Skill: Compare simple fractions using benchmarks

To compare fractions, think about where each one belongs compared with a benchmark such as $0$, $\frac{1}{2}$, or $1$.

Example: Compare $\frac{3}{8}$ and $\frac{5}{6}$

Step 1: Compare $\frac{3}{8}$ with $\frac{1}{2}$.

One-half of 8 equal parts is 4 parts:

$$\frac{1}{2}=\frac{4}{8}$$

Since 3 parts is less than 4 parts,

$$\frac{3}{8}<\frac{1}{2}$$

Step 2: Compare $\frac{5}{6}$ with $\frac{1}{2}$.

One-half of 6 equal parts is 3 parts:

$$\frac{1}{2}=\frac{3}{6}$$

Since 5 parts is more than 3 parts,

$$\frac{5}{6}>\frac{1}{2}$$

Step 3: Compare the fractions.

$\frac{3}{8}$ is less than $\frac{1}{2}$, while $\frac{5}{6}$ is greater than $\frac{1}{2}$. Therefore,

$$\boxed{\frac{3}{8}<\frac{5}{6}}$$

The denominator tells how many equal parts make the whole, so a larger denominator does not automatically mean a larger fraction. Use benchmarks to decide where each fraction is located.