Download Ratios, Proportions, and the Geometric Mean

Section 6.1-Ratios, Proportions, and the Geometric Mean
Vocab
Ratio – if a and b are two number quantities and b is not 0, then the ratio of a to b is:
Proportion – an equation that states two
are
Geometric Mean – the number x that satisfies
.
. Ex:
a x
 for two positive numbers a and b.
x b
Simplifying Ratios
Step 1 – Take care of the units
If the units are the same, eliminate them:
If the units are different, use a conversion factor:
12 gallons
3gallons
16quarts
2 gallons
Step 2 – Simplify
4
2
12
3
Cross Product
Step 1 – Multiply the numerators with the denominators of the opposite side:
Step 2 – Simlify
6 x

7 14
x
5

33 11
9 27

x 12
1
35

100 x
Geometric Mean
a x
 or more directly using x  ab
x b
Example: Find the geometric mean of 4 and 16
This can be solved using the proportion
8
16

x  1 10
Additional Properties of Proportions (short cuts)
You can turn the proportion
upside down!
a c
b d
If  , then  .
b d
a c
The denominator and
numerator on opposite sides
can be swapped!
a c
a b
If  , then  .
b d
c d
The denominators can be
added to both sides!
a c
ab cd

If  , then
.
b d
b
d