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:bb

a

What is the ratio of girls to boys if there are 13 girls and 22 boys?

13 to 22 13:2222

13

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 326 148:326326

148

74 to 163 74:163163

74

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 $0.90 for 18 oz

045$.1

045$.

16

72$.

oz05.0$

1

05.0$

18

90.0$

oz

Real-world and the Unit Rate

How much does a person earn if they work 50 hours and receive $475?

You have paid $44 to skate at a skateboard park for 8 hours. What is the cost per hour (unit rate)?

hourper 50.9$50

475$

hourper 50.5$8

44$

Proportions (an equation that states two ratios are equal)

Use Multiplication Property of Equality to Solve Proportions

84

3 x

884

38

x

x6

Cross Products of Proportions(Use ONLY when one ratio or

fraction equals another)

84

3 x

x 483

x424

4

4

4

24 x

x6

Use Cross-Products to Solve the Proportions

1. Solve the proportion:

2. Solve the proportion:

596 c

96

5 c

7.5c

456

c

7

2

5

4

xx)2(5)4(7 xx

105287 xx

19x

xxxx 51055287 10282 x

281028282 x382 x

Distributive Property

Simplify

SPE

Simplify

SPE

Simplify

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 heightTallness

13 .125

x 5

=

513125. x65125. x

125.

65

125.

125.x

520x

Answer the questionA person could jump to a height of 520 feet.

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?

363092.5 =

295t

3630t = 92.5(295) Write cross products.

t = Divide each side by 3630.92.5(295)

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.

Write and Solve a Proportion