# Thinking Mathematically by Robert Blitzer

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```					  Thinking
Mathematically
Ratio, Proportion, and Variation
“Ratios”

A “ratio” is one quantity divided by another.
For example if a basketball player makes 7
out of 10 free throws, the ratio of “made”
free throws to total free throws is 7/10.
Written as a decimal this is .7 and multiplied
by 100 it is 70%. This is called his “free
throw percentage.”
The Cross Products Principle for
Proportions
If a/b = c/d,
then ad = bc. (b and d do not equal zero.)
The cross products ad and bc are equal.
Example: 63/x = 7/5             This is given
63•5 = 7x         Cross products
315 = 7x          Simplify
315/7 = 7x/7      Divide by 7
45 = x            Simplify
The solution set is {45}.
Solving Applied Problems Using
Proportions
1. Read the problem and represent the
unknown quantity by x (or any letter).
2. Set up a proportion by listing the given
ratio on one side and the ratio with the
unknown quantity on the other side.
3. Drop the units and apply the cross
products principle.
4. Solve for x and answer the question.
“Direct Variation”
Two quantities are said to “vary directly” if their
ratio is constant. Then one of them is a constant
multiple of the other. If one goes up the other
will go up and if one goes down the other will go
down.
If a and b vary directly, then a equals b times a
constant and a/b does not change as a and b
change together.
“Inverse Variation”

Two quantities are said to “vary inversely”
if their product is constant. Then if one of
them goes up the other must go down.

If a and b vary inversely, then a times b is a
constant and a x b does not change as a and
b change together.
Thinking
Mathematically
Ratio, Proportion, and Variation

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 views: 4 posted: 8/11/2012 language: pages: 7