Lesson 3: Find common units or number of units to compare two fractions.

Property

To compare two fractions with the same denominator, compare their numerators.
The fraction with the greater numerator is the greater fraction.
If $a > c$, then $\frac{a}{b} > \frac{c}{b}$.

Examples

Property

When two fractions have the same numerator, the fraction with the smaller denominator is greater because its pieces are larger.
If $a > 0$ and $b > c > 0$, then $\frac{a}{b} < \frac{a}{c}$.

Examples

Property

To efficiently compare two fractions, choose a strategy by checking for relationships:

1. Common Denominator: Use when denominators are the same or one is a multiple of the other.
2. Common Numerator: Use when numerators are the same or one is a multiple of the other.
3. Benchmark Comparison: Use when one fraction is clearly greater than a benchmark (like $\frac{1}{2}$) and the other is clearly less.

Examples