Unit 1: Relationships between Quantities and Expressions

1. Unit 1: Relationships between Quantities and Expressions Metric Conversion, English Conversion, Metric to English Conversion

2. Units of Measurement • You are making a measurement when you ¨Check you weight ¨Read your watch ¨Take your temperature ¨Weigh a bag of potatoes

3. Tools for Measurement

4. Learning Check What are some U.S. units that are used to measure each of the following? A. length B. volume C. weight D. temperature

5. Solution Some possible answers are A. length inch, foot, yard, mile B. volume cup, teaspoon, gallon, pint, quart C. weight ounce, pound (lb), ton D. temperature °F

6. Units in the Metric System • length meter m • volume liter L • mass gram g • temperatureCelsius °C

7. Learning Check Identify the measurement in metric units. A. John’s height is 1) 1.5 yards 2) 6 feet 3) 2 meters B. The volume of saline in the IV bottle is 1) 1 liters 2) 1 quart 3) 2 pints C. The mass of a lemon is 1) 12 ounces 2) 145 grams 3) 0.6 pounds

8. METRIC CONVERSION The metric system is based on units of 10 and used by scientists and mathematicians around the world.

9. The pneumonic to help us remember: King Henry Died Unexpectedly Drinking Chocolate Milk i e e n e ei l c k i c n l o t a t i t l o ii

10. Let’s draw a line to use the pneumonic device. Above the tick marks write the abbreviations for the King Henry pneumonic: k h d u d c m m L g m: meter L: liter g: grams Write the units in the middle under the “U”.

11. Add in all the units: k h d u d c m km hm dam m dm cm mm kl hl dal l dl cl ml kg hg dag g dg cg mg

12. How to use your line: Look at the problem. Look at the unit that has a number. On the device put your pencil on that unit. Move to new unit, counting spaces and noticing the direction of the move (left or right). 3. Move decimal in original number the same # of spaces and in the same direction.

13. Example #1: • Look at the problem. 56 cm = _____ mm Look at the unit that has a number. 56 cm On the device put your pencil on that unit. k h d u d c m km hm dam m dm cm mm

14. Example #1: Move to new unit, counting jumps and noticing the direction of the jump! k h d u d c m km hm dam m dm cmmm One jump to the right!

15. Example #1: Move decimal in original number the same # of spaces and in the same direction. 56 cm = _____ mm 56.0. One jump to the right! Move decimal one jump to the right. Add a zero as a placeholder.

16. Example #1: 56 cm = _____ mm 56cm = 560 mm

17. Example #2: • Look at the problem. 7.25 L = ____ kL Look at the unit that has a number. 7.25 L On the device put your pencil on that unit. k h d u d c m kl hl dal L dl cl ml

18. Example #2: • Move to new unit, counting jumps and noticing the direction of the jump! k h d u d c m kl hl dal L dl cl ml Three jumps to the left!

19. Example #2: (3) Move decimal in original number the same # of spaces and in the same direction. 7.25 L = ____ kL .007.25 Three jumps to the left! Move decimal to the left three jumps. Add two zeros as placeholders.

20. Example #2: 7.25 L = ____ kL 7.25 L = .00725 kL

21. Example #3: Try this problem on your own: 45,000 g = ____mg k h d u d c m kg hg dag g dg cg mg

22. Example #3: 45,000 g = 45,000,000 mg Three jumps to the right!

23. WARNING: Do NOT count the spot you start from (where you put your pencil point). Only count the jumps!

24. WARNING: 5 cm = _____km k h d u d c m km hm dam m dm cm mm Five jumps to the left! Notice, you do not count the cm, you start counting at dm.

25. Examples #4-8: (4) 35 mm = ____ cm 3.5 (5) 14,443 L = ____ kL 14.443 (6) 0.00056 kg = ____ g .56 (7)35.4 L = ____ mL 35,400 (8)16 mm = ____ km .000016

26. Unit conversion Converting English units and metric to English units

27. Dimensional Analysis • Imagine multiplying two fractions (don’t panic, we have calculators) • Imagine the numerator of one fraction matches the denominator of the second • The numerator and denominator cancel! • In dimensional analysis, we use this idea to cancel UNITS of measurements.

28. Equalities State the same measurement in two different units length 10.0 in. 25.4 cm

29. Conversion Factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different units Example: 1 in. = 2.54 cm Factors: 1 in. and 2.54 cm 2.54 cm 1 in.

30. Fill in the Missing Numbers 12 1 foot = _____ inches 1 meter = _____ centimeters 1 pound = _______ ounces 1 minute = ______ seconds 1 hour = ________ minutes 1 day = __________ seconds 100 16 60 60 86,400

31. Unit conversion factor A unit conversion factor is a fraction whose numerator and denominator are equivalent measures. Some common unit conversion factors are given below. You can also use the reciprocal of these.

32. Choose a unit conversion factor that… • Introduces the unit you want in the answer (unit you want is in the numerator) • Cancels out the original unit so that the one you want is all that is left. (unit you want to get rid of is in the denominator)

33. “Canceling” out Words

34. Practice: Choose the appropriate conversion factor. Inches to feet Minutes to hours Meters to centimeters

35. Convert 8 yards to feet… Make a decision: What conversion factor will you use? Set up the problem: Multiply the measurement by the conversion factor. Hint! The unit you want must be in the numerator Solve the problem: Perform the multiplication

36. A bucket holds 16 quarts. How many gallons of water will fill the bucket? Use a unit conversion factor to convert the units. What are the two conversion factors comparing quarts and gallons? Which one will “cancel” quarts? 16 qt

37. You Try it! One bag of apples weighs 64 ounces. How many pounds does it weigh? Darren drank 2 liters of water. How many milliliters of water did he drink?

38. Making Rate Conversions Use a unit conversion to convert the units within each rate

39. Convert 80 miles per hour to feet per hour. Convert 63,360 feet per hour to miles per hour.

40. You Try it! Convert 32 feet per second to inches per second. A craft store charges $1.75 per foot for lace. How much per yard is this?

41. Word Problems The average American eats 23 pounds of pizza per year. Find the number of ounces the average American eats per year. The average American eats 368 ounces of pizza per year.