Skill: Order fractions with unlike denominators

To order fractions with unlike denominators, rewrite them with a common denominator. Then compare the numerators.

Example: Order $\frac{3}{4}$, $\frac{2}{3}$, and $\frac{5}{8}$ from least to greatest.

1. Find a common denominator.
   The least common denominator of $4$, $3$, and $8$ is $24$.

2. Rewrite each fraction with denominator $24$:

$$\frac{3}{4}=\frac{18}{24}$$ $$\frac{2}{3}=\frac{16}{24}$$ $$\frac{5}{8}=\frac{15}{24}$$

3. Compare the numerators. Since

$$15<16<18,$$

we have

$$\frac{15}{24}<\frac{16}{24}<\frac{18}{24}.$$

4. Replace the equivalent fractions with the original fractions:

$$\boxed{\frac{5}{8}<\frac{2}{3}<\frac{3}{4}}$$

Remember: A larger denominator does not automatically mean a larger fraction. Rewrite the fractions with a common denominator before comparing them.