If a map at a scale of 1:50,000 is reduced by half, what is the new scale of the map?

When a map is "reduced by half," every distance on the paper is halved. This means that 1 cm on the new (reduced) map corresponds to what 2 cm represented on the original map.

On the original map at a scale of 1:50,000, each 1 cm on paper represents 50,000 cm on the ground. Therefore, 2 cm on the original map represents:

\[2 \times 50{,}000 = 100{,}000 \text{ cm on the ground}\]

After reduction, that same ground distance of 100,000 cm is now represented by just 1 cm on the new map. The new scale is therefore 1:100,000.

A useful rule to remember: when a map is reduced by half, the scale denominator doubles (the map becomes smaller-scale, showing less detail). Conversely, if a map were enlarged to twice its size, the denominator would halve (the map becomes larger-scale, showing more detail).