🎯 Learning Objectives
By the end of this lesson, you should be able to:
- Convert a statement scale to a ratio scale.
- Convert units before forming a ratio.
- Simplify a scale ratio to 1 : n.
- Use ratio scales in calculations.
🤔 Start with the Idea
To write a scale as a ratio, both quantities must first be expressed in the same unit. This unit-conversion step is the key to avoiding mistakes.
📖 Converting a Statement Scale
Convert 1 cm represents 3 km into ratio form.
3 km× 100 000300 000 cm
1 cm : 300 000 cm = 1 : 300 000
Never write 1 : 3 directly when the original quantities are centimetres and kilometres.
🎮 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 plan has the scale 2 cm represents 5 m. Write the scale as 1 : n.
5 m = 500 cm, so the ratio is 2 : 500.
Divide both parts by 2.
2 : 500 = 1 : 250
Answer: 1 : 250.
✏️ Practice Questions
Build confidence- Convert 1 cm = 2 km to RF form.
- Convert 2 cm = 8 m to the form 1 : n.
- A scale is 1 : 75 000. Write it as a statement scale in metres.
✅ Check your answers
- 1 : 200 000
- 1 : 400
- 1 cm represents 750 m
⚠️ 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.