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Expressing Fractions as Sums of Unit Fractions

Expressing Fractions as Sums of Unit Fractions

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A unit fraction is a fraction with a numerator of \(1\) and a positive integer as the denominator, e.g., \(\frac{1}{2},\,\frac{1}{3},\,\frac{1}{5}...\) Express the following fractions as a sum of distinct unit fractions. Any valid decomposition is accepted.

  1. \(\frac{9}{10}\)
  2. \(\frac{8}{13}\)
  3. \(\frac{10}{17}\)
  4. \(\frac{13}{28}\)

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Answer:(a) \(\frac12+\frac13+\frac1{15}\). (b) \(\frac12+\frac19+\frac1{234}\). (c) \(\frac12+\frac1{12}+\frac1{204}\). (d) \(\frac13+\frac18+\frac1{168}\).

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