Exploring Data: Rates & Ratios

• Objectives:

• Learn how to use rates to relate quantities measured in different units

• Learn how to use ratios to relate quantities measured in the same units

Rate: Rates are used to compare quantities with

different units by division.

If a & b are 2 quantities that are different units, then the average rate of a per b is b

a

Common Rates:

gallon

miles

hour

miles

hour

dollarspound

dollars

If you drive 250 miles and use 10 gallons, how many miles did you get per gallon?

g

m

gallons

miles

10

250

Reduce fraction to:

.

.25

gal

mi25

miles/gallonor

If you earn $300 in 50 hours, how much did you earn per hour?

Per hour = Total pay

Total hours

hours

dollars

50

300 Reduce when possible

Divide to find pay per hour

hourper /6$5

30

Money Exchange Rates

Canada is $1.1515 to one US dollar. If you have $175 US how much

Canadian?

Rate:

$175$

$1

1515.1US

Canadian

US

Words cancel out and you have

$51.201 Canadian

If you spend all but $32.50 C$ how many US$

do you have left?Rate:

1515.1

50.32$50.32

$1515.1

$1 C

C

US

22.28$ US $ leftSet fractions up so the unit

you want left is in the numerator!

Ratio: Ratios, like rates, compare quantities by division, but ratios compare quantities measured in the same unit. In itself, a ratio has NO units.

a to b=b

a=a:b

Ratios are often left as fractions with no units

shown

Basketball team won 10 games, lost 6 games

Win to loss ratio: 3

5

6

10

Rate or Ratio?

Compare the area of 2 rooms. One is 10 by 10

the other 15 by 15.

#1: 2.

1.

rooma

rooma

1515

1010

225

100

25.2

1

9

4

#2: 1

2

Room

Room

1010

1515

100

225

1

25.2

Which is easier to read?

2nd way shows that the 2nd room is over twice as large as the first

(ratio)