Unit Fraction Math Example 3

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

Example 3

easy
Order the unit fractions 13\dfrac{1}{3}, 110\dfrac{1}{10}, 15\dfrac{1}{5}, 12\dfrac{1}{2} from least to greatest.

Solution

  1. 1
    For unit fractions, larger denominator means smaller value.
  2. 2
    Denominators in decreasing order: 10>5>3>210 > 5 > 3 > 2, so the fractions in increasing order are 110<15<13<12\dfrac{1}{10} < \dfrac{1}{5} < \dfrac{1}{3} < \dfrac{1}{2}.

Answer

110<15<13<12\dfrac{1}{10} < \dfrac{1}{5} < \dfrac{1}{3} < \dfrac{1}{2}
The key property of unit fractions is that they decrease as the denominator increases. Ordering them is therefore as simple as reversing the order of their denominators — no computation needed.

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.

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More Unit Fraction Examples

Example 1 easy

Express [formula] as a sum of distinct unit fractions with denominator at most [formula].

Example 2 medium

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

Example 4 medium

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

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