Picture 1
Setting up crossproportions (crossmultiplications)
A crossproportion is a mathematical expression of a problem that you are usually given in a form of a
written text. For instance:
If a dozen of donuts costs 4.95$, then
how much does one donut cost?
Let’s simplify:
if
12
donuts
cost
4.95 $
then
1
donut costs
x
Notice how “donut” lies underneath “donuts”. “Donuts” can be considered to be the “
units
“ of the
goods you are buying. Consequently, you can expect the “$” units to accompany the result for x.
Let’s simplify the above even further, by losing the “if” and “then”, and replacing the “cost(s)” by a
dash (
not
a minus sign):
12
donuts

4.95 $
1
donut

x
The above can be written into a four compartment box:
12
donuts
4.95 $
1
donut
x
To solve for x, multiply the numbers in the two compartments that lie daigonally across from each
other by each other, and divide the result by the number in the compartment that lies diagonally across
from the one in which the x is located.
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 Fall '08
 Cook
 Light, Kilogram, Orders of magnitude, Conversion of units, ml

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