Scales and the Representative Fraction
≈ 36 minScales and the Representative Fraction
Most objects are the wrong size for the paper. A house will not fit; a watch part is too small to see. A scale states the fixed relationship between drawn length and real length, written as a representative fraction (RF) such as 1 : 50 (reduction) or 5 : 1 (enlargement). 1 : 1 is full size.
The rule in both directions:
- drawn length = real length ÷ scale factor (for a reduction 1 : n)
- real length = drawn length × scale factor
Worked example. A room wall is 4 500 mm long, drawn at 1 : 50. Drawn length = 4 500 ÷ 50 = 90 mm. Reading the other way, a line measuring 62 mm on that same drawing represents 62 × 50 = 3 100 mm on site.
Core checkpoint: Dimensions on a drawing always state the real size, never the drawn size — no matter what scale the drawing is at.
A wall is 4 500 mm long and is drawn at a scale of 1 : 50. What is its drawn length, in millimetres?
On a drawing at 1 : 50, a line measures 62 mm. What real length in millimetres does it represent?
A 4 500 mm wall is drawn 90 mm long at 1 : 50. What figure should be written as its dimension on the drawing?
A small watch component is drawn at 5 : 1. What does this scale tell you?