Unit Fraction Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Express 712\dfrac{7}{12} as a sum of distinct unit fractions with denominator at most 1212.

Solution

  1. 1
    A unit fraction has numerator 11, such as 12,13,14,…\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{4}, \ldots
  2. 2
    Start with the largest unit fraction ≤712\leq \dfrac{7}{12}: 12=612\dfrac{1}{2} = \dfrac{6}{12}. Remainder: 712−612=112\dfrac{7}{12} - \dfrac{6}{12} = \dfrac{1}{12}.
  3. 3
    So 712=12+112\dfrac{7}{12} = \dfrac{1}{2} + \dfrac{1}{12}. Both denominators are at most 1212. ✓

Answer

712=12+112\dfrac{7}{12} = \dfrac{1}{2} + \dfrac{1}{12}
Any positive fraction can be written as a sum of distinct unit fractions. The greedy approach — always subtracting the largest possible unit fraction — is a systematic method. Unit fractions were central to ancient Egyptian mathematics.

About Unit Fraction

A fraction with numerator 1, like 13\frac{1}{3} or 18\frac{1}{8}, representing exactly one equal part of a whole.

Learn more about Unit Fraction →

More Unit Fraction Examples

Example 2 medium

Which is larger, [formula] or [formula]? Explain using the meaning of unit fractions, then verify wi

Example 3 easy

Order the unit fractions [formula], [formula], [formula], [formula] from least to greatest.

Example 4 medium

A recipe uses [formula] cup of flour. Express this as a sum of unit fractions using only [formula] a

← All Unit Fraction Examples Unit Fraction Concept