What is Scale? — Mathematics

Definition 49.7 Primary & Middle School Mathematics · Chapter 49 — Proportionality

On a map or model at scale $\frac{1}{n}$ (written $1 : n$ ), the distances on the map are proportional to the real distances, with coefficient $\frac1n$ :

\text{map distance} = \frac{1}{n} \times \text{real distance},

both measured in the same unit.

A scale is a proportionality: map distances against real distances line up on a straight line through the origin (here 1 cm 4 km; the dashes read 7 cm 28 km). — A scale is a proportionality: map distances against real distances line up on a straight line through the origin (here $1$ cm $\leftrightarrow$ $4$ km; the dashes read $7$ cm $\leftrightarrow$ $28$ km).

Examples

Example 49.8

On a $1 : 50\,000$ map, two towns are $7$ cm apart. Real distance:

7 \times 50\,000 = 350\,000 \text{ cm} = 3\,500 \text{ m} = 3.5 \text{ km}.

Conversely, a $12$ km hiking trail measures on the map $12$ km $= 1\,200\,000$ cm, so $1\,200\,000 \div 50\,000 = 24$ cm.

Read in context →

Examples

Related terms