Proportions & Cross-Multiplication
📋 What it is
A proportion sets two ratios equal; cross-multiplying solves for a missing part.
🗣️ Coach says
A proportion says two ratios are equal: 2/3 = x/9. To find x, cross-multiply (2 × 9 = 3 × x) and solve. It's the engine behind scaling recipes, maps and mixtures.
🧠 Memory hook
Two equal ratios → cross-multiply (diagonal × diagonal) → solve for the unknown.
😂 Giggle
Why did the fraction apply for a job at the ratio department?
Because it wanted to be part of something bigger!
😲 Whoa!
Pharmacists use proportions to scale a medicine dose to a patient's weight — a real-life cross-multiplication.
✅ Quick check: Solve the proportion 2/3 = x/9.
Say your answer out loud first — then reveal.
x = 6 — cross-multiply: 2 × 9 = 18, then 18 ÷ 3 = 6.
Cross-multiplication turns a proportion into a solvable equation.
🧪 Try it! (2 minutes)
Set up 1/2 = x/10 and cross-multiply to find x (= 5).