Grade 7 Mathematics
A scale drawing is a drawing that shows a real object with accurate sizes reduced or enlarged by a certain amount (called the scale factor).
Maps, blueprints, and model cars are all scale drawings. We use proportions to find real-world measurements!
What does "Scale: 1 inch = 10 feet" mean?
Every 1 inch on the drawing represents 10 feet in real life.
The scale factor is 10 (real life is 10 times bigger)
Drawing: 2 in x 3 in
Actual: 20 ft x 30 ft
Problem: A map has scale 1 cm = 25 km. Two cities are 6 cm apart on the map. How far apart are they really?
Write a proportion: 1 cm / 25 km = 6 cm / x km
OR use multiplication: 6 cm x 25 km/cm = 150 km
Answer: The cities are 150 km apart in real life.
Problem: A room is 18 feet long. Draw it using scale 1 inch = 6 feet. How long should you draw it?
Write a proportion: 1 in / 6 ft = x in / 18 ft
OR use division: 18 ft / 6 ft per inch = 3 inches
Answer: Draw the room 3 inches long.
WRONG: Always multiply the scale factor to find the answer.
RIGHT: Ask yourself: "Should my answer be BIGGER or SMALLER?"
- Drawing to Actual: Answer should be BIGGER - MULTIPLY by scale factor
- Actual to Drawing: Answer should be SMALLER - DIVIDE by scale factor
1. A map has scale: 1 inch = 50 miles
a) Two cities are 4 inches apart on the map. Actual distance: miles
b) Two towns are 175 miles apart. Distance on map: inches
2. A blueprint has scale: 1 cm = 2 meters
a) A wall is 5 cm on the blueprint. Actual length: meters
b) A room is 8 meters wide. Width on blueprint: cm
3. A model car has scale 1:24 (1 inch on model = 24 inches on real car)
a) The model is 7 inches long. Actual car length: inches = feet
b) The real car is 72 inches wide. Model width: inches
4. Find the scale factor:
a) Drawing: 3 inches, Actual: 15 feet. Scale factor: 1 inch = feet
b) Drawing: 4 cm, Actual: 100 km. Scale factor: 1 cm = km