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A quick, calm intro — then you choose when to climb.
A ratio compares two quantities in order — a recipe in miniature.
Order matters — 2 : 3 means 2 parts of the first, then 3 parts of the second
Scaling — multiply BOTH parts by the same number — the ratio stays the same
Never add — ratios scale; you cannot add the two parts together
Every step explained — why we do it, and what happens.
Why: Read it as a recipe: for every 2 of the first thing, exactly 3 of the second.
What happens: A 2 : 3 recipe.
Why: Scaling keeps the taste: multiply both parts by the same number, 4.
What happens: Both parts × 4.
Why: 2 × 4 = 8 and 3 × 4 = 12 — the same recipe, four times bigger.
What happens: 8 : 12 ✓ — same ratio, bigger batch.
A hiking map has the scale 1 cm : 5 km. Two mountain huts are 7 cm apart on the map. How far apart are they in real life?
Why: Every centimetre on the map stands for 5 km on the ground — that is the scale, a ratio.
What happens: The recipe of the map.
Why: Scale up by 7: the map distance is 7 cm, so the real distance is 7 × 5 km.
What happens: 35 km.
Why: The glitch: adding instead of scaling. Centimetres and kilometres are different units — you cannot add them; the ratio multiplies.
What happens: Ratios scale, they never add.
Why: The check: both parts scaled by 7 give the same ratio.
What happens: 35 km ✓ — scale obeyed.
Two classic glitches:
1.Scaling only one side
Wrong: → double only the first:
Right:Both parts scale together: .
2.Adding instead of scaling
Wrong:1 cm : 5 km, so km
Right:Multiply both parts: km.
You've got the concept! Let's lock it in with practice.
Learning is optional — the ladder is always open.