RSPT 1060 MODULE A MATHEMATICS TIPS FOR SUCCESS

RSPT 1060 MODULE A MATHEMATICS

TIPS FOR SUCCESS • Math concepts are crucial. • The math is not difficult. Ø 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! • If you get behind, see the instructor or a tutor immediately.

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

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

OBJECTIVES (Positive and Negative Numbers & Rounding Rules) • At the end of this module, the student will be able to… Ø Ø Ø 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.

Part 1: Positive & Negative Numbers

CLINICAL EXAMPLE • The pressure in the pleural space at rest is -3 cm. H 2 O. • The pressure in the pleural space at end-inspiration changes to -8 cm. H 2 O. • How much did the pressure change?

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

PRACTICE • 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 _____.

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

ADDITION Rules • 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

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

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

CLINICAL EXAMPLE • Pleural space at rest = -3 cm. H 2 O • Pleural space during inspiration = -8 cm. H 2 O • How much did the pressure change? • -3 – (-8) = ___ + ___ = ___ cm. H 2 O

MULTIPLICATION Rules • Same signs - positive answer 5 x 3 = 15 -5 x (-3) = 15 • Opposite signs - negative answer 5 x (-3) = -15 -5 x 3 = -15

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

DIVISION Rules • Same sign - positive answer 4/2=2 -4 / -2 = 2 • Opposite signs - negative answer 4 / -2 = -2 -4 / 2 = -2

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

Part 2: Rounding

Rounding Rules 1. Number of decimal places needed 2. When to round 3. Measurement & accuracy

Rounding – Rule #1 Size of number # of decimal places used when working # of decimal places used in answer Decimal . XXX . XX Three places Two places Small number 1. XX 1. X < 100 Two places One place Large number 111. X 111 > 100 One place Zero places

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.

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

EXAMPLES Rounding while working without a calculator Round the numbers before doing the math to make calculation easier. Decimal 0. 74433 = Small # 8. 6666 = Decimal 0. 11711 = Large # 1544. 225 = Small # 7. 44559 =

ROUNDING EXAMPLES Rounding answers Decimal 0. 74433 = Small # 8. 6666 = Decimal 0. 11711 = Large # 1544. 225 = Small # 7. 44559 =

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

Measurement & Precision • Precision often depends on the measurement instrument? • EXAMPLE: How much does a tennis ball weigh? Ø Bathroom scale = 0 lbs Ø Common laboratory balance = 54. 07 g Ø Analytical research lab balance = 54. 07138 g

Rounding - Rule #3 • A calculation can only be as accurate as the accuracy of the measurements. Ø Example: Mileage = miles / gallons Ø 278 mi / 11. 70 gallons = 23. 760684 (mpg) Ø How do you know how many digits to keep? Ø Follow the rounding rules!

Rounding - Rule #3 • A calculation can only be as accurate as the accuracy of the measurements. Ø Example: 3. 18 L+ 0. 01315 L= 3. 19315 L Ø How do you know how many digits to keep? Ø Follow the rounding rules!

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

Respiratory Therapy examples of exceptions to the rounding rules • Temperature: Ø Do not round 101. 8 to 102 • Acid-Base measurement of p. H: Ø Do not round p. H of 7. 35 to 7. 4 • Ideal body weight Ø Usually rounded to whole number (86 rather than 86. 2)

ROUNDING PRACTICE 1. 13. 79 - 0. 102938 _____ - _____ = _____ or ____ • Answer with rounding (w/o calculator)_____ • Answer without rounding (with calculator) ______

ROUNDING PRACTICE TRY WITHOUT A CALCULATOR! 2. 7. 4444 x 4 _____ x _____ = _____ or ____ 3. 0. 666222 / 2 _____ / _____ = _____ or ____

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 _______

Rounding – Rule #1 Size of number Decimal Small number < 100 Large number > 100 # of decimal places used when working # of decimal places used in answer 3 2 2 1 1 0

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

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

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