Scale | Mathematics for GCSE/IGCSE - Year 11 PDF Download

What is scale?

• In mathematics, scale can have various interpretations, but concerning accurate drawings and constructions, scale denotes a ratio.
• Maps are typically crafted to a specific scale.
• The selection of the scale relies on the area being charted. For instance:
  • A map of a classroom necessitates a large scale to exhibit intricate details.
  • In contrast, a map of a country or the world utilizes a small scale to represent a broader area with less detail.

How can scale be used to convert lengths?

• A scale ratio does not include units and is applicable to any unit of length on both sides.
  • For instance, the scale 1:50000 can mean 1 cm = 50000 cm, 1 km = 50000 km, or 1 yard = 50000 yards.
• When measuring from a map, it is easiest to use centimeters.
• The scale converts map lengths to real-life lengths.
• To convert a map length to a real-life length:
  • Step 1: Measure the distance on the map accurately with a ruler, e.g., 5.8 cm from A to B.
  • Step 2: Use the scale to find the actual distance in the same units, typically cm. For a scale of 1:150000, the actual distance is 5.8 cm × 150000.
  • Step 3: Convert the actual distance to a more suitable unit. For instance, 5.8 × 150000 = 870000 cm = 8.7 km.
• To convert real-life lengths to a map length:
  • Step 1: Convert the scale into a ratio of 1 cm to the actual distance unit. For example, if the scale is 1:500000 and the distance is in km, convert 500000 cm into km. So, 1:500000 becomes 1 cm: 5 km.
  • Step 2: Use this ratio to convert the actual distance to the scale distance. For instance, if the actual distance is 20 km, the scale distance will be 20 ÷ 5 = 4 cm.