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!

• If you get behind, see the instructor or a tutor immediately.

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

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… 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 cmH2O.

• The pressure in the pleural space at end-inspiration changes to -8 cmH2O.

• 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

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

Practice

• 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 larger absolute value.

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

Practice

• 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) = ___ + ___ = ___

CLINICAL EXAMPLE

• Pleural space at rest = -3 cmH2O

• Pleural space during inspiration = -8 cmH2O

• How much did the pressure change?

• -3 – (-8) = ___ + ___

= ___ cmH2O

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

Practice

• Same sign:(positive)

12 x 4 = _____

-12 x (-4) = _____

• Opposite signs:(negative)

-12 x 4 = ____

12 x (–4 ) = ____

DIVISIONRules

• Same sign - positive answer

4 / 2 = 2 -4 / -2 = 2

• Opposite signs - negative answer

4 / -2 = -2 -4 / 2 = -2

Practice

• Same sign:(positive)

8 / 2 = ____

-8 / -2 = ____

• Opposite signs:(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

Three places

.XX

Two places

Small number

< 100

1.XX

Two places

1.X

One place

Large number

> 100

111.X

One place

111

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

EXAMPLESRounding while working without a calculator

Decimal 0.74433 =

Small # 8.6666 =

Decimal 0.11711 =

Large # 1544.225 =

Small # 7.44559 =

Round the numbers beforebefore doing the math

to make calculation easier.

ROUNDING EXAMPLESRounding answers

Decimal 0.74433 =

Small # 8.6666 =

Decimal 0.11711 =

Large # 1544.225 =

Small # 7.44559 =

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!

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

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!

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!

Measurement & Precision

• QUESTION: So how precise do we have to be?

• ANSWER: In most cases just follow the rounding rules!

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)

ROUNDING PRACTICE

1.    13.79 - 0.102938

__________ - __________ = _____ or ____

• Answer with rounding (w/o calculator)_____

• Answer without rounding (with calculator) ______

ROUNDING PRACTICE

2.    7.4444 x 4

__________ x __________ = _____ or ____

3.    0.666222 / 2

__________ / __________= _____ or ____

TRY WITHOUT A CALCULATOR!

ROUNDING PRACTICE

4.    2 x 145.189

__________ x __________ = ______ or ____

5.    494.91 - 94.826

__________ - __________= _______ or ______

6.    0.4825 - 0.12

__________ - __________= ________ 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 # of decimal places used

when working

# of decimal places used in

answer

Decimal

Small number

< 100

Large number

> 100

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 ….

rounded up

• If the number to be dropped is smaller than 5, the preceding …

number stays the same

Rounding – Rule #3

• QUESTION: So how precise do we have to be? How do we know how many digits to keep?

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