Skill: Order fractions

To order fractions, rewrite them so they have the same denominator. Then compare the numerators: with the same denominator, the fraction with the greater numerator is larger.

Example: Order these from least to greatest:

$$\frac{2}{3},\quad \frac{3}{4},\quad 1\frac{1}{6},\quad \frac{5}{6}$$

1. Change the mixed number into an improper fraction:

$$1\frac{1}{6}=\frac{7}{6}$$

2. Find a common denominator. The least common denominator of $3$, $4$, and $6$ is $12$.

3. Rewrite each fraction with denominator $12$:

$$\frac{2}{3}=\frac{8}{12}$$ $$\frac{3}{4}=\frac{9}{12}$$ $$\frac{7}{6}=\frac{14}{12}$$ $$\frac{5}{6}=\frac{10}{12}$$

4. Compare the numerators:

$$8<9<10<14$$

5. Write the fractions in the original form:

$$\boxed{\frac{2}{3}<\frac{3}{4}<\frac{5}{6}<1\frac{1}{6}}$$

Remember: a larger denominator does not automatically mean a larger fraction. Use equivalent fractions or a benchmark such as $1$ to compare accurately.