Skill: Order fractions

To order fractions, compare their sizes and place them from least to greatest. Make sure the fractions refer to wholes that are the same size.

Example: Order $\frac{3}{8},\frac{1}{2},\frac{5}{8}$ from least to greatest.

1. Two fractions already have the same denominator: $\frac{3}{8}$ and $\frac{5}{8}$. Since eighths are the same size, compare the numerators:

$$3<5,$$

so

$$\frac{3}{8}<\frac{5}{8}.$$

2. Rewrite $\frac{1}{2}$ as an equivalent fraction with denominator $8$:

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

3. Now compare:

$$\frac{3}{8},\quad \frac{4}{8},\quad \frac{5}{8}.$$

4. Order the numerators from least to greatest:

$$3<4<5.$$

Therefore, the fractions from least to greatest are

$$\boxed{\frac{3}{8}<\frac{1}{2}<\frac{5}{8}}.$$

Remember: the denominator tells how many equal parts make the whole, so the denominator alone does not tell which fraction is greater.