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Order fractions

Ordering fractions involves determining relative size, including fractions with unlike denominators and mixed numbers, by reasoning with equivalent fractions, common denominators, benchmark values such as 0, 1/2, and 1, or positions on a number line. A larger denominator does not by itself indicate a larger fraction; the scope is positive fractions and mixed numbers, not negative fractions or generalized algebraic methods for ordering rational numbers.

Detailed Explanation: Order fractions

To order fractions, rewrite them so they have the same denominator. Then compare the numerators: with the same denominator, the fraction with the greater numerator is larger.

Example: Order these from least to greatest:

23,34,116,56\frac{2}{3},\quad \frac{3}{4},\quad 1\frac{1}{6},\quad \frac{5}{6}
  1. Change the mixed number into an improper fraction:
116=761\frac{1}{6}=\frac{7}{6}

  1. Find a common denominator. The least common denominator of 33, 44, and 66 is 1212.

  2. Rewrite each fraction with denominator 1212:

23=812\frac{2}{3}=\frac{8}{12} 34=912\frac{3}{4}=\frac{9}{12} 76=1412\frac{7}{6}=\frac{14}{12} 56=1012\frac{5}{6}=\frac{10}{12}
  1. Compare the numerators:
8<9<10<148<9<10<14
  1. Write the fractions in the original form:
23<34<56<116\boxed{\frac{2}{3}<\frac{3}{4}<\frac{5}{6}<1\frac{1}{6}}

Remember: a larger denominator does not automatically mean a larger fraction. Use equivalent fractions or a benchmark such as 11 to compare accurately.

Learn by doing: Order fractions

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    Fraction Strips - Two Strips to Ordering

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