Skill: Compare fraction strategies

To compare fractions, compare their values, not just their numerators or denominators. A helpful strategy is to rewrite the fractions with a common denominator.

Compare:

$$\frac{3}{4} \quad \text{and} \quad \frac{5}{6}$$

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 equivalent fractions:

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

Therefore,

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

Both fractions now describe parts of the same-sized whole: twelfths. Since $9$ twelfths is less than $10$ twelfths, $\frac{3}{4}$ is less than $\frac{5}{6}$.