Section 3-4: Ratio and Proportion

Objectives:

1) To find ratios and rates

2) To solve proportions

Definitions

Ratio: A relationship between two numbers through division

Rate: In a ratio, when each term represents a quantity measured in different units

Unit Rate: a rate with a denominator of 1.

Unit Analysis: The process of converting from one unit to another

Proportion: An equation that states that two ratios are equal

Extremes of the Proportion: the numerator the 1st ratio and the denominator of the 2nd ratio.

Means of the Proportion: the numerator of the 2nd ratio and the denominator of the 1st ratio

Cross Product Property

If d

c

b

a , then bcad

Ex:

12

8

3

2 83122 2424

Since 24 = 24, we know that the proportion is valid

extremes means

Unit Pricing …In Real Life

Example: Using Unit Rates

The table below gives 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 Volume

$0.72 16 oz

$1.20 32 oz

$1.60 64 oz

Using Unit Rates

oz16

72.0$

oz32

20.1$

oz64

60.1$

Divide

Divide

Divide

oz

045.0$

oz

0375.0$

oz

025.0$ This has the lowest cost per ounce.

Real-World Example

In 2004, Lance Armstrong won the Tour de France, completing the 2291 km course in about 83.6 hours. Find Lance’s unit rate, which is his average speed. Write a rule to describe the distance he cycles d as a function of the time t he cycles. Cycling at his average speed, about how long would it take Lance to cycle 185km?

Real-World Example

Distance Time 6.83

2291km hrkm /4.27

rtd td 4.27

t4.27185 4.27

t75.64.27

Another Cross Product Example

7

2

5

4

xx

Solve the proportion

)2(5)4(7 xx

105287 xxx5 x5

10282 x28 28

382 x

2 219x