# Fractions and ratios

Authored explanation; editorial review pending.

A fraction a/b compares quantity a to quantity b, or tells us how many parts of size 1/b make up a. When b is not zero, dividing a by b calculates how many units of b are contained within a.

In physical science, a ratio often carries units: dividing displacement in micrometres by time in seconds produces a rate in micrometres per second. A dimensionless ratio occurs when both quantities share the same units, such as the fraction of an ensemble that moves in a given direction.

## Worked example

1. If 1 particle out of 4 moves by 3 units, the proportion is 1/4 = 0.25.
2. If the ensemble doubles to 8 particles and 2 move by 3 units, the proportion is 2/8 = 0.25.
3. Multiplying both the count and the total by 2 preserves the underlying ratio.

A ratio compares relative magnitudes; always state whether the physical units cancel or combine.