Transcript Algebra 11.1

Objectives:
Solve proportions
Algebra 11.1 - Problem
Solving Using Proportions
• Jamie: Is your new
girlfriend goodlooking?
• Hamish: Yes, except
for her pedestrian
eyes.
• Jamie: What are
pedestrian eyes?
• Hamish: They look
both ways before they
cross.
Ratio
A ratio is a quotient of two numbers
Example: the ratio of 5 meters to 3 meters
can be written in any of the following ways.
5
3
5:3
5 to 3
5 3
Note: The first number is the numerator. Ratios are usually given in lowest terms.
Proportion
A proportion is an equation stating that two
or more ratios are equal.
1 5

2 10
4 10

6 15
5 :15  15 : 45
x 2

y 3
Proportion
a is called the first term
b is called the second term
a c

b d
c is called the third term
d is called the fourth term
The first and fourth terms are called the extremes
The second and third terms are called the means
8 w

s 40
Identify the means and the extremes.
Properties of Proportions
1. If two ratios are equal, their reciprocals
are also equal. (Reciprocal Property)
a c
b d
If
 , then 
b d
a c
2. The product of the extremes equals the
product of the means. (Cross-Multiplying
Property)
a c
If
b

d
, then ad  bc
Solving a Proportion
Example -
3 7
if  , solve for x
x 14
3(14) = x(7)
42 = 7x
6=x
Solving a Proportion
x
2
if
 , solve for x
x4 x
x( x)  2( x  4)
x  2x  8
2
x  2x  8  0
x  4x  2  0
2
x  4 or x  -2
Homework
•Pg. 565
•7-26