Overview

Comparing Fractions

January 15, 2025

1 min read

Table of Contents

Sections

Case 1: Same Denominator

If the denominators (fractional units) are the same, just compare the numerators.

\frac{4}{7} \text{ vs } \frac{6}{7}

Since $6 > 4$ , clearly $\frac{6}{7} > \frac{4}{7}$ .

If the numerators are the same (same number of pieces), compare the denominators. Remember: Larger denominator = Smaller pieces.

\frac{3}{4} \text{ vs } \frac{3}{7}

Shares of $\frac{1}{4}$ are bigger than shares of $\frac{1}{7}$ . So $\frac{3}{4} > \frac{3}{7}$ .

To compare $\frac{4}{5}$ and $\frac{7}{9}$ , we must make their units (denominators) the same.

\frac{4}{5} = \frac{4 \times 9}{5 \times 9} = \frac{36}{45}

\frac{7}{9} = \frac{7 \times 5}{9 \times 5} = \frac{35}{45}

Compare: $\frac{36}{45} > \frac{35}{45}$ . Therefore, $\frac{4}{5} > \frac{7}{9}$ .