1\). (\(0.\overline{9}\) is exactly 1, not a little less than 1. Adding 0.3 + 0.6 gives \(\frac{9}{10}\). Adding 0.33 + 0.66 gives \(\frac{99}{100}\). Adding \(\frac{3}{9} + \frac{6}{9}\) as \(\frac{3 + 6}{9 + 9}\) gives \(\frac{1}{2}\).)