3.4 Ratio and Proportion
A ratio is a comparison of two numbers by division.
- the ratio of a to b is
a:b
or
a
b
- If a and b represent quantities measured in different units,
then the ratio of a to b is a rate.
A unit rate is a rate with denominator of 1.
Ex: 40 mph or 40 mi/hr.
Ex 1: The table below gives the prices for different sizes of the same
brand of apple juice. Find the unite rate (cost per ounce) for
each. Which has the lowest cost per ounce?
Price of Apple Juice
Price
$0.72
Volume
16 oz
$1.20
32 oz
$1.60
64 oz
1
1
Ex 2 In 2000, Lance Armstrong completed the 3630-km Your
de France course in 92.5 hours. Traveling at his average
speed, how long would it take Lance Armstrong to ride
295 km?
Guided Practice
1. Suppose you walk 2 miles in 35 minutes.
a. Find the average walking speed. Write a rule to describe the
distance d you walk as a function of the time t you walk?
b. Use the function to find how far you would walk in an hour.
Ex 3 A cheetah ran 300 feet in 2.92 seconds. What is the
cheetah's average speed in miles per hour?
Homework: Pages 145 - 147 # 1-7, 47 - 51
2
3.4 Ratio and Proportions (continued)
A proportion is an equation that states that two ratios are equal.
for b ≠ 0 and d ≠ 0
This is read " a is to b as c is to d "
Extremes of the proportion:
Means of the proportion:
Using the Multiplication Property of Equality to Solve Proportions
=
Ex: Solve
y
3
3
4
3
3
Guided Practice:
Solve each equation
1.
x
8
=
5
6
2.
y
3
=
12
8
We can use the Multiplication Property of Equality to prove
an important property of proportions
c
a
=
d
b
Cross Products of a Proportion
Ex: Use the cross products to solve the proportion.
12
4
x = 25
(z - 4)
(z + 3)
=
6
4
4
4
Pages 146 - 147 # 16 - 22, 26 - 31, 44, 38 - 46 even
5