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)