Ratios · Proportions · 3.5

Proportion word problems.

Word problems often hide a proportion: keep the same two quantities in the same order on both sides, then solve. “3 apples cost $4; how much for 12 apples?” → 3/4 = 12/x.

01 / THE IDEA

See it work.

Watch the method

Proportion word problems

Set up matching ratios, then cross-multiply.

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.

Match the units

Put the same kind of quantity in the same position (top with top), then solve the proportion.

Why it works

apples/cost = apples/cost.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

If 4 go with 6, how many go with 12?

1

Cross-multiply

Set the cross-products equal. 4 × 12 = 6 × ?

2

Solve for the unknown

Divide to isolate the missing value. x = 8

EX 2medium

If 5 go with 5, how many go with ??

1

Cross-multiply

Set the cross-products equal. 5 × ? = 5 × 20

2

Solve for the unknown

Divide to isolate the missing value. x = 20

EX 3hard

If 2 go with 5, how many go with 30?

1

Cross-multiply

Set the cross-products equal. 2 × 30 = 5 × ?

2

Solve for the unknown

Divide to isolate the missing value. x = 12

04 / COMMON TRAPS

Where students slip.

Trap

Mismatching the units across the proportion.

Fix

Keep the same quantity on top on both sides.

Trap

Setting it up upside down.

Fix

Be consistent with the order.

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

If 3 go with 2, how many go with ??

Need a hint?
  • Write the two ratios in the same order.
  • Cross-multiply and solve.
C2

If 6 go with 3, how many go with 9?

Need a hint?
  • Write the two ratios in the same order.
  • Cross-multiply and solve.
C3

If 6 go with 3, how many go with ??

Need a hint?
  • Write the two ratios in the same order.
  • Cross-multiply and solve.
C4

If 5 go with 4, how many go with 8?

Need a hint?
  • Write the two ratios in the same order.
  • Cross-multiply and solve.
Apply

Apply (4)

A1

If 2 go with 6, how many go with ??

Need a hint?
  • Write the two ratios in the same order.
  • Cross-multiply and solve.
A2

If 4 go with 3, how many go with ??

Need a hint?
  • Write the two ratios in the same order.
  • Cross-multiply and solve.
A3

If 2 go with 5, how many go with 30?

Need a hint?
  • Write the two ratios in the same order.
  • Cross-multiply and solve.
A4

If 4 go with 3, how many go with 18?

Need a hint?
  • Write the two ratios in the same order.
  • Cross-multiply and solve.
Extension

Extension (4)

E1

If 3 go with 6, how many go with 24?

Need a hint?
  • Write the two ratios in the same order.
  • Cross-multiply and solve.
E2

If 3 go with 4, how many go with 16?

Need a hint?
  • Write the two ratios in the same order.
  • Cross-multiply and solve.
E3

If 2 go with 4, how many go with 8?

Need a hint?
  • Write the two ratios in the same order.
  • Cross-multiply and solve.
E4

If 6 go with 2, how many go with 12?

Need a hint?
  • Write the two ratios in the same order.
  • Cross-multiply and solve.