1. 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]

2. hour day week month year 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 20 $ x 8 hours x 5 days x 4 weeks x 12 months (1)

3. hour day week month year 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 20 $ x 8 hours x 5 days x 4 weeks x 12 months (1)

4. hour day week month year 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 20 $ x 8 hours x 5 days x 4 weeks x 12 months (1)

5. hour day week month year 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 20 $ x 8 hours x 5 days x 4 weeks x 12 months (1)

6. hour day week month year 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 20 $ x 8 hours x 5 days x 4 weeks x 12 months (1)

7. 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 year 20 x 8 x 5 x 4 x 12 $ hour day week month year 20 $ x 8 hours x 5 days x 4 weeks x 12 months (1)

8. Ill 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 year 20 x 8 x 5 x 4 x 12 $ = 38,400 year $ hour day week month year 20 $ x 8 hours x 5 days x 4 weeks x 12 months (1)

9. Ill 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 year 20 x 8 x 5 x 4 x 12 $ = 38,400 year $ hour day week month year 20 $ x 8 hours x 5 days x 4 weeks x 12 months (1) Anyone see the problem?

10. 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

11. Set up the Fractions 0.5 iPods x 500 songs x 30 students x 100 classrooms student iPod classroom school

12. Cancel Units 0.5 iPods x 500 songs x 30 students x 100 classrooms student iPod classroom school

13. Cancel … 0.5 iPods x 500 songs x 30 students x 100 classrooms student iPod classroom school

14. Keep going… 0.5 iPods x 500 songs x 30 students x 100 classrooms student iPod classroom school

15. 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

16. Answer 0.5 x 500 x 30 x 100 songs school = 750,000 songs/school 0.5 iPods x 500 songs x 30 students x 100 classrooms student iPod classroom school

17. 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??

18. Set up the Fractions Electricity: 10,000 kWh x 3,412 BTU x 1 MMBTU year kWh 1,000,000 BTU

19. 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

20. Set up the Fractions Natural Gas: 200 ccf x 105,000 BTU x 1 MMBTU year ccf 1,000,000 BTU

21. 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 Year1,000,000 = 21.0 MBTU Year

22. Set up the Fractions Oil: 50 gallons x 138,095 BTU x 1 MMBTU year gallon 1,000,000 BTU

23. 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 Year1,000,000 = 6.9 MBTU Year

24. The Answer Electricity:34.1 MMBTU/year Natural Gas:21.0 MMBTU/year Oil: 6.9 MMBTU/year TOTAL:62.0 MMBTU/year