Ratios · Proportions · 3.1

What is a proportion?

A proportion is a statement that two ratios are equal, like 2:3 = 6:9. You can check it because equivalent ratios have equal cross-products.

01 / THE IDEA

See it work.

Watch the method

What is a proportion?

2:3 = 6:9 is a proportion (both equal 2/3).

1 / 1
2:32 : 3
1

Simplify

Reduce the ratio.

2:3=2:32:3 = 2:3
— / WHY IT WORKS

The idea underneath.

Equal ratios

Two ratios form a proportion when they simplify to the same value (equal cross-products).

Why it works

2/3 = 6/9.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Is 6:4 equal to 12:8?

1

Answer

Yes

EX 2medium

Is 5:4 equal to 15:12?

1

Answer

Yes

EX 3hard

Is 4:6 equal to 16:26?

1

Answer

No

04 / COMMON TRAPS

Where students slip.

Trap

Assuming any two ratios are proportional.

Fix

Only equal ratios form a proportion.

Trap

Comparing parts loosely.

Fix

Check the cross-products.

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

Is 2:4 equal to 6:12?

Need a hint?
  • Simplify both ratios.
  • Equal means a proportion.
C2

Is 4:6 equal to 16:25?

Need a hint?
  • Simplify both ratios.
  • Equal means a proportion.
C3

Is 6:6 equal to 24:25?

Need a hint?
  • Simplify both ratios.
  • Equal means a proportion.
C4

Is 4:2 equal to 8:6?

Need a hint?
  • Simplify both ratios.
  • Equal means a proportion.
Apply

Apply (4)

A1

Is 5:4 equal to 15:12?

Need a hint?
  • Simplify both ratios.
  • Equal means a proportion.
A2

Is 4:2 equal to 16:10?

Need a hint?
  • Simplify both ratios.
  • Equal means a proportion.
A3

Is 5:6 equal to 10:13?

Need a hint?
  • Simplify both ratios.
  • Equal means a proportion.
A4

Is 6:5 equal to 12:10?

Need a hint?
  • Simplify both ratios.
  • Equal means a proportion.
Extension

Extension (4)

E1

Is 3:2 equal to 12:8?

Need a hint?
  • Simplify both ratios.
  • Equal means a proportion.
E2

Is 3:4 equal to 9:12?

Need a hint?
  • Simplify both ratios.
  • Equal means a proportion.
E3

Is 3:2 equal to 12:7?

Need a hint?
  • Simplify both ratios.
  • Equal means a proportion.
E4

Is 5:5 equal to 15:16?

Need a hint?
  • Simplify both ratios.
  • Equal means a proportion.