Transcript 1-3 convert unit rates

PO
D
Write your own
complex fraction
that simplifies to
¼
PO
D
If Cole ran 12¼
miles on Sunday
in 3½ hours, what
what his speed in
basic
PO
D
After the first 15 games of
the season, Stephen Curry
had 31½ steals. How many
steals per game did he
have?
advanced
James Harden averages
27.2 points per game. A
game is usually 48 minutes
long. How many points per
second does he average?
1-3 Convert Unit Rates
Smaller
Larger
Smaller
Larger
12 inches
1 foot
100 centimeters
1 meter
16 ounces
1 pound
1000 grams
1 kilogram
8 pints
1 gallon
1000 milliliters
1 liter
3 feet
1 yard
10 millimeters
1 centimeter
5,280 feet
1 mile
1000 milligrams
1 gram
Each of these relationships in the
tables can be written as a unit ratio.
12
inches
1 foot
16 ounces
1 pound
100 centimeters
1 meter
1-3 Convert Unit Rates
Smaller
Larger
Smaller
Larger
12 inches
1 foot
100 centimeters
1 meter
16 ounces
1 pound
1000 grams
1 kilogram
8 pints
1 gallon
1000 milliliters
1 liter
3 feet
1 yard
10 millimeters
1 centimeter
5,280 feet
1 mile
1000 milligrams
1 gram
Each of these relationships in the
tables can be written as a unit ratio.
12
inches
1 foot
16 ounces
1 pound
100 centimeters
1 meter
You can convert one rate to an equivalent
rate by multiplying by a unit ratio or its
reciprocal.
You must include units in your
computation.
The process of including units of
measure as factors when you compute
is called dimensional analysis.
10 ft
1s
=
10 ft
1s
×
12 in
1 ft
=
10 × 12 in
1s×1
=
120 in.
1s
Example
1.) A remote control car travels at a rate of 10 feet per
second. How many inches per second is this?
10 ft
1s
=
10 ft
1s
=
10 ft
1s
=
=
×
12 in
1 ft
Use 1 foot = 12 inches. Multiply by
×
12 in
1 ft
Divide out common units
10 × 12 in
1s×1
120 in.
1s
Simplify
Simplify
12 in.
1 ft.
2.) A swordfish can swim at a rate of 60 miles per hour.
How may feet per hour is this?
60 mi
1 hr
×
5280 ft
1 mi
5280 ft.
Multiply by 1 mi.
×
5280 ft
1 mi
Divide out common units
=
60 mi
1 hr
=
60 mi
1 hr
=
60 × 5280 ft
1 hr × 1
Simplify
=
316,800 ft
1 hr
Simplify
3.) Marvin walks at a speed of 7 feet per second. How
many feet per hour is this?
7 ft
1s
=
=
7 ft
×
1s
7 ft
×
1s
60 s
×
1 min
60 s
×
1 min
60 min
1h
60 min
1h
60 s
Multiply by 1 min and
Divide out common units
=
7 × 60 × 60ft
1 ×1 × 1h
Simplify
=
25,200 ft
1 hr
Simplify
60 min
1h
4.) A gull can fly at a speed of 22 miles per hour. About
how many feet per hour can the gull fly?
22 mi
1h
=
=
22 mi ×
1h
5280ft
1 mi
22 mi
× 5280 ft
1h
1 mi
5280 ft
Multiply by 1 mi
Divide out common units
=
22 × 5280ft
1h × 1
Simplify
=
116,160 ft
1h
Simplify
5.) An Amtrak train travels at 125 miles per hour.
Convert the speed to miles per minute. Round to the
nearest tenth.
125 mi
1h
=
125 mi ×
1h
=
1h
60 min
125 mi
× 1h
1h
60 min
1h
Multiply by 60 min
Divide out common units
=
125 mi × 1
1 × 60 min
Simplify
=
2.1 mi
1 min
Simplify