NapkinCalc

Pre-Algebra — Numbers & First Variables

Ratios & proportions

continues from lesson 3 — values defined earlier in the course stay live here

ELI5: a ratio compares two amounts (3 apples to $2). A proportion sets two ratios equal and lets you scale up: if 3 apples cost $2, then 12 apples (4× as many) cost 4 × $2 = $8.

applescost=2⋅123apples_{cost} = 2 \cdot \frac{12}{3} = 88 scale the cost by 12/3 = 4: \$8
✓ pass applescost==8apples_{cost} == 8 four times the apples, four times the price

Real-world hook: proportions scale recipes, convert map distances to real ones, mix paint and concrete, and read unit prices at the store.

Try it yourself: a recipe uses 2 cups of flour for 3 cookies. How much flour for 12 cookies?

flouryou=2⋅123flour_{you} = 2 \cdot \frac{12}{3} = 88 ✏️ Your turn: scale 2 cups by how many times bigger 12 cookies is than 3. (Multiply 2 by 12/3.)
✓ pass abs(flouryou−2⋅123)<10−9\mathrm{abs}\left(flour_{you} - 2 \cdot \frac{12}{3}\right) < 10^{-9} green when your amount scales the ratio correctly