Ratios · Proportions · 3.4

The unit-rate method.

You can also solve a proportion using the unit rate: find the per-1 amount, then scale. Both methods give the same answer — pick whichever is cleaner.

01 / THE IDEA

See it work.

Watch the method

The unit-rate method

2/5 = x/20 → scale ×4 → x = 8.

1 / 2
25=?20\frac{2}{5} = \frac{?}{20}
1

Cross-multiply

Set the cross-products equal.

2×20=5×?2 \times 20 = 5 \times ?
2

Solve for the unknown

Divide to isolate the missing value.

x=8x = 8
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.

Scale instead

Find what one ratio is multiplied by to reach the other, then apply it to the unknown.

Why it works

5 × 4 = 20, so 2 × 4 = 8.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Solve the proportion for x: 2/4 = x/12

1

Cross-multiply

Set the cross-products equal. 2 × 12 = 4 × ?

2

Solve for the unknown

Divide to isolate the missing value. x = 6

EX 2medium

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

1

Cross-multiply

Set the cross-products equal. 5 × ? = 6 × 30

2

Solve for the unknown

Divide to isolate the missing value. x = 36

EX 3hard

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

1

Cross-multiply

Set the cross-products equal. 6 × 6 = 2 × ?

2

Solve for the unknown

Divide to isolate the missing value. x = 18

04 / COMMON TRAPS

Where students slip.

Trap

Mixing the two methods mid-solve.

Fix

Pick one method and finish it.

Trap

Scaling by the wrong factor.

Fix

Use the factor between the known parts.

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: 6/2 = 30/x

Need a hint?
  • Find the scale factor between the denominators.
  • Apply it to the numerator.
C2

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

Need a hint?
  • Find the scale factor between the denominators.
  • Apply it to the numerator.
C3

Solve the proportion for x: 5/2 = x/6

Need a hint?
  • Find the scale factor between the denominators.
  • Apply it to the numerator.
C4

Solve the proportion for x: 6/2 = 30/x

Need a hint?
  • Find the scale factor between the denominators.
  • Apply it to the numerator.
Apply

Apply (4)

A1

Solve the proportion for x: 2/5 = 4/x

Need a hint?
  • Find the scale factor between the denominators.
  • Apply it to the numerator.
A2

Solve the proportion for x: 2/4 = x/12

Need a hint?
  • Find the scale factor between the denominators.
  • Apply it to the numerator.
A3

Solve the proportion for x: 4/5 = 24/x

Need a hint?
  • Find the scale factor between the denominators.
  • Apply it to the numerator.
A4

Solve the proportion for x: 3/6 = x/12

Need a hint?
  • Find the scale factor between the denominators.
  • Apply it to the numerator.
Extension

Extension (4)

E1

Solve the proportion for x: 6/3 = x/18

Need a hint?
  • Find the scale factor between the denominators.
  • Apply it to the numerator.
E2

Solve the proportion for x: 6/2 = x/12

Need a hint?
  • Find the scale factor between the denominators.
  • Apply it to the numerator.
E3

Solve the proportion for x: 4/3 = x/12

Need a hint?
  • Find the scale factor between the denominators.
  • Apply it to the numerator.
E4

Solve the proportion for x: 3/5 = 6/x

Need a hint?
  • Find the scale factor between the denominators.
  • Apply it to the numerator.