Skill: Compare fractions with unlike denominators

When fractions have unlike denominators, their pieces are different sizes, so compare them by rewriting them with a common denominator.

Example: Compare $\frac{3}{4}$ and $\frac{5}{6}$.

1. Find a common denominator.
   The least common multiple of $4$ and $6$ is $12$.

2. Rewrite each fraction with denominator $12$:

$$\frac{3}{4}=\frac{3\times3}{4\times3}=\frac{9}{12}$$ $$\frac{5}{6}=\frac{5\times2}{6\times2}=\frac{10}{12}$$

3. Compare the numerators. Since $9<10$,

$$\frac{9}{12}<\frac{10}{12}.$$

Therefore,

$$\boxed{\frac{3}{4}<\frac{5}{6}}.$$

Remember: a larger denominator does not automatically mean a larger fraction. Rewrite the fractions so they describe the same-sized parts before comparing.