Section 4.5 Ratios and Proportions
A Ratio is a comparison of numbers.
(example: The student to teacher ratio of 35 to 1 means that for every
35 students in an LBCC math class, there is only one teacher.)
We can express this several ways:
35 to 1
or
35:1
or
35
1
We will use the fraction form most of the time. Note that the order of
the ratio determines which value is the numerator and which is the
denominator:
numerator:denominator or numerator "to" denominator
EXAMPLE: In 2010­2011, there were 5685 students aged 18 to 25 compared to 800 students aged 46 to 65 at LBCC.
a) What was the ratio of students aged 18 to 25 compared to students aged 46­65? Simplify your answer.
b) What was the ratio of students aged 46 to 65 compared to students aged 18 to 25? Simplify your answer.
Two ratios set equal to each other is called a proportion.
In any true proportion, the cross products are equal:
c
a
=
d
b
If
, then ad = bc
We can use proportions and cross products to solve for
a variable!
EXAMPLE: Solve the proportion:
12
x
=
16
9
EXAMPLE: Use a proportion to solve the problem.
CPR should be done on a cycle of 30 chest compressions per 2 rescue breaths. If a total of 2940 chest compressions were done during a rescue, how many rescue breaths should have been administered? (pay attention to units and their "position" in the ratios.)
Sides of Similar Triangles are Proportional!
If we know that
ABC is similar to
DEF, then we know :
If two triangles are similar, their corresponding sides have the same
ratio.
Let's set up and solve Your Turn 5 on p. 425:
We have PQR is similar to STU. Find the length of side TU.
S
18 m
25 m
P
U
Q
15 m
20 m
R
T