Comparing unit fractions

In a nutshell

A unit fraction is any fraction which has a numerator of $$1$$ and a denominator that is a whole number. When comparing unit fractions, the larger the denominator, the smaller the fraction.

Example 1

If you were offered $$\frac{1}{8}$$ or $$\frac{1}{6}$$ of a pizza, which slice would be larger?

$$\frac{1}{8}$$

$$\frac{1}{6}$$

$$\longrightarrow \frac{1}{8} < \frac{1}{6}$$

These two unit fractions have different denominators. Therefore  $$\frac{1}{8}$$  is the smaller fraction, as it has the larger denominator of the two fractions.

Fraction bar models

Fractions can also be compared using bar models.  Bar models are helpful because they allow you to compare the size of different unit fractions.

Procedure

1. Draw two 'bars' of equal length, one above the other.
   
2. Look at the denominator of the first fraction. Split the first bar into the number of parts given by the denominator. They should all be equal sized.
   
3. Shade in one of the parts.
   
4. Repeat steps 2 and 3 with the second fraction.
   
5. Compare the marked lengths.
   

Example 2

Which fraction is larger, $$\frac{1}{3}$$ or $$\frac{1}{5}$$ ? Fraction bar models: From the bar models, you can see that $$\frac{1}{3}}$$ is larger than $$\frac{1}{5}$$.    If you want to use greater than or less than signs, you could write $$\frac{1}{3} > \frac{1}{5}$$.

Example 3

Which fraction is bigger, $$\frac{1}{10}$$ or $$\frac{1}{8}$$?

From the bar models, you can see that $$\frac{1}{8}$$ is bigger than $$\frac{1}{10}$$, so you can write that like this: $$\frac{1}{8}>\frac{1}{10}$$.