## Unit Fractions: Part of the Number One

When it comes to unit fractions, each unit fraction is a part of the number 1. For example, 1/2 is a half of 1, 1/3 is a third of 1, 1/4 is a fourth of 1, and so on. To illustrate this, let's consider your pie.

Let your pie represent the number 1. If you slice the pie into *n* equal sized slices, then you split the pie, or 1, into *n* equal parts, where each slice is a part of the pie, or a part of 1. For instance, if we cut the pie into 6 equal slices, then 1 slice represents 1/6 of the whole pie. In the same way, if we break 1 into 6 equal parts, 1 part represents 1/6 of 1.

Unit fractions are 1 part of the number 1. Notice that the more pieces you slice the pie into, the smaller the pieces of pie become. This tells us that the larger the denominator of a unit fraction, the smaller the part of 1 it represents.

Let's break this down even further to solidify our understanding of these types of fractions. In general, a fraction's denominator tells us the number of parts we are breaking the whole into. Since the numerator's always 1 in unit fractions, the denominator tells us how many parts you're breaking 1 into, and you call these parts units. Therefore, the denominator of a unit fraction tells us the unit.

## Fractions Made Up of Unit Fractions

You're probably getting a little impatient now because you want to eat your pie, but let's illustrate a few more things. Notice that if you break the pie into *n* equal slices and then take a certain number of those slices, let's say *m* slices, those *m* slices represent *m*/*n*. In the same way, if we break 1 into *n* equal parts and then take *m* parts, we have *m*/*n* of 1. This fact illustrates that all fractions are made up of unit fractions.

For example, cut your pie into 4 equal parts. 1 slice is 1/4 of the pie, two slices is 2/4 of the pie, three slices is 3/4 of the pie, and four slices is 4/4 of the pie (or the whole pie). Again letting the pie represent the number 1 and the slices each represent the unit fraction 1/4, we see that 1/4, 2/4, 3/4, and 4/4 are all made up of the unit fraction 1/4.

In general, the fraction *m*/*n* is made up of *m* copies of the unit fraction 1/*n*. *n* is the unit and *m* tells us how many of them there are. Use the facts about unit fractions to work with unit fractions and perform operations on unit fractions.

## Example

Assume you have cut your pie into 8 equal slices. If you consider the whole pie to be the number 1, then 1 slice of the pie represents the unit fraction 1/8. Now, suppose you eat 2 slices of the pie, and your friend eats 1 slice of the pie, so 3 slices have been eaten all together. How much of the pie do those three slices represent?

To answer this, consider the pie to be the number 1, and each slice to represent the unit fraction 1/8. Since you've eaten 3 slices of pie, you have 3 copies of the unit fraction 1/8. Thus, those 3 slices represent 3/8 of the pie. Eight represents the **unit**, or how many equal parts the pie is split into, and 3 tells you there are three of those parts. Seeing this relationship helps you better understand how unit fractions are parts of the number 1, and that all fractions are made up of unit fractions.

## Lesson Summary

**Unit fractions** are fractions with numerators that are 1. These types of fractions are a part of the number 1. Break the number 1 into *n* equal parts; each part represents the unit fraction 1/*n*.

In general, a fraction's denominator tells us how many parts we are breaking the fraction's numerator into. Every fraction is made up of unit fractions. In general, *m*/*n* is *m* copies of the unit fraction 1/*n*. Use this information to better analyze unit fractions and to perform operations with unit fractions.