Transcript 4-1 PPT Ratio and Proportion

Section 4-1 Ratio and Proportion
SPI 12F: select ratios and proportions to represent real-world problems
SPI 41B: calculate rates involving cost per unit to determine best buy
Objectives:
• To find ratios, unit rates, rates, and solve proportions
Ratio: comparison of two numbers by division
Rate: a ratio where a and b represent quantities measured
in different units.
Unit rate: A rate with a denominator of 1.
Proportion: an equation that states two ratios are equal.
Ratio
(comparison of 2 numbers by division)
The ratio of two quantities a and b, can be written as:
a to b
a:b
a
b
What is the ratio of girls to boys if there
are 13 girls and 22 boys?
13 to 22
13:22
13
22
Real-world and Ratios
In the plains of Africa, zoologist
tagged zebras to discover that
there exists 178 female zebras to
148 male zebras.
What is the ratio of male to total
number of zebra?
There are 148 male zebras.
There is a total of 326 zebras.
The ratio is
148 to 326
74 to 163
148:326
148
326
74:163
74
163
Rate
(Ratio where a and b represent quantities measured in different units)
Unit Rate
Rate with a denominator of 1
Since your income is limited, you want to shop
for the best bargains in a grocery store. You
are purchasing apple juice. The price of apple
juice is $0.72 for 16 oz or $0.90 for 18 oz.
Which is the better buy?
$0.72 for 16 oz
$.72 $.045

 $.045
16oz
1
$0.90 for 18 oz
$0.90 $0.05

 $0.05
18oz
1
Real-world and the Unit Rate
How much does a person earn if they work 50
hours and receive $475?
$475
 $9.50 per hour
50
You have paid $44 to skate at a skateboard
park for 8 hours. What is the cost per hour
(unit rate)?
$44
 $5.50 per hour
8
Proportions
(an equation that states two ratios are equal)
Use Multiplication Property of
Equality to Solve Proportions
Cross Products of Proportions
(Use ONLY when one ratio or
fraction equals another)
3 x

4 8
3 x

4 8
3 x
8  8
4 8
3 8  4  x
6 x
24  4x
24 4 x

4
4
6 x
Use Cross-Products to Solve the Proportions
1. Solve the proportion:
5 c

6 9
2. Solve the proportion:
x4 x2

5
7
6c  9  5
6c  45
c  7.5
Distributive Property
7( x  4)  5( x  2)
Simplify
7 x  28  5x 10
7 x  28  5x  5x 10  5x SPE
Simplify
2x  28  10
2x  28  28  10  28 SPE
2x  38 Simplify
x  19
Setting up to Write a Proportion
If people could jump as high as a flea, how high could a
person, that is 5 feet tall jump if a flea that is .125 inches
tall can jump to a height of 13 inches?
Jump height
Tallness
13 =
.125
x
5
.125x  13  5
.125x  65
.125
65
x
.125
.125
x  520
Answer the question
A person could jump
to a height of 520 feet.
Write and Solve a Proportion
In 2000, Lance Armstrong completed the 3630-km Tour de France
course in 92.5 hours. Traveling at his average speed, how long would
it take Lance Armstrong to ride 295 km?
3630
295
=
92.5
t
3630t = 92.5(295)
Write cross products.
t=
92.5(295)
3630
Divide each side by 3630.
t
7.5
Simplify. Round to the nearest tenth.
Traveling at his average speed, it would take Lance approximately
7.5 hours to cycle 295 km.