Skill: Compose a whole from unit fractions

Explanation and Free Practice Resources

A whole is composed of a specific number of equal unit fractions: $b$ copies of $1/b$ make $1$ , such as $3$ copies of $1/3$ or $8$ copies of $1/8$ . This understanding connects equal partitioning of a bar or number line with the relationship $b \times \frac{1}{b}=1$ , using denominators such as 2, 3, 4, 6, and 8; it does not include adding unlike fractions or more advanced fraction operations.

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Detailed Explanation: Compose a whole from unit fractions

A unit fraction has a numerator of $1$ , such as $\frac{1}{6}$ . The denominator, $6$ , tells us that one whole is split into $6$ equal parts.

Example: How many copies of $\frac{1}{6}$ make one whole?

The denominator is $6$ , so divide the whole into $6$ equal parts.
Each part is $\frac{1}{6}$ .
Count all $6$ parts:

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

So, $6$ copies of $\frac{1}{6}$ make one whole.

This can also be written as:

6 \times \frac{1}{6}=1

In general, $b$ copies of $\frac{1}{b}$ make $1$ .

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Fractions Fourths - Which Set Makes a Whole

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