Map → Real
Multiply by the distance represented by 1 cm.
real = map × scale value
🎯 Learning Objectives
By the end of this lesson, you should be able to:
- Find real distance from map distance.
- Find map distance from real distance.
- Choose multiplication or division correctly.
- Solve route problems containing more than one section.
🤔 Start with the Idea
Scale questions may ask for the real distance or the map distance. The direction of the calculation tells us whether to multiply or divide.
📖 Choose the Correct Operation
Real → Map
Divide by the distance represented by 1 cm.
map = real ÷ scale value
🎮 Explore the Scale
Change the map or drawing length and the scale value. Notice how the real distance changes proportionally.
🧠 Let’s Think Together
A 72 km road is shown on a map with scale 1 cm represents 8 km. Find its map length.
We are moving from real distance to map distance, so divide.
72 ÷ 8 = 9 cm
Answer: 9 cm.
✏️ Practice Questions
Build confidence- Scale 1 cm = 6 km. Find the real distance for 7.5 cm.
- Scale 1 cm = 15 km. Find the map distance for 120 km.
- A route has map sections 3 cm, 4.5 cm and 2 cm at 1 cm = 8 km. Find the full real route.
✅ Check your answers
- 45 km
- 8 cm
- 76 km
⚠️ Common Mistakes
- Using different units on the two sides of a ratio scale.
- Multiplying when the question requires division, or dividing when it requires multiplication.
- Leaving out the unit or using a linear unit for an area.
- Rounding too early in a multi-step calculation.
🎯 Exam Focus
Write what the scale means before calculating. Show unit conversions clearly, keep full calculator values until the final step, and include the correct unit in the answer.
📌 One-Minute Summary
- A scale connects a drawing or model to the corresponding real object.
- Use multiplication when moving from a drawing measurement to a real measurement.
- Use division when working backwards from real size to drawing size.
- Ratio scales require the same unit on both sides.
- Area changes by the square of the linear scale factor.