A scale like 1 : 100 means 1 cm on the drawing stands for 100 cm in real life. To find a real length, multiply the drawn length by the scale number. The answer is in the same unit as the drawing, usually centimetres, so convert it: 100 cm = 1 m and 100 000 cm = 1 km. To go from real life to the map, convert to centimetres first, then divide by the scale number.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- scale
- how many real units one unit on the drawing stands for
- ratio
- a comparison of two amounts, such as 1 : 100
Worked examples
A scale drawing uses the scale 1 : 10. A desk is drawn 8 cm long. How long is the real desk, in centimetres?
- 1.1 cm stands for 10 cm.
- 2.8 × 10 = 80.
= 80
A map has the scale 1 : 50 000. Ashby and Brook are 4 cm apart on the map. How far apart are they in real life, in kilometres?
- 1.4 × 50 000 = 200 000 cm.
- 2.200 000 cm = 2000 m = 2 km.
= 2
A wall that is 12 m long is drawn 6 cm long on a plan. The scale of the plan is 1 : ?. What number goes in place of the question mark?
- 1.12 m = 1200 cm.
- 2.1200 ÷ 6 = 200, so the scale is 1 : 200.
= 200
For parents
Method: Multiply by the scale, then convert
What to say: What does 1 cm on the drawing stand for? What units does the question want?
Common mistakes:
- Adds the scale number instead of multiplying by it (additive thinking about ratio).
- Uses the wrong operation with the scale: divides when going from drawing to real, or multiplies when going from real to map.
- Forgets to change units, giving the answer in centimetres when metres or kilometres are asked for.
- Converts centimetres to metres but stops there, giving metres when kilometres are needed (or the reverse).
- Uses the wrong conversion factor between units (e.g. 10 cm in a metre, or 1000 cm in a kilometre).