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RSPT 1060

RSPT 1060. MODULE A MATHEMATICS. TIPS FOR SUCCESS. Math concepts are crucial. The math is not difficult. BUT…You won’t be able to use a calculator! Do all the homework. Look for additional practice in other R.T. or math books if needed. Practice! Practice! Practice! Practice!

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RSPT 1060

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  1. RSPT 1060 MODULE A MATHEMATICS

  2. TIPS FOR SUCCESS • Math concepts are crucial. • The math is not difficult. • BUT…You won’t be able to use a calculator! • Do all the homework. • Look for additional practice in other R.T. or math books if needed. • Practice! Practice! Practice! Practice! • If you get behind, see the instructor or a tutor immediately.

  3. RESOURCES • Tutor schedules • Learning Center • 2nd yr. Students • http://www.macomb.edu/LearningCenter/Tutoring/TutoringQ&A.asp • Classmates • Math Videotapes • Library books on reserve • Instructor

  4. MODULE A • Positive & Negative Numbers • Rounding • Decimals & Order of Operation • Proportions, ratios & fractions • Measurement Systems • Conversion & Canceling • Rearranging Equations

  5. OBJECTIVES(Positive and Negative Numbers & Rounding Rules) • At the end of this module, the student will be able to… • Define terms associated with positive and negative numbers. • List the rules for solving problems associated with positive and negative numbers. • Given a mathematical problem involving positive or negative numbers, derive the correct answer. • List the rules used for rounding numbers. • Given a mathematical problem, round the answer correctly.

  6. Part 1: Positive & Negative Numbers

  7. CLINICAL EXAMPLE • The pressure in the pleural space at rest is -3 cmH2O. • The pressure in the pleural space at end-inspiration changes to -8 cmH2O. • How much did the pressure change?

  8. DEFINITIONS • Number Line • Real Number • Origin • Positive Number • Negative Number • Absolute Value • Additive Inverse __|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__ -7 -6 -5 -4 -3 -2 -1 0+1 +2 +3 +4 +5 +6 +7 http://www.mathwords.com

  9. Absolute Value of: +3 would be _____. -5 would be _____. -12 would be _____. +22 would be _____. Additive Inverse of: +3 would be _____. -5 would be _____. -12 would be _____. +22 would be _____. PRACTICE

  10. MEMORIZE THE RULES! • Addition • Subtraction • Multiplication • Division

  11. ADDITIONRules • Same signs - Add the absolute values of the numbers and give the answer the same sign as the original numbers. 1 + 1 = 2 -1 + -1 = -2 • Different signs – “Tug-O-War” Subtract smaller number’s absolute value from larger number’s absolute value and give answer the sign of the number with the larger absolute value. 5 + (-3) = 2 -5 + 3 = -2

  12. Same Sign: 2 + 5 = +_____ 5 + 13 = +_____ -12 + (- 3) = -_____ -4 + (-7) = -_____ * Add the absolute values of the numbers and give the answer the same sign as the original numbers. Different Signs: 2 + (-5) = _____ -5 + 13 = ____ -12 + 3 = _____ 4 + (-7) = _____ * Subtract the smaller number’s absolute value from larger number’s absolute value and give the answer the sign of the number with the largerabsolute value. Practice

  13. SUBTRACTIONRules • There is no subtraction! • Change to an addition problem. • Apply the addition rules • Change sign of second number to it’s additive inverse. • If second number is a positive number then change to negative • -10 – 5 change to • If second number is a negative number then change to positive. • 10 – (-5) change to

  14. Second # Positive: -10 – 5 = -10 + (-5) = -15 15 – 5 = ___ +___= ___ 8 - 12 = ___ + ___ = ___ 3 – 14 = ___ + ___ = ___ -4 – 11 = ___ + ___ = ___ Second # Negative: 10 – (-5) = 10 + (+5) = 15 15 – (-5) = ___ + ___ = ___ 8 – (-12) = ___ + ___ = ___ 3 – (-14) = ___ + ___ = ___ -2 – (-8) = ___ + ___ = ___ Practice

  15. CLINICAL EXAMPLE • Pleural space at rest = -3 cmH2O • Pleural space during inspiration = -8 cmH2O • How much did the pressure change? • -3 – (-8) = ___ + ___ = ___ cmH2O

  16. MULTIPLICATIONRules • Same signs - positive answer 5 x 3 = 15 -5 x (-3) = 15 • Opposite signs - negative answer 5 x (-3) = -15 -5 x 3 = -15

  17. Same sign: (positive) 12 x 4 = _____ -12 x (-4) = _____ Opposite signs: (negative) -12 x 4 = ____ 12 x (–4 ) = ____ Practice

  18. DIVISIONRules • Same sign - positive answer 4 / 2 = 2 -4 / -2 = 2 • Opposite signs - negative answer 4 / -2 = -2 -4 / 2 = -2

  19. Same sign: (positive) 8 / 2 = ____ -8 / -2 = ____ Opposite signs: (negative) -8 / 2 = ____ 8 / -2 = ____ Practice

  20. Part 2: Rounding

  21. Rounding Rules • Number of decimal places needed • When to round • Measurement & accuracy

  22. Rounding – Rule #1

  23. Calculator Use • If you do not have a calculator, round the numbers before performing the math then round the answers. • If you have a calculator, do the math then just round the answer.

  24. Rounding – Rule #2 • If the number to be dropped is larger than or equal to 5, the preceding number is rounded up. 23.45 rounds to 23.5 • If the number to be dropped is smaller than 5, the preceding number stays the same. 23.43 rounds to 23.4

  25. Decimal 0.74433 = Small # 8.6666 = Decimal 0.11711 = Large # 1544.225 = Small # 7.44559 = EXAMPLESRounding while working without a calculator Round the numbers before doing the math to make calculation easier.

  26. Decimal 0.74433 = Small # 8.6666 = Decimal 0.11711 = Large # 1544.225 = Small # 7.44559 = ROUNDING EXAMPLESRounding answers

  27. Let’s not make this complicated! • Calculators • Make life simpler - you only need to round answer • Rule for rounding if number to be dropped is a 5 • Don’t worry about it! Just round up! • Significant figures • Don’t worry about it! • Just follow the rounding rules!

  28. Measurement & Precision • Precision often depends on the measurement instrument? • EXAMPLE:How much does a tennis ball weigh? • Bathroom scale = 0 lbs • Common laboratory balance = 54.07g • Analytical research lab balance = 54.07138g

  29. Rounding - Rule #3 • A calculation can only be as accurate as the accuracy of the measurements. • Example: Mileage = miles / gallons • 278 mi / 11.70 gallons = 23.760684 (mpg) • How do you know how many digits to keep? • Follow the rounding rules!

  30. Rounding - Rule #3 • A calculation can only be as accurate as the accuracy of the measurements. • Example: 3.18 L+ 0.01315 L= 3.19315 L • How do you know how many digits to keep? • Follow the rounding rules!

  31. Measurement & Precision • QUESTION: • So how precise do we have to be? • ANSWER: • In most cases just follow the rounding rules!

  32. Respiratory Therapy examples of exceptions to the rounding rules • Temperature: • Do not round 101.8 to 102 • Acid-Base measurement of pH: • Do not round pH of 7.35 to 7.4 • Ideal body weight • Usually rounded to whole number (86 rather than 86.2)

  33. ROUNDING PRACTICE 1.    13.79 - 0.102938 __________ - __________ = _____ or ____ • Answer with rounding (w/o calculator)_____ • Answer without rounding (with calculator) ______

  34. ROUNDING PRACTICE TRY WITHOUT A CALCULATOR! 2.    7.4444 x 4 __________ x __________ = _____ or ____ 3.    0.666222 / 2 __________ / __________ = _____ or ____

  35. ROUNDING PRACTICE 4.    2 x 145.189 __________ x __________ = ______ or ____ 5.    494.91 - 94.826 __________ - __________ = _______ or ______ 6.    0.4825 - 0.12 __________ - __________ = ________ or ______

  36. ROUNDING PRACTICE 7.    12309.2 + 9.2456 __________ + __________ = _________ or _______ 8.    5.463 + 0.2367890 _________ + __________ = _______ or _____ 9.    1234.876 - 34.445 __________ - __________ = __________ or ______ 10. 2.3692 + 54.93276 __________ + __________ = ________ or _______

  37. Rounding – Rule #1 2 3 1 2 0 1

  38. Rounding – Rule #2 • If the number to be dropped is larger than or equal to 5, the preceding number is …. • rounded up • If the number to be dropped is smaller than 5, the preceding … • number stays the same

  39. Rounding – Rule #3 • QUESTION: • So how precise do we have to be? • How do we know how many digits to keep?

  40. ASSIGNMENTS & SUGGESTIONS • Flash Cards & Memorizing: • Positive & negative number rules • Rounding rules • Complete the practice problems. • Note: Answers posted on website • Complete assignment in Math Book: • Read Chapter 1: page 1 & 6 • Complete Sample Problems Fourth Set, page 6 • Note: Answers in back of chapter • Complete Practice Problems 36 – 70, page 9 - 11 • Note: Answers in back of book

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