Ratio and rate · Usually met around P6
Map and model scales
Map to real: multiply. Real to map: divide.
How to do it
Method
Map to real: multiply. Real to map: divide
1 : 50000, 4 cm on the map → 200000 cm = 2 km
Another way
The scale bar
1 bar = 2 km; 4 bars long → 8 km
In full
A scale tells you how a distance on the map compares with the real distance. “1 cm to 2 km”: each 1 cm on the map is 2 km on the ground, so 4 cm on the map is 4 × 2 = 8 km; the other way, 10 km on the ground is 10 ÷ 2 = 5 cm on the map. A scale can be written as a ratio, like 1 : 50000: 1 cm on the map stands for 50000 cm on the ground, which is 500 m (100 cm = 1 m, 1000 m = 1 km). Models work the same way: a 1 : 20 model car 20 cm long stands for a real car 20 × 20 = 400 cm long, which is 4 m. Or use the scale bar in the map's corner and see how many of its lengths fit along the distance.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The map's scale is 1 cm to 8 km. Read the ruler: how far apart are ⭐ and 🌳 really, in km?
Show the answer and working
Answer: 48 km
They are 6 cm apart on the map, each cm 8 km: 6 × 8 = 48.
Example 2
1 m = 100 cm. A map's scale is 1 : 5000. How many metres does 2 cm on the map stand for?
Show the answer and working
Answer: 100 m
2 × 5000 = 10000 cm; 100 cm = 1 m, so 10000 ÷ 100 = 100 m.
Example 3
1 m = 100 cm. What does a scale of 1 : 2000 mean?
- A. 2000 cm on the map stands for 1 cm
- B. 1 cm on the map stands for 200 m
- C. 1 cm on the map stands for 20 m
- D. 1 cm on the map stands for 2000 m
Choose the right answer
Show the answer and working
Answer: C. 1 cm on the map stands for 20 m
1 cm stands for 2000 cm, and 2000 ÷ 100 = 20: 20 m.
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