Scale Drawings and Maps
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Learning Objectives
- 1Read a map scale and use it to convert map distance into real distance
- 2Apply a scale factor to find a real length from a drawing length
- 3Find a drawing length when given the real length and the scale
- 4Compare two maps or drawings by their scale factors
Mini Lesson
A scale drawing is a small picture of something big — a town on a map, a house on a blueprint, a stadium on a poster. The drawing shows real shapes, just shrunk down. The scale tells you exactly how much it has been shrunk so you can measure on paper and still talk about real distances.
Three ways to write a scale
- Word form: "1 inch = 50 miles". Easy to read out loud.
- Equation form: "1 cm represents 10 km". Same idea, slightly more formal.
- Ratio form: "1:400". Drawing length to real length, both in the same units.
Map distance to real distance
- Measure on the map. Use a ruler. Example: the road is 3 inches long.
- Read the scale. Example: 1 inch = 50 miles.
- Multiply. Real distance = map distance x scale = 3 x 50 = 150 miles.
- Check the units. The answer should be in real-world units (miles, km, m), not paper units.
A map uses the scale 1 cm = 10 km. The route measures 6.5 cm. How long is the real route?
Real distance = map distance x scale = 6.5 cm x 10 km/cm = 65 km. Always multiply by the second number in the scale.
Scale factor (the ratio form)
A scale factor is a single number — a ratio — that tells you how many times bigger the real object is than the drawing. If the scale is 1:400, then 1 cm on the drawing is 400 cm in real life. To convert: drawing length x scale factor = real length. The reverse works too: real length / scale factor = drawing length.
- Scale 1:400 means real is 400 times bigger than the drawing.
- A 5 cm line on the drawing represents 5 x 400 = 2000 cm = 20 m in real life.
- A 12 m wall in real life shrinks to 1200 / 400 = 3 cm on the drawing.
- Same units on both sides of the ratio — never mix cm with km.
Going backwards: real to drawing
Sometimes you know the real distance and you need to draw it. Use division. If 1 cm = 50 m and the real building is 200 m wide, the drawing should be 200 / 50 = 4 cm wide. The trick is the same idea as before — just divide instead of multiply.
Comparing scales
- A SMALLER scale factor (like 1:100) shows MORE detail in a smaller real area — good for floor plans.
- A LARGER scale factor (like 1:1,000,000) covers a HUGE real area in a small picture — good for country maps.
- When comparing two maps, the one with the bigger second number covers more real ground per cm.
Tip: write the scale as a labeled fraction before you compute. "1 cm / 10 km" makes it obvious that you multiply by 10 km per cm. Mislabeled units cause more wrong answers than bad math.
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