🎯 Learning Objectives
By the end of this lesson, you should be able to:
- Explain what an RF scale means.
- Keep both sides in the same unit.
- Convert centimetres to metres and kilometres.
- Calculate real distances from RF scales.
🤔 Start with the Idea
A representative fraction, often shortened to RF, writes a scale as a ratio such as 1 : 50 000. It has no written unit because both sides use the same unit.
📖 Reading an RF Scale
1 : 50 000
This can mean 1 cm represents 50 000 cm, or 1 mm represents 50 000 mm. In map problems we usually measure the map in centimetres.
100 cm=1 mand100 000 cm=1 km
🎮 Try It Yourself
Change the corresponding lengths and watch the scale factor update.
🧠 Let’s Think Together
A map uses RF 1 : 250 000. Find the real distance represented by 3.2 cm.
Step 1: 3.2 × 250 000 = 800 000 cm.
Step 2: Convert centimetres to kilometres.
800 000 ÷ 100 000 = 8 km
Answer: 8 km.
✏️ Practice Questions
Build confidence- At RF 1 : 100 000, what does 1 cm represent in kilometres?
- At RF 1 : 50 000, find the real distance for 6 cm.
- At RF 1 : 200 000, what map length represents 14 km?
✅ Check your answers
- 1 km
- 3 km
- 7 cm
⚠️ 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.