Ratios · Proportions · 3.3

Solve by cross-multiplying.

To find a missing value in a proportion, cross-multiply and solve. For 3/4 = x/12: 3×12 = 4×x → 36 = 4x → x = 9.

01 / THE IDEA

See it work.

Watch the method

Solve by cross-multiplying

3/4 = x/12 → 3×12 = 4x → x = 9.

1 / 2
34=?12\frac{3}{4} = \frac{?}{12}
1

Cross-multiply

Set the cross-products equal.

3×12=4×?3 \times 12 = 4 \times ?
2

Solve for the unknown

Divide to isolate the missing value.

x=9x = 9
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.

Cross-multiply & solve

Set the cross-products equal, then solve the resulting equation for the unknown.

Why it works

3×12 = 4x → x = 9.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Solve the proportion for x: 4/3 = 20/x

1

Cross-multiply

Set the cross-products equal. 4 × ? = 3 × 20

2

Solve for the unknown

Divide to isolate the missing value. x = 15

EX 2medium

Solve the proportion for x: 2/4 = x/8

1

Cross-multiply

Set the cross-products equal. 2 × 8 = 4 × ?

2

Solve for the unknown

Divide to isolate the missing value. x = 4

EX 3hard

Solve the proportion for x: 4/2 = x/4

1

Cross-multiply

Set the cross-products equal. 4 × 4 = 2 × ?

2

Solve for the unknown

Divide to isolate the missing value. x = 8

04 / COMMON TRAPS

Where students slip.

Trap

Multiplying straight across.

Fix

Cross-multiply diagonally.

Trap

Forgetting to divide at the end.

Fix

Divide to isolate the unknown.

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

Solve the proportion for x: 2/4 = x/20

Need a hint?
  • Set a×d = b×c.
  • Divide to find the unknown.
C2

Solve the proportion for x: 3/3 = 15/x

Need a hint?
  • Set a×d = b×c.
  • Divide to find the unknown.
C3

Solve the proportion for x: 4/2 = 16/x

Need a hint?
  • Set a×d = b×c.
  • Divide to find the unknown.
C4

Solve the proportion for x: 2/6 = 6/x

Need a hint?
  • Set a×d = b×c.
  • Divide to find the unknown.
Apply

Apply (4)

A1

Solve the proportion for x: 3/6 = 15/x

Need a hint?
  • Set a×d = b×c.
  • Divide to find the unknown.
A2

Solve the proportion for x: 4/3 = 8/x

Need a hint?
  • Set a×d = b×c.
  • Divide to find the unknown.
A3

Solve the proportion for x: 3/3 = x/12

Need a hint?
  • Set a×d = b×c.
  • Divide to find the unknown.
A4

Solve the proportion for x: 6/6 = 36/x

Need a hint?
  • Set a×d = b×c.
  • Divide to find the unknown.
Extension

Extension (4)

E1

Solve the proportion for x: 4/5 = x/10

Need a hint?
  • Set a×d = b×c.
  • Divide to find the unknown.
E2

Solve the proportion for x: 6/5 = x/30

Need a hint?
  • Set a×d = b×c.
  • Divide to find the unknown.
E3

Solve the proportion for x: 5/5 = 10/x

Need a hint?
  • Set a×d = b×c.
  • Divide to find the unknown.
E4

Solve the proportion for x: 2/3 = x/9

Need a hint?
  • Set a×d = b×c.
  • Divide to find the unknown.