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Math · Grade 7 Math

Chapter 1: Scale Drawings

Reading a Scale

One centimeter on the map, half a kilometer on the ground.

Lesson
3
Time
About 18 minutes
0 of 7 done
Part 1 of 7Let's Learn

Step 1: Let's Learn

Read it, or press Listen and follow the words.

Watch the idea first — 58 seconds. Then read on, and try it yourself in the next step.

A scale of 1 cm to 50 km says every centimeter on the drawing stands for 50 km on the ground.

A scale is a rate

It behaves exactly like £3 per kilogram. Multiply to go one way, divide to go the other.

Drawing to real

4 cm on the map is 4 × 50 = 200 km on the ground.

Real to drawing

350 km on the ground is 350 ÷ 50 = 7 cm on the map.

Step 2: Try It Yourself

Set the scale and read the pairs off the table.

One centimeter stands for a fixed distance. Scale it up to read any length.
A ratio table for 1 to 5
Centimeters on the mapKilometers on the ground
15
210
315
420
Centimeters on the mapKilometers on the ground0015210315420

Every row is the same ratio. 1 to 5 is the same comparison as 4 to 20.

Step 3: In Real Life

A hiking map

A map says 1 centimeter is half a kilometer. The trail is 7 centimeters on the map: 3.5 kilometers of walking. The scale turns paper into distance.

Step 4: Watch an Example

One step at a time.

Watch Ana Use a Map Scale

A map has a scale of 1 cm to 20 km. Two towns are 6.5 cm apart on it.

  1. Step 1

    She checks which way she is going: from the map to the ground, so multiply.

Step 5: Your Turn

Practice makes it stick.

The Map

Problem 1 of 2

Scale 1 cm to 20 km. How many km is 8 cm?

The Other Way

Problem 2 of 2

Scale 1 cm to 20 km. How many cm on the map is 300 km?

Map and Ground

1 of 4

Scale 1 cm to 5 km. Real distance for 7 cm, in km?

2 of 4

Scale 1 cm to 5 km. Map length for 60 km, in cm?

3 of 4

Scale 1 cm to 250 m. Real distance for 4 cm, in meters?

4 of 4

Going from a real length to a map length, do you multiply or divide?

Step 6: Quick Check

Show what you know.

Question 1 of 1

Scale 1 cm to 30 km. Real distance for 5 cm, in km?

What You Learned

  • A scale is a rate between drawing length and real length.
  • Drawing to real multiplies; real to drawing divides.
  • Estimate first so a wrong operation shows up immediately.
For the grown-up

A scale is a ratio between two lengthsA scale of 1 cm to 0.5 km says that every centimeter measured on the map stands for half a kilometer on the ground. It is a ratio, so it scales: 4 cm on the map is 2 km on the ground.

Scales written as a pure ratioA scale of 1 : 50,000 means one unit on the map is 50,000 of the same units on the ground. Because no unit is named, the ratio works for any: 1 cm represents 50,000 cm, which is 500 m. Converting to a sensible unit is usually the first step.

Using it in both directionsMap to ground, multiply by the scale factor. Ground to map, divide. Deciding the direction first is what stops you producing a map distance of 40 km. A quick sanity check — real distances are bigger — catches an inverted calculation.

Areas on a mapAt a scale of 1 : 50,000, an area on the map represents 50,000² times the ground area — because area scales by the square of the length factor. This is why small patches on a map can represent surprisingly large tracts of land.

Turn the scale into a multiplierScale 1 cm : 50 km. On the map, two towns are 7 cm apart. 7 × 50 = 350 350 km apart. Going the other way, a real 200 km is 200 ÷ 50 = 4 cm on the map.