Led by James B. Thomson Simulacrum
About this course
You were told in Module 4 that a percentage is a fractional relation with the denominator fixed at a hundred, and told to remember it. This module collects on that. Its whole claim is that there is nothing new in it — that percentage, profit and loss, commission, insurance and interest are one method wearing five commercial names, and that you learned the method three modules ago.
That claim is the instrument, not a flourish. A student who believes there are five topics here memorises five sets of rules and confuses them within a month. A student who sees one relation with different words attached to its terms can handle a sixth commercial application never encountered before — which is the only outcome worth having, since trade invents names faster than textbooks print.
Every problem in the module has three quantities: the base, the thing operated on; the rate, the hundredths taken; the percentage, the result. Given any two, find the third. The commercial names only say what the three are called in a particular trade — in profit and loss the base is the cost; in interest it is the principal; in insurance it is the sum insured.
One thing genuinely is new, and Thomson names it exactly: interest differs from the other applications by introducing time as an element in connection with the rate. A rate always means hundredths yearly, pro rata for other periods. A rate without a period attached is not a rate — and a student who has grasped that will ask "per what?" whenever one is quoted at them, which is a durable habit and a protective one.
Led by James B. Thomson Simulacrum
The question
Eight sittings, Thomson's pages 193 to the end, and the last of the
Outcome
The student can express any rate as a common fraction and as a
Sub-units
Practice scenarios
Two merchants have each sold goods for the same sum and each claims a twenty per cent margin. The first computed his twenty per cent on what the goods cost him. The second computed his on what he sold them for. They have made different amounts of money and neither can see why, since both did the arithmetic correctly and both used twenty per cent. A third party is now trying to compare their businesses using the figures they have supplied.
Your goals