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Order fractions

Ordering fractions means determining their relative size and placing them from least to greatest or greatest to least, understanding that fractions refer to equal-sized wholes. Comparisons may use common numerators or denominators, simple equivalent fractions, benchmarks such as 0, 1/2, and 1, and positions on a number line; the denominator alone does not determine which fraction is greater. General algorithms such as cross-multiplication and comparisons involving arbitrary large or complex fractions are beyond this scope.

Detailed Explanation: Order fractions

To order fractions, compare their sizes and place them from least to greatest. Make sure the fractions refer to wholes that are the same size.

Example: Order 38,12,58\frac{3}{8},\frac{1}{2},\frac{5}{8} from least to greatest.

  1. Two fractions already have the same denominator: 38\frac{3}{8} and 58\frac{5}{8}. Since eighths are the same size, compare the numerators:
3<5, 3<5,

so

38<58. \frac{3}{8}<\frac{5}{8}.
  1. Rewrite 12\frac{1}{2} as an equivalent fraction with denominator 88:
12=48. \frac{1}{2}=\frac{4}{8}.
  1. Now compare:
38,48,58. \frac{3}{8},\quad \frac{4}{8},\quad \frac{5}{8}.
  1. Order the numerators from least to greatest:
3<4<5. 3<4<5.

Therefore, the fractions from least to greatest are

38<12<58.\boxed{\frac{3}{8}<\frac{1}{2}<\frac{5}{8}}.

Remember: the denominator tells how many equal parts make the whole, so the denominator alone does not tell which fraction is greater.

Learn by doing: Order fractions

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    Fraction Strips - Two Strips to Ordering

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