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# Proportion

"The statement of equality of two ratios is called a proportion."

Find an unknown ratio with a proportion

Eg. If x:4 = 7:12

Make them fractions
make them simple as possible
solve for x
(if x on left, multiply both sides by denominator under x. if x on right, multiply both sides by denominator on opposite and x)

Eg. x:4 = 7:12
x/4 = 7/12
4 * x/4 = 4 * 7/12
x = 28/12
x = 2 and 4/12
x = 2 and 1/3

Eg. If 4: x = 16:20
4/x = 16/20
4/x = 4/5
5x * 4/x = 5x * 4/5
20 = 4x
5 = x

Mean Proportion

"If a: x = x:b, then x is called a mean proportion of a and b."

Make them fractions.
Solve for x

Eg. find a mean proportion of 1 and 2.
1: x = x:2
1/x = x/2
2x * 1/x = 2x * x/2
2 = x^2
plus or minus sqrt.2 = x

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Real Life Application

Gears and belts

tD/tF = rF/rD

That means:

number of teeth on the driver wheel divided by number of teeth on the follower wheel
is equal to
the number of revolutions on the follower wheel divided by the number of revs on the driver wheel.

Note: that they are inverse...

On a belt it is measured, not by teeth, but by the diametre of the wheels. Essentially though, it is the same formula.

dD/dF = rF/rD

Therefore, if you know how many teeth there are, you can figure out how many revolutions by using mean proportion.