Comparing Fractions

Same Denominator

When fractions have the same denominator, compare numerators:

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

(3 parts < 5 parts)

Different Denominators

Find a common denominator first, then compare:

Example: Compare $\frac{1}{2}$ and $\frac{2}{5}$

Common denominator is 10:

• $\frac{1}{2} = \frac{5}{10}$
• $\frac{2}{5} = \frac{4}{10}$

Since $\frac{5}{10} > \frac{4}{10}$, we know $\frac{1}{2} > \frac{2}{5}$

Using Benchmarks

Compare to common fractions:

• Is it close to $0$, $\frac{1}{2}$, or $1$?

Example:

• $\frac{1}{8}$ is close to 0
• $\frac{7}{8}$ is close to 1

So $\frac{7}{8} > \frac{1}{8}$ (obviously!)

Tips

• Same numerator? Smaller denominator = larger fraction
  • $\frac{3}{4} > \frac{3}{8}$