Types of Fractions

Proper Fraction

Numerator is less than denominator: $\frac{2}{5}$, $\frac{7}{10}$

Improper Fraction

Numerator is greater than or equal to denominator: $\frac{7}{4}$, $\frac{9}{9}$

Mixed Number

A whole number and a fraction: $2\frac{1}{3}$, $5\frac{3}{8}$

Comparing Fractions

Same Denominator

Compare the numerators: $\frac{3}{8} < \frac{5}{8}$

Different Denominators

Find a common denominator first, then compare

Equivalent Fractions

Fractions that represent the same value: $\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8}$

Multiply or divide both numerator and denominator by the same number.

$\frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18}$

Compare: $\frac{15}{18} > \frac{14}{18}$

Answer: $\frac{5}{6}$ is greater

$\frac{5}{8} = \frac{15}{24}$

$\frac{3}{4} = \frac{18}{24}$

Order: $\frac{15}{24} < \frac{16}{24} < \frac{18}{24}$

Answer: $\frac{5}{8}, \frac{2}{3}, \frac{3}{4}$