Lesson 5: Use Benchmarks to Compare Fractions

Property

To compare a fraction $\frac{a}{b}$ to the benchmarks $0$, $\frac{1}{2}$, and $1$:

• If the numerator $a$ is very small compared to the denominator $b$, the fraction is close to $0$.
• If the numerator $a$ is about half of the denominator $b$ (i.e., $a \approx \frac{b}{2}$), the fraction is close to $\frac{1}{2}$.
• If the numerator $a$ is very close to the denominator $b$, the fraction is close to $1$.

Examples

Property

To compare a fraction to a benchmark using an area model, shade the area representing the fraction and visually compare it to the area representing the benchmark (e.g., $\frac{1}{2}$ or $1$).

Examples