RSPT 1060 MODULE A MATHEMATICS. TIPS FOR SUCCESS Math concepts are crucial. The math is not...
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Transcript of RSPT 1060 MODULE A MATHEMATICS. TIPS FOR SUCCESS Math concepts are crucial. The math is not...
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