Download NOTES 3-6 Ratios and Proportions Pages 155-157

NOTES 3-6 Ratios and Proportions Pages 155-157
I can determine whether two ratios form a proportion and I can solve for an
unknown using proportions.
Main Idea
Ratio
Details
A comparison of two numbers by division.
x
x to y x:y
y
An equation stating that two ratios are equal.
Proportion
Determining if two ratios
form a proportion
4 6 
 is a proportion.
2 3
Method 1: If both the numerator and denominator
of one ratio can be multiplied or divided by the
same
number to obtain the second ratio, then the
ratios form a proportion.
See Example 1 on page 155
Method 2: If the cross products (numerator of one
ratio multiplied by the denominator of the other
ratio) are equal, then the ratios form a proportion.
See Example 2 on page 156
In the proportion
a c

b d
Extremes of a proportion
a and d are the extremes.

 In the proportion
Means of a proportion
a c

b d
b and c are the extremes.

In a proportion, the product of the extremes is equal
to the product of the means.
Means-Extremes Property
of Proportion
If
a c
 , then ad = bc.
b d
4 6
Since  , 4(3) = 6(2) or 12 = 12.
2 3

Rate
A ratio of two measurements having different units

of measure.
Scale
A ratio or rate that is used in the making of a model
or drawing of something that is too large or too
small to be conveniently drawn at actual size.
Example 1:
Determine whether the ratios
7
49
and
form a proportion.
8
56

0.25 1.25
,
0.6 2

Example 2:
Use cross products to
determine whether each pair
of ratios form a proportion.

4 16
,
5 20

Example 3:
Solve the proportion
n 3

12 8

Example 4:
The gear on a bicycle is 8:5.
This means that for every 8
turns of the pedals, the
wheels turn 5 times.
Suppose the bicycle wheel
turns about 2435 times
during a trip. How many
times would you have to
crank the pedals during the
trip?
Example 5:
In a road atlas, the scale for
the map of Connecticut is
5 inches = 41 miles. The
scale for the map of Texas is
5 inches = 144 miles. What
are the distances in miles
represented by 2 12 inches on
each map?

Homework: Workbook Page 22 #3-33 multiples of 3 and #34, 35