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
A Ratio is a comparison of two quantities
by division.
a
, a : b, and a to b
b

Usually a and b are in the same units and
the ratio is expressed in simplest form.

A building is 20 yds tall and a person
going through the front door is 5 ft, 4
inches tall. What is the ratio of the height
of the building to the height of the
person?
a 20 yds 60 ft 720in 45




b 5 ft 4in 64in 64in
4

An Extended Ratio is a comparison of
three or more numbers.
a:b:c

When using an extended ratio if there
are no variables already in place, then
put some in yourself.
4 : 3: 6
4x : 3x : 6x

The angles in a triangle are in an
extended ratio of 4 : 5: 6 , what is the
measure of the largest angle?
4x  5x  6x  180
15x  180
x  12
6 x  Largest Angle
6(12)  72

A Proportion is an equation that states
that two ratios are equal.
extremes
a:b  c:d
extremes
means
means

a c
=
b d
The Cross Products Property says:
ad  bc

Solve for x in the following proportions.
6 5

x 4
5x  24
24
x
5
x4 x

9
3
9 x  3( x  4)
9x  3x 12
6x  12
x2

In the following proportions a, b, c, and d
do not equal zero.
a c
1. b = d
a c
2. b = d
a c
3. b = d
is equivalent to
b d
=
a c
is equivalent to
a b
=
c d
is equivalent to
ab cd
=
b
d

Solve for the equivalent proportion.
If
6 5

x y
If
x y

9 3
x ?
Then 
y ?
9 ?
Then 
? y
x 6

y 5
9 3

x y

P. 436 #’s 9-32, 38, 40-44, 49-54, 61-65