4.1 Ratio and Proportion• Ratio – comparison of two numbers by division.

– Can be written:• a to b• a : b

• where b ≠ 0.

• 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 a denominator of 1.– Ex.

a

b

40

1

miles

hour

Using Unit RatesFind the rate (cost per ounce).

$1.20

32oz

$.045/oz

$1.60

64oz

$.0375/oz

$.72

16oz

$.025/oz

Converting RatesA cheetah ran 300 feet in 2.92 seconds. What was the

cheetah’s speed in miles per hour?

You need to convert feet to miles and seconds to hours.

1080000

15417.6

300 1 60 60min

2.92 5280 1min 1

ft mi s

s ft h

70 /mi h

300 1 60 60min

2.92 5280 1min 1

ft mi s

s ft h

Solving Proportions• A proportion is an equation that states that two

ratios are equal.

a = c for b ≠ 0 and d ≠ 0.

b d

You read this proportion as “a is to b as c is to d”.

• The extremes of the proportion – are a and d.

• The means of the proportion – are b and c.

• Another way you can see this proportion written is a : b = c : d.

Cross Products• The products ad and bc are the cross products of the

proportion

• For example,

2 12 8 3

2 8

3 12

.a c

b d

Using Cross Products

• Use cross products to solve the proportion

(4) (2.5)( 3)y

3

2.5 4

y

1.875y

4 7.5y

3.

2.5 4

y

Using Multi-Step Proportions• Solve the proportion

7( 4) 5( 2)x x

4 2

5 7

x x

2 28 10x 7 28 5 10x x

4 2.

5 7

x x

2 38x 19x

More Practice!!!!

• Textbook – p. 185 #2 – 28 even, p. 186 #32 – 36 even.

• Homework – Worksheet 4.1