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Unit Conversions Units are Wonderful and Horrible! Do unit conversions when you want an answer in different units than the original information you have Familiar Units Salary : dollars per hour [$/hr --> $/year] Price : dollars per pound [$/lb --> $/turkey]

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unit conversions
Unit Conversions
  • Units are Wonderful and Horrible!
  • Do unit conversions when you want an answer in different units than the original information you have
  • Familiar Units
    • Salary: dollars per hour [$/hr --> $/year]
    • Price: dollars per pound [$/lb --> $/turkey]
    • Speed: miles per hour [m/h, or miles/trip]
  • Examples of “Unity” fractions (ones that equal “1”)
    • Time: minutes per hour [60 min/1 hour]
    • Weight: ounces per pound [16 oz/1 lb]
example salary
Example: Salary
  • It all boils down to multiplying your starting info by a series of “unity” fractions (1) , set up to get the final units you want
  • When you add “units” (words) to fractions, you can treat them just like numbers, i.e. cancel matching units

(1)

(1)

(1)

(1)

20$ x 8 hours x 5 days x 4 weeks x 12 months

hour day week month year

cancel units
Cancel Units
  • It all boils down to multiplying your starting info by a series of “unity” fractions (1) , set up to get the final units you want
  • When you add units (“words”) to fractions, you can treat them just like numbers

(1)

(1)

(1)

(1)

20$ x 8 hours x 5 days x 4 weeks x 12 months

hour day week month year

cancel
Cancel …
  • It all boils down to multiplying your starting info by a series of “unity” fractions (1) , set up to get the final units you want
  • When you add units (“words”) to fractions, you can treat them just like numbers

(1)

(1)

(1)

(1)

20$ x 8 hours x 5 days x 4 weeks x 12 months

hour day week month year

cancel5
Cancel …
  • It all boils down to multiplying your starting info by a series of “unity” fractions (1) , set up to get the final units you want
  • When you add units (“words”) to fractions, you can treat them just like numbers

(1)

(1)

(1)

(1)

20$ x 8 hours x 5 days x 4 weeks x 12 months

hour day week month year

cancel6
Cancel …
  • It all boils down to multiplying your starting info by a series of “unity” fractions (1) , set up to get the final units you want
  • When you add units (“words”) to fractions, you can treat them just like numbers

(1)

(1)

(1)

(1)

20$ x 8 hours x 5 days x 4 weeks x 12 months

hour day week month year

calculate
Calculate
  • It all boils down to multiplying your starting info by a series of “unity” fractions (1) , set up to get the final units you want
  • When you add units (“words”) to fractions, you can treat them just like numbers

(1)

(1)

(1)

(1)

20$ x 8 hours x 5 days x 4 weeks x 12 months

hour day week month year

20 x 8 x 5 x 4 x 12 $

year

i ll take the job
I’ll take the job!
  • It all boils down to multiplying your starting info by a series of “unity” fractions (1) , set up to get the final units you want
  • When you add units (“words”) to fractions, you can treat them just like numbers

(1)

(1)

(1)

(1)

20$ x 8 hours x 5 days x 4 weeks x 12 months

hour day week month year

20 x 8 x 5 x 4 x 12 $

year

$

= 38,400

year

i ll take the job9
I’ll take the job!
  • It all boils down to multiplying your starting info by a series of “unity” fractions (1) , set up to get the final units you want
  • When you add units (“words”) to fractions, you can treat them just like numbers

(1)

(1)

(1)

(1)

20$ x 8 hours x 5 days x 4 weeks x 12 months

hour day week month year

20 x 8 x 5 x 4 x 12 $

year

$

= 38,400

year

Anyone see the problem?

example songs
Example: Songs
  • How many songs are in all the iPods at school?
  • Start by collecting data
    • 0.5 iPods/student
    • 250 songs/iPod
    • 30 students/classroom
    • 100 classrooms/school
set up the fractions
Set up the Fractions

0.5 iPods x 500 songs x 30 students x 100 classrooms

student iPod classroom school

cancel units12
Cancel Units

0.5 iPods x 500 songs x 30 students x 100 classrooms

student iPod classroom school

cancel13
Cancel …

0.5 iPods x 500 songs x 30 students x 100 classrooms

student iPod classroom school

keep going
Keep going…

0.5 iPods x 500 songs x 30 students x 100 classrooms

student iPod classroom school

calculate15
Calculate

0.5 iPods x 500 songs x 30 students x 100 classrooms

student iPod classroom school

0.5 x 500 x 30 x 100 songs

school

answer
Answer

0.5 iPods x 500 songs x 30 students x 100 classrooms

student iPod classroom school

0.5 x 500 x 30 x 100 songs

school

= 750,000 songs/school

energy unit conversions
Energy Unit Conversions
  • Question: How important is each type of energy use in my home?
    • 10,000 kilowatt-hours (kWh)/year of electricity
    • 200 thousand cubic feet (ccf) of natural gas
    • 50 gallons of heating oil
    • Apples and Oranges -- How can you express these in “common units”??
set up the fractions18
Set up the Fractions

Electricity: 10,000 kWh x 3,412 BTU x 1 MMBTU

year kWh 1,000,000 BTU

cancel multiply answer
Cancel, Multiply --> Answer

Electricity: 10,000 kWh x 3,412 BTU x 1 MMBTU

year kWh 1,000,000 BTU

= 10,000 x 3412 x 1 MBTU

Year

1,000,000

= 34.1 MBTU

Year

set up the fractions20
Set up the Fractions

Natural Gas: 200 ccf x 105,000 BTU x 1 MMBTU

year ccf 1,000,000 BTU

cancel multiply answer21
Cancel, Multiply --> Answer

Natural Gas: 200 ccf x 105,000 BTU x 1 MMBTU

year ccf 1,000,000 BTU

= 200 x 105,000 x 1 MBTU

1,000,000

Year

= 21.0 MBTU

Year

slide22

Set up the Fractions

Oil: 50 gallons x 138,095 BTU x 1 MMBTU

year gallon 1,000,000 BTU

slide23

Cancel, Multiply --> Answer

Oil: 50 gallons x 138,095 BTU x 1 MMBTU

year gallon 1,000,000 BTU

= 50 x 138,095 x 1 MBTU

1,000,000

Year

= 6.9 MBTU

Year

the answer
The Answer

Electricity: 34.1 MMBTU/year

Natural Gas: 21.0 MMBTU/year

Oil: 6.9 MMBTU/year

TOTAL:62.0 MMBTU/year