Ratios · Scaling & similar figures · 5.1

Scale factor.

A scale factor multiplies every measurement by the same number. A factor of 3 makes everything 3 times as big; a factor of 1/2 halves it. Scale 8 by 3 → 24.

01 / THE IDEA

See it work.

Watch the method

Scale factor

Scale 8 by a factor of 3 → 24.

1 / 1
8×38 \times 3
1

Multiply by the scale factor

Scale 8 by 3.

8×3=248 \times 3 = 24
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.

Multiply by the factor

Scaling multiplies each measurement by the scale factor — bigger than 1 enlarges, less than 1 reduces.

Why it works

×3 triples; ×½ halves.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Scale 6 by a factor of 4.

1

Multiply by the scale factor

Scale 6 by 4. 6 × 4 = 24

EX 2medium

Scale 8 by a factor of 3.

1

Multiply by the scale factor

Scale 8 by 3. 8 × 3 = 24

EX 3hard

Scale 7 by a factor of 5.

1

Multiply by the scale factor

Scale 7 by 5. 7 × 5 = 35

04 / COMMON TRAPS

Where students slip.

Trap

Adding the scale factor.

Fix

Scaling multiplies, not adds.

Trap

Scaling some lengths but not others.

Fix

Apply the factor to every measurement.

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

Scale 5 by a factor of 4.

Need a hint?
  • Multiply by the scale factor.
  • Apply it to every length.
C2

Scale 12 by a factor of 3.

Need a hint?
  • Multiply by the scale factor.
  • Apply it to every length.
C3

Scale 2 by a factor of 2.

Need a hint?
  • Multiply by the scale factor.
  • Apply it to every length.
C4

Scale 11 by a factor of 3.

Need a hint?
  • Multiply by the scale factor.
  • Apply it to every length.
Apply

Apply (4)

A1

Scale 6 by a factor of 3.

Need a hint?
  • Multiply by the scale factor.
  • Apply it to every length.
A2

Scale 11 by a factor of 5.

Need a hint?
  • Multiply by the scale factor.
  • Apply it to every length.
A3

Scale 9 by a factor of 3.

Need a hint?
  • Multiply by the scale factor.
  • Apply it to every length.
A4

Scale 10 by a factor of 5.

Need a hint?
  • Multiply by the scale factor.
  • Apply it to every length.
Extension

Extension (4)

E1

Scale 12 by a factor of 5.

Need a hint?
  • Multiply by the scale factor.
  • Apply it to every length.
E2

Scale 6 by a factor of 5.

Need a hint?
  • Multiply by the scale factor.
  • Apply it to every length.
E3

Scale 9 by a factor of 2.

Need a hint?
  • Multiply by the scale factor.
  • Apply it to every length.
E4

Scale 10 by a factor of 5.

Need a hint?
  • Multiply by the scale factor.
  • Apply it to every length.