Unit Fraction — Definition, Formula & Examples

A unit fraction is a fraction that has 1 as its numerator. Examples include

\frac{1}{2}

\frac{1}{3}

\frac{1}{4}

, and

\frac{1}{10}

A unit fraction is any fraction of the form $\frac{1}{n}$ , where $n$ is a positive integer greater than zero. It represents exactly one equal part of a whole divided into $n$ parts.

Key Formula

\frac{1}{n}

Where:

$n$ = A positive whole number representing how many equal parts the whole is divided into

How It Works

Every fraction can be built from unit fractions. For example,

\frac{3}{4}

is the same as three copies of

\frac{1}{4}

. Think of slicing a pizza into 4 equal pieces — each single slice is

\frac{1}{4}

of the pizza, and that is a unit fraction. The larger the denominator, the smaller the unit fraction becomes:

\frac{1}{8}

is smaller than

\frac{1}{3}

because you are splitting the whole into more pieces.

Worked Example

Problem: Write 5/6 as a sum of unit fractions.

Identify the unit fraction: The denominator is 6, so the unit fraction is:

\frac{1}{6}

Add copies of the unit fraction: Since the numerator is 5, you need five copies of 1/6:

\frac{5}{6} = \frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6}

Answer:

\frac{5}{6}

equals five unit fractions of

\frac{1}{6}

added together.

Why It Matters

Unit fractions are the building blocks of all fractions. Understanding them helps you compare fractions, add fractions with like denominators, and later work with ratios and division in upper grades.

Common Mistakes

Mistake: Thinking a larger denominator means a larger fraction

Correction: A larger denominator actually means a smaller unit fraction.

\frac{1}{10}

is smaller than

\frac{1}{2}

because the whole is split into more pieces, making each piece smaller.