Ratios · Scaling & similar figures · 5.2

Scale drawings & maps.

A map scale like 1:50 means 1 unit on the map stands for 50 real units. To find a real distance, multiply the map length by the scale. 4 units at 1:50 → 200 real units.

01 / THE IDEA

See it work.

Watch the method

Scale drawings & maps

4 on a 1:50 map → 4 × 50 = 200 real.

1 / 1
1:50,41 : 50 , 4
1

Use the scale

Each drawing unit stands for 50 real units.

4×501=2004 \times \frac{50}{1} = 200
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number, e.g. 40.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Read the scale

The scale tells you how many real units each drawing unit represents; multiply to convert.

Why it works

1:50 → each cm is 50 km.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

A map scale is 1:20. A length of 2 on the map is how long in real life?

1

Use the scale

Each drawing unit stands for 20 real units. 2 × 20/1 = 40

EX 2medium

A map scale is 1:100. A length of 6 on the map is how long in real life?

1

Use the scale

Each drawing unit stands for 100 real units. 6 × 100/1 = 600

EX 3hard

A map scale is 1:100. A length of 5 on the map is how long in real life?

1

Use the scale

Each drawing unit stands for 100 real units. 5 × 100/1 = 500

04 / COMMON TRAPS

Where students slip.

Trap

Dividing instead of multiplying.

Fix

To go from map to real, multiply by the scale.

Trap

Ignoring the units.

Fix

Keep the real-world units.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

A map scale is 1:50. A length of 6 on the map is how long in real life?

Need a hint?
  • Multiply the map length by the scale.
  • That gives the real length.
C2

A map scale is 1:100. A length of 4 on the map is how long in real life?

Need a hint?
  • Multiply the map length by the scale.
  • That gives the real length.
C3

A map scale is 1:10. A length of 8 on the map is how long in real life?

Need a hint?
  • Multiply the map length by the scale.
  • That gives the real length.
C4

A map scale is 1:50. A length of 6 on the map is how long in real life?

Need a hint?
  • Multiply the map length by the scale.
  • That gives the real length.
Apply

Apply (4)

A1

A map scale is 1:100. A length of 3 on the map is how long in real life?

Need a hint?
  • Multiply the map length by the scale.
  • That gives the real length.
A2

A map scale is 1:100. A length of 9 on the map is how long in real life?

Need a hint?
  • Multiply the map length by the scale.
  • That gives the real length.
A3

A map scale is 1:20. A length of 4 on the map is how long in real life?

Need a hint?
  • Multiply the map length by the scale.
  • That gives the real length.
A4

A map scale is 1:10. A length of 5 on the map is how long in real life?

Need a hint?
  • Multiply the map length by the scale.
  • That gives the real length.
Extension

Extension (4)

E1

A map scale is 1:50. A length of 9 on the map is how long in real life?

Need a hint?
  • Multiply the map length by the scale.
  • That gives the real length.
E2

A map scale is 1:10. A length of 7 on the map is how long in real life?

Need a hint?
  • Multiply the map length by the scale.
  • That gives the real length.
E3

A map scale is 1:10. A length of 2 on the map is how long in real life?

Need a hint?
  • Multiply the map length by the scale.
  • That gives the real length.
E4

A map scale is 1:50. A length of 7 on the map is how long in real life?

Need a hint?
  • Multiply the map length by the scale.
  • That gives the real length.