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Select the group of fractions in an ascending order :

  • A.\(\frac{1}{4} \lt \frac{1}{3} \lt \frac{1}{2}\)
  • B.\(\frac{1}{2} \lt \frac{1}{4} \lt \frac{1}{3}\)
  • C.\(\frac{1}{2} \lt \frac{1}{3} \lt \frac{1}{4}\)
  • D.\(\frac{1}{3} \lt \frac{1}{4} \lt \frac{1}{2}\)

Answer: A

The ascending order is \(\frac{1}{4} \lt \frac{1}{3} \lt \frac{1}{2}\).

All three fractions have numerator 1, so the larger the denominator, the smaller each part: a whole cut into four parts gives smaller pieces than one cut into three or two. So one quarter is the smallest and one half the largest.

Checking with a common denominator of 12: \(\frac{1}{4} = \frac{3}{12}\), \(\frac{1}{3} = \frac{4}{12}\) and \(\frac{1}{2} = \frac{6}{12}\). The other options put a larger fraction before a smaller one; option C is the descending order, the common error of ranking by the size of the denominator.

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