Lesson 1: Reason using benchmarks to compare two fractions on the number line.

Property

To estimate a fraction's position on a number line, first compare it to the benchmark $\frac{1}{2}$.
If the numerator is less than half the denominator, the fraction is less than $\frac{1}{2}$ and belongs between 0 and $\frac{1}{2}$.
If the numerator is more than half the denominator, the fraction is greater than $\frac{1}{2}$ and belongs between $\frac{1}{2}$ and 1.

Examples

Property

When comparing two fractions on the same side of a benchmark, determine their distance from that benchmark.
The fraction with the smaller distance is closer.
A larger denominator creates a smaller unit fraction, which represents a smaller distance (e.g., a distance of $\frac{1}{12}$ is smaller than a distance of $\frac{1}{8}$).

Examples