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Lesson 1 · Reading rates
Money wears uniforms
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Money wears uniforms

Welcome to the money chapter — and here is the trick that carries the whole thing: read the unit before the number. Plain dollars ($24\$24) are a total — money, full stop. Dollars wearing a slash ($6/kg\$6/\mathrm{kg}) are a rate — money per something, and the slash is how it tells you. Kilograms with no dollars in sight (2.5 kg2.5\ \mathrm{kg}) are a quantity — the stuff itself.

And a percent? The % sign is a unit too — the per-hundred unit. 25% is not 25 dollars and not 25 kilograms: it is 25 out of every hundred of whatever it touches. That is its superpower and its trap in one: a percent means nothing until you know what it is a percent OF. No calculating this lesson — just look at each number's outfit and name it. The units will do the pointing all chapter long.

mCp

p=Cmp = \frac{C}{m}

  • pp= Unit price (cost per mass)
  • CC= Total price (money)
  • mm= Quantity (mass)
Unit Price (Price per Unit Quantity) solver →
cxoldxnew

c=xnew−xoldxoldc = \frac{x_{\text{new}} - x_{\text{old}}}{x_{\text{old}}}

  • cc= Relative change
  • xnewx_{\text{new}}= New value
  • xoldx_{\text{old}}= Old value
Percent Change solver →