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RSPT 1325 Respiratory Care Sciences Lecture by Elizabeth Kelley Buzbee A.A.S., R.R.T.-N.P.S.,R.C.P. Part II: Intermediate math KEY [pp. 33-36] Be able to calculate proportions. Ratio A Ratio B 450:950 35 : X 12.5: 200 X : 950 1: 35.7 X: 87 The numbers on the outside are multiplied together, while the numbers on the inside are multiplied together 450 : 950 = 35 : X 450 (X) = 950 (35) 450 X = 33,250 450 450 X = 73.88 12.5: 200 as X :950 12.5 (950) = 200 X 11,875 = 200 x 11,875 = 200 x 200 200 59.375 = X 1: 35.7 as X: 87 (1) 87 = 35.7 x 87= 35.7 x 87 = 35.7 x 35.7 35.7 X= 2.436 In respiratory care the therapist may have to figure out an inspiratory time with a known inspiratory: expiratory ratio [I:E]. You solve these: If the I:E ratio is: 1:3 1: 4 1:5 The inspiratory The expiratory time time is: is: 1:3 as 1.5 : x 1.5 seconds 2 seconds 1:5 as x : 6 1(6) = 5 x 6=5x 6/5 = 5/5 x 1.2 seconds = x X= 3(1.5) X = 4.5 1:4 as 2: x X= 4(2) X= 8 seconds 6 seconds 1:1.5 4.5 seconds 1: 1.5 as x : 4.5 1(4.5) = 1.5 x 4.5 / 1.5 = 1.5/1.5 x 3 seconds = x Another way we use proportions is to calculate drug dosages. You solve these: If the ratio is: 1 mg: 2.5 ml When You have: 3 mg Then you would have: 7.5 ml 1 mg: 2.5 ml as 3 mg : x 1(x) = 2.5 (3) x = 7.5 2.5 mg : 3 ml 5 mg 6 2.5 mg : 3 ml as 5 mg: x 2.5 x = 3 (5) ml 2.5 x = 3 (5) 2.5 2.5 X=6 45 grams: 150 ml 900 grams 3000 ml 45 grams: 150 ml as x : 3000 ml 45 (3000) = 150 x 135,000 = 150 x 135,000 = 150 x 150 150 X = 900 6 grams: 300 ml .5 grams 25 6 grams: 300 ml as .5 gram : x 6x = 300 (.5) 6 x = 150 6 x = 150 6 6 X = 25 .5 mg: 3 ml 1 .5 mg: 3 ml as 1 mg :x .5 x = 3 (1) .5 x = 3 .5 x = 3 .5 .5 X=6 mg. 6 ml ml Another example of using ratio is to compare the VD/VT ratio. When the VD/VT ratio is: 1:4 The VD is: The VT is: 450 1800 200 500 1:4 as 450: x 1x = (4) 450 X = 1800 1:2.5 1:2.5 as x : 500 1(500) = 2.5 x 500 = 2.5 x 2.5 2.5 200 = x 1:3 600 200 1:3 as 200: x 1(x) = (3) 200 x = 600 Still another way that respiratory therapists use ratios is to determine how much extra oxygen we need to give a patient. Patient Pa02 55 torr Current Fi02: .45 We want Pa02: We need Fi02 of: 85 torr .695 .35 64 .5o 55: .45 as 85 : x 55 x = .45(85) 55 x = 38.25 55 x = 38.25 55 55 X = .6954 45 torr 45: .35 as x : .5 45 (.5) = .35x 22.5 = 35 x 22.5 = 35 x 35 35 .642 = x 45 torr .28 65 torr .40 .21 160 .45 45: .28 as 65: x 45x = .28 (65) 45x = 18.2 45x = 18.2 45 45 X = .4044 75 torr 75: .21 as x : .45 75(.45) = .21 x 33.75 = .21 x 33.75 = .21 x .21 .21 X = 160 1. [pp. 36-41] Be able to calculate proportions. a. Directly proportional relationships result in numbers that increase or decrease as their related numbers increase or decrease. V T V =k 1800 T 40 K [Pressure] 45 900 20 45 100 2.22 45 200 4.44 45 V/T = k x/40 = 45 40 (x/40) = 45 (40) X = 1800 V/T = k x/20 = 45 20 (x/20) = 45 20) X = 900 V/T = k 100/x = 45 x (100/x) = 45 x 100 = 45 x 100 = 45 x 45 45 2.222 = x Based on the above table, discuss the relationship between the V and the T when the P stays the same. As the V drops the T drops As the V rise the T rises b. Inverse proportional relationships result in numbers that decrease as the other number increases, or increases as the other number decreases. P (V) = k [temperature constant] Example :If the temperature is constant at 20 degrees, calculate the P when the V is 15 P (V) = k P (15) =20 P (15) =20 15 15 P = 1.33 Do these: V 30 k [temperature] 35 45 35 .777 60 35 .58 90 35 .388 Based on the above table, discuss the relationship between the V & the P when the temperature is constant. 2. P 1.166 When the V drops, the P rises When the V rises, the P drops [pp 59-64] Be able to perform dimensional analysis. a. When the respiratory therapist has to compare items with different units, we must use dimensional analysis. b. Conversion between different units is an example of dimensional analysis. EXAMPLE: You have a patient who weighs 150 pounds; you need to know how many kg he weighs. The conversion from pounds to kg is pounds /2.2 = kg You do these: Your patient weighs: His weight in kg: 235 pounds 106.8 15 pounds 6.8 185 pounds 84 5 pounds 2.27 The conversion between these two units of pressure is 1.46 mmHg /1 cmH20. the conversion from mmHg to cmH20 is .735cmH20/1 mmHg. You do these: Your airway pressure is: 20 cmH20 In mmHg, this would be 27.21 15 cmH20 20.4 30.8 45 mmHg 24.48 35.5 mmHg Another common formula used by the respiratory therapist is to calculate the lung compliance [stiffness] of the lung. The stiffer the lung the more pressure it takes to get a smaller volume into the lungs C= VT/P C= 50 ml/10 cmH20 C= 5 ml/cmH20 Do these: If you have VT: A. 100 ml And a P: 25 cmH20 Calculate the C: 100/25=4 4 ml/cmH20 B. 300 ml 15 cmH20 C. 750 ml 45 cmH20 300/15= 20 20 ml/cmH20 750/45= 16.66 16.66 ml/cmH20 If a high compliance is good, which of the above patients [A, B or C] has the best compliance? B has the highest compliance Another use of these types of formula by the RCP is the comparison of the patient VT in ml to their ideal body weight in kg [IBW]. VT/IBW = Vt in ml/kg. VT IBW Vt in ml/kg. A 500 ml 45 kg 500/ 45= 11.1 ml/kg. B 750 ml 68 kg 750/68= 11.02 ml/kg. C 675 ml 53 kg 675/53= 12.73 ml/kg. If you prefer your patient to breathe at 10 ml/kg, which of the above patients: A, B or C is closest to this ideal? 3. B is closest to 10 ml/kg [pp. 4-12] be able to calculate problems with scientific notation and exponents. a. In medicine, we work with extremely large or extremely small figures. To make it easer to understand and to work with these figures, sometimes we have to use scientific notation and exponents. b. For example: Instead of writing 1000, we could write this same number as 103 which is a short cut for 10 x 10 x 10. The number: As an exponent: 100 10 102 100 104 10,000 105 100,000 When we change a number to an exponent we are telling ourselves to move the decimal a certain number of spaces to the left to discuss large numbers. The exponent: We would move the decimal how many spaces to the left? 101 1 102 2 103 3 1030 30 We can also use exponents to discuss really small numbers such as .00001 which would be referred to as 10-5 a number less than 1 is also a fraction. .01 is 10-2 and it is also the fraction 1/100 The number As an exponent 10-1 10-3 10-5 10-6 As a fraction 1/10 .1 1/1000 .001 1/100,000 correction .00001 1/1,000,000 .000001 In this case, we are moving the decimal a certain number of spaces to the right to discuss tiny numbers. The exponent We would move the decimal how many spaces to the right? 1 101 10-2 2 10-3 3 10-30 30 IF you had a huge number such as 230,000 you could call it 2.3 x 105 NOTE: When using exponents, we have to reduce the number to a number between 1 and 10 so 230,000 is not 23 x 104 The number As an exponent .5 5 x 10-1 5000 5 x 103 .007 7 x 10-3 700 7x 102 .00008 8 x 10-5 880,000 8.8 x 106 .000009 9 x 10-6 Multiplying or dividing exponents When multiplying numbers with exponents we would add the exponents: 105 ( 103) = 10 5 + 3 = 108 Exponent Multiplied by: Equals: 2 8 1010 10 10 1022 1020 102 106 103 103 1030 105 1025 When exponents are divided we would subtract the exponents 1025 = 10 25-2 = 10 23 102 Exponent Divided by: Equals: 106 108 102 1018 1020 102 100 103 103 1034 1059 1025 4. [pp. 136-138]Work with negative and positive numbers. Respiratory therapists must understand pressure and vacuum. A negative number is one that is less than 0 A positive number is one that is more than 0 [the origin] If you have a pressure that is 3 cmH20 below zero, we would call this -3 cmH20. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 If you have a pressure that is 14 mmHg above zero, it is called 14 mmHg. Addition of negative and positive numbers: If a negative number is added to a positive number, the resulting number will move toward the zero. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -2 + 2 = 0 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -6 + 2= -4 You do these: number -125 add 100 equals -25 -250 -18 15 22 -235 4 Addition of two negative numbers: would move away from the zero: -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -2 + -2 = -4 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -2 + -5 = -7 You do these: number -125 -250 -18 add -100 -15 -22 equals -225 -265 -40 subtraction of negative and positive numbers If a negative number is subtracted from a positive number, we need to convert the formula to addition then follow those rules If both numbers are negative, it's just like adding positive numbers, except that the answer is negative. http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i15/bk7_15i1.htm Subtracting a negative number is just like adding a positive number: 1 – (-3) = 1 + 3 & -3 – (-8) = -3 + 8 EXAMPLES: subtraction Convert to addition 3–9= 3+-9 -2 - 9 -2 + 9 -150-125 -150 + 125 equals -6 7 -25 You do these: subtraction 31 - 19 -12 - 8 -15 -1 Convert to addition 31 + (-19) -12 + (-8) -15 + (-1) equals 12 - 20 -16 Situations in which the RCP might subtract positive and negative numbers: As a person breathes in his chest creates negative pressure because as his chest wall volume increases, the pressure inside the chest decreases [remember Boyle’s Law] If the pressure at the mouth is considered zero, and the airway pressure is zero, once the volume rises and the pressure drops to -5 cmH20, we would have 0- -5 cmH20 = 0 + (-5) = 5 cmH20 of driving pressure. Air moves into this vacuum. 5. Be able to answer word problems based on the math skills in Part II