🧱 See It
A recipe uses 2 cups of flour for every 1 cup of sugar. Double the recipe, and both numbers double — 4 cups flour, 2 cups sugar. The ratio between them (2 to 1) never changes, even as the actual amounts grow.
✏️ Draw It
| Batches | Flour (cups) | Sugar (cups) |
|---|---|---|
| 1× | 2 | 1 |
| 2× | 4 | 2 |
| 3× | 6 | 3 |
Every row keeps the same 2-to-1 ratio — only the batch size changes.
🔢 Write It
Write two equal ratios as a proportion, then cross-multiply to find a missing value:
a/b = c/d ⇒ a × d = b × c
Label what each position means (flour, sugar, cost, apples...) before cross-multiplying — matching positions must hold the same kind of thing.
💡 Worked Examples
Example 1 — 3 apples cost $2. How much do 12 apples cost?
- Set up matching positions:
3 apples / $2 = 12 apples / $x - Cross-multiply:
3 × x = 2 × 12 - Simplify:
3x = 24 - Divide both sides by 3:
x = 8 - Answer: $8
Example 2 — A map scale is 1 cm = 5 km. A distance measures 7 cm on the map. What's the real distance?
- Set up matching positions:
1 cm / 5 km = 7 cm / x km - Cross-multiply:
1 × x = 5 × 7 - Answer:
x = 35 km
🧠 Quick Reference
Set up the proportion with matching positions labeled (same unit in the same spot on both sides). Cross-multiply: top-left × bottom-right = bottom-left × top-right. Then solve like a one-step equation.