Ratios · Capstone · C1

Pick the tool.

Proportional problems can be solved several ways: build a ratio table, find the unit rate and scale, or cross-multiply. The skill is choosing the cleanest tool for the numbers.

01 / THE IDEA

See it work.

Watch the method

Pick the tool

Read the problem, then pick the easiest method.

1 / 2
3/4=?/123/4 = ?/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.

The decision

Nice scale factor → ratio table or unit rate. Awkward numbers → cross-multiply. All give the same answer.

Why it works

Match the method to the numbers.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Solve 9 * 2

1

Multiply by the scale factor

Scale 9 by 2. 9 × 2 = 18

EX 2medium

Solve 30:20

1

Find the common factor

10 divides both 30 and 20. gcd(30,20) = 10

2

Divide both parts

Divide each part by the common factor. 30:20 = 3:2

EX 3hard

Solve 18:12

1

Find the common factor

6 divides both 18 and 12. gcd(18,12) = 6

2

Divide both parts

Divide each part by the common factor. 18:12 = 3:2

04 / COMMON TRAPS

Where students slip.

Trap

Forcing cross-multiplication when scaling is easier.

Fix

Use the unit rate when the factor is clean.

Trap

Setting up the ratio in the wrong order.

Fix

Keep the quantities consistent.

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 6, 24

Need a hint?
  • Look at the numbers first.
  • Pick the cleanest method.
C2

Solve 2, 8

Need a hint?
  • Look at the numbers first.
  • Pick the cleanest method.
C3

Solve 24 / 8

Need a hint?
  • Look at the numbers first.
  • Pick the cleanest method.
C4

Solve 6, 48

Need a hint?
  • Look at the numbers first.
  • Pick the cleanest method.
Apply

Apply (4)

A1

Solve 3, 21

Need a hint?
  • Look at the numbers first.
  • Pick the cleanest method.
A2

Solve 9:9

Need a hint?
  • Look at the numbers first.
  • Pick the cleanest method.
A3

Solve 72 / 8

Need a hint?
  • Look at the numbers first.
  • Pick the cleanest method.
A4

Solve 14 / 2

Need a hint?
  • Look at the numbers first.
  • Pick the cleanest method.
Extension

Extension (4)

E1

Solve 2 * 4

Need a hint?
  • Look at the numbers first.
  • Pick the cleanest method.
E2

Solve 3 * 5

Need a hint?
  • Look at the numbers first.
  • Pick the cleanest method.
E3

Solve 4, 16

Need a hint?
  • Look at the numbers first.
  • Pick the cleanest method.
E4

Solve 3/4 = 9/?

Need a hint?
  • Look at the numbers first.
  • Pick the cleanest method.