CphT Calculation     Last updated on 2010     1     29, a full moon day;

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1; one; I;

2; two; II;

3; three; III;

4; four; IV;

5; five; V;

6; six; VI;

7; seven; VII;

8; eight; VIII;

9; nine; IX;

10; ten; X;

   20; twenty; XX;

   30; thirty; XXX;

   40; forty; XL;

50; fifty; L;

60; sixty; LX;

70; seventy; LXX;

80; eighty; LXXX;

90; ninety; XC;

   100; one hundred; C;

   500; five hundred; D;

   1000; one thousand; M;

 

phT calculation no. 21:

Roman numeral CVIII is equivalent to:

(a) -98 (b) -102 (c) 58 (d) 108;

Answer: 108.

 

 

 

Arithmetic:

99 is based10 number, which can be written as 99 = IC;

be very very careful WHEN using = equation sign, because nowadays with humanoids who can become very confuse after a few steps of algebra, such as 1+1=0; 1+1=1; +1 = -1; ... ; In Kanji, 2 strokes don't mean much meaning ... ;

 

 

 

Fraction:

2/3 is a fraction; 3/4 is also a fraction; aka N/D; aka Numerator/Denominator;

a fraction must be with whole number; for example 11/2 is NOT eleven by two; 11/2 is whole number one with fraction 1/2; therefore, in calculation, whenever N>D, whole number must be with its fraction; for example 5 1/2;

in 24mm natural time [ think reversely "space of time" ] aka solar powered calculator, fraction such as 2/3 aka 0.66666666666666666666666... solves math's infinity problem by its time slicing technology without energy map in ACT1 stage was;

reciprocal of fraction, 2/3 reciprocal is 3/2 aka flip notice that math calculation risks begin because N>D;

in common putting 1 over the whole number is called reciprocal; for example, reciprocal of whole number two is 1/2 aka two's reciprocal, reciprocal of whole number three is 1/3 aka three's reciprocal, reciprocal of whole number four is 1/4 ...;

statement saying "reciprocal of zero does not exist" because 0/2 is 0; 0/3 is 0; 0/4 is 0; notice that another math calculation risks begins because if zero 0 is nothing as whole number but NOT as tens, but NOT as hundreds, but NOT as thousands; especially in based 10 with zero?

basically, in ACT1, reciprocal of zero 0 does not exist, because nothing can NOT be divided by 2, i.e. 0/2 [aka zero divided by two] is 0 which does not exist as reciprocal; on the other hand, concerning zero 0, whole number cannot be divided by zero 0 either aka infinity problem;

fraction can be converted to decimals by deploying approx. method; for example: fraction 2/3 can be written as decimal 0.6666 6666 6666 6666 6666 667 IFF floating point math calculation's 23rd mantissa is truncated AND rounded up; in common 2/3 can be written 0.67; fraction 3/4 can be written as decimal 0.750;

0.750 is decimal AND  its 10ths is 7 AND its 100ths is 5 AND its 1000ths is 0; therefore five hundred can be written as 500; five hundredths can be written as 0.05; another example: eight hundred is 800; eight hundredths is 0.08; another example: twenty four thousandths is 0.024;

must reduce fraction to its lowest term; for example: fraction 6/9 must reduce to its lowest term 2/3; notice that the whole number 3 is a factor;

another example, fraction 18/27 must reduce to its lowest term 2/3; notice that factor is whole number 3 but its greatest common factor is whole number 9; therefore, must reduce fraction to its lowest term by its greatest common factor; concerning fraction 18/27, prime factor of Numerator N 18 is 1, 2, 3, 9, 18 AND prime factor of Denominator D 27 is 1, 3, 9, 27; notice that greatest common factor is whole number 9;

another example, fraction 24/108 must reduce to its lowest term 2/9; prime factor for N 24 is 1, 2, 3, 4, 6, 8, 12[its greatest common factor], 24; prime factor for D 108 is 1, 2, 3, 4, 6, 9, 12[its greatest common factor], 18, 27, 36, 108;

 

 

 

()

M

D

A

S

Order: () Multiply Divide Add Subtract, aka algebra order

whole number, fraction number, decimal number, ... can be multiplied, divided, added, subtracted;

to add fractions, for example: 1/3 + 1/2 is 5/6; common denominator 6 is used, aka least common denominator; notice that common denominator 6 by multiplying fractions' denominators;

 

to subtract fractions, e.g.: 4/5 - 1/3 is 7/15; because (4/5)x(3/3) is (12/15), then (1/3)x(5/5) is (5/15); now, (12/15) and (5/15) have same denominator whole number 15; (12/15)-(5/15) is 7/15;

to multiply fractions, for example: 4/5 of 1/3 is 4/15, because (4/5)x(1/3) is (4/15);

to divide fractions, e.g.: 1/3 by 1/5 is 1 2/3; because reciprocal 1/5 is 5/1; multiplying (1/3)x(5/1) is 5/3, therefore, 1 2/3; notice that 1/5 flips to be its reciprocal and then multiply ... ;

 

 

 

Round: 1st to understand fraction; 2nd to understand its decimals; 3rd to understand significant digit;

non-zero digits are significant; zero between non-zero digits are significant; final zero after decimal point is significant [ because numbers of zero shows its technological precision in calculation ] ;

00000002.01's significant digit is 2.01, and its significant figure is 3;

00000002.0100000's significant digit is 2.0100000, and its significant figure is 8;

0.012's significant digit is 0.012, and its significant figure is 2; because 0 is used for spacing the decimal; therefore significant figure is significant digit WHICH is measured actually;

rounding 2.0154321 to nearest thousandths is 2.015;

rounding 2.0154321 to nearest hundredths is 2.02; because 5 rounded up thus 1 becomes 2;

rounding 2.0154321 to nearest tenths is 2.0; because "1 is less than 5"; number<5 cannot be rounded up;

 

 

 

Children dose: dose for child = ( wt of child / average adult's weight ) x adult dose;

average adult weight may be measured by ( father's weight + mother's weight ) / 2;

Remark: in USA, average adult weight is 150 lb; thus, above formula can be written as  

dose for child = ( child's weight / 150 ) x adult dose; ;

 

 

 

Rx study:

Rx sample 1a,   doctor wrote: Acetaminophen oral susp 8 mg/ml/lb Sig: po 5 ml tid x 7 d

[acetaminophen is Tx for: reduce fever AND relieve pain]

since mg/ml is by weight wt pound, it is written for a child;

assume that child's wt is 10 kg, aka 22 lb; assume that average adult weight is ( 144 lb + 133 lb ) / 2 becomes 277/2, is 138.5 lb; assume that adult dose is 160 mg per ml;

since dose for child is (wt of child / average adult weight) x adult dose

(22 lb / 138.5 lb) x 160 mg per ml; therefore 25.4 mg per ml;

po is medical abbreviation, derived from Latin language per os, therefore by mouth as route;

5ml is 1 tsp;     tid is three times a day;     7d is seven days;

CphT would write doctor's Rx as: Take 1 tea-spoonful by mouth 3 times a day for 7 days;

CphT would dispense 105 ml (5 ml x 3 x 7) of Acetaminophen 25.4 mg/ml dose oral suspension;

Rx sample 1b,   doctor wrote: Nystatin susp 100,000 U/ml Sig: po 5 ml qid x 7 d

[nystatin is Tx for: antifungal]

CphT would write doctor's Rx as: Take 1 tea spoonful orally 4 times a day for 7 days;

CphT would dispense 140 ml WHICH means (5 ml x 4 x 7) of Nystatin 500,000 Unit dose; Notice that dose has been clearly defined by Unit per ml, therefore it is easy to calculate and understand the dose (100,000 x 5); Remark: above sample 1a' dose is complicated because it has been specific as mg/ml/wt dose, so technician processes specific dose by defined wt 1st, and then such defined specific dose [ if CphT multiples 5 ml x 3 x 7 x 25.4 mg/ml ] in mg might be a pitfall/fallacy/mistake because oral susp should be in ml volume [ NOT in wt ];

CphT would apply warning label such as SHAKE WELL.

 

Rx sample 2,   doctor wrote: Ciprofloxacin 500 mg tab po bid x 7d

[ciprofloxacin is Tx for: anti-infection among airway/bone/joint/lung/skin/... Oh! my lord, it is out of tract!]

CphT would write doctor's Rx as: Take 1 tablet orally twice a day until gone;

CphT would dispense (14) tablets of Ciprofloxacin 500 mg dose;

CphT would apply warning label such as MEDICATION SHOULD BE TAKEN WITH PLENTY OF WATER;

CphT would apply warning label such as AVOID DIRECT EXPOSURE TO SUN.

 

Rx sample 3,   doctor wrote: Multivitamin 150 mg tab hs po qd x 180d Refill 1

CphT would write doctor's Rx as: Take 1 tablet by mouth at bedtime everyday;

CphT would dispense (180) tablets of Multivitamin 150 mg dose;

CphT would write: please call 48 hours in advance for Refills Left: 1; Discard After: 1yr;

CphT would write: KEEP IT IN ROOM TEMPERATURE.

 

 

 

Ratio, Proportion, Percentage:

comparison between 2 numbers, so called ratio;

example 1,

fraction 2/3 can be written as 2 to 3; notice that logical expression has been changed;

2 to 3 can be written as 2:3, so called a ratio;

example 2,

fraction 3/4 can be written as 3 to 4; logical expression has changed from fraction to statement;

3 to 4 can be written as 3:4, so called a ratio;

WHERE 2+ ratios are equal to each other, aka proportion;

example 1,

fraction a/b is equal to fraction x/y; can be written as a/b = x/y;

a to b is a:b; x to y is x:y;

proportion can be written as a:b = x:y;

example 2,

20:30 = 4:6

if proportion seems difficult to be, and then CC normality is CC normality,

a way to be short cut also, tic-tac-toe is dispensing goal;

Remark; common dimensions in CphT are time, volume, weight, dosage form, dose, ... ;

liquid % = volume in ml / 100 ml;   solid % = wt in gm / 100 ml;

 

phT calculation no. 1:

How many caps will be dispensed IFF Rx is written as amoxicillin 250 mg/cap tid x 7d ?

its form is in cap aka capsule, so CphT will dispense capsules only;

its route has been defined by manufacturer, so CphT would label "orally";

tid is three times a day, so 3 doses per day AND 1 dose is 250 mg amoxicillin; 7d is 7 antibiotic days;

therefore, CphT dispenses 21 capsules;

therefore, CphT labels "Take 1 capsule orally with plenty of water, 3 times a day for 7 days".

 

 

 

Alligate: al + lig bind + ...

2 well known techniques are

CALCULATION Tech1,   CC normality is CC normality, aka cc * normality = cc * normality, aka 3known-to-solve-1unknown;

CALCULATION Tech2,   tic-tac-toe ;

 

phT calculation no. 2:

500 ml of 5% dextrose solution is ordered. 20% dextrose solution and 30% dextrose solution are in stock. How many ml each of dextrose solution CphT needs to prepare?

1st, draw a tic-tac-toe,

2nd, write accordance with CALCULATION Tech2 technique, so

3rd, to calculate total is 40, because 15 + 25;

Therefore, (15/40) x 500 ml = 187.5 ml of 30% dextrose solution, AND

therefore, (25/40) x 500 ml = 312.5 ml of 20% dextrose solution;

A must to counter check the answer by adding 187.5 + 312.5 must be 500, so that CphT does not make mistake in calculation.

 

phT calculation no. 3:

300 g of 2% ointment is ordered. 5% ointment and 10% ointment are in stock. How many grams each of ointment CphT needs to prepare?

1st, draw a tic-tac-toe,

2nd, write accordance with CALCULATION Tech2 technique, so

3rd, to calculate total is 11, because 3 + 8;

Therefore, (3/11) x 300 g = 81.82 g of 10% ointment, AND

therefore, (8/11) x 300 g = 218.18 g of 5% ointment;

A must to counter check the answer by adding 81.82 + 218.18 must be 300, so that CphT does not make mistake in calculation.

 

phT calculation no. 4:

50 ml of 2:300 dilute solution is ordered. 1:200 w/v dilute solution and 1:3000 w/v dilute solution are in stock. How many ml each of dilute solution will be required?

1st, draw a tic-tac-toe,

2nd, write accordance with CALCULATION Tech2 technique, so

then

3rd, to calculate total is 0.0079, because 0.0063 + 0.0016;

Therefore, (0.0063/0.0079) x 50 ml = 39.87 ml of 1:200 w/v dilute solution, AND

therefore, (0.0016/0.0079) x 50 ml = 10.13 ml of 1:3000 w/v dilute solution;

A must to counter check the answer by adding (39.87 + 10.13) must be 50 ml, so that CphT does not make mistake in calculation.

 

phT calculation no. 5:

300 ml of 2.5% boric acid solution is ordered. 30% boric acid solution and ph7 water are in stock. How many ml each of boric acid solution and ph7 water CphT needs to prepare?

1st, draw a tic-tac-toe,

2nd, write accordance with CALCULATION Tech2 technique, so ; 0% because of water;

3rd, to calculate total is 30, because  2.5 + 27.5;

Therefore, (2.5/30) x 300 ml =  25 ml of 30% boric acid solution, AND

therefore, (27.5/30) x 300 ml =  275 ml of ph7 water;

A must to counter check the answer by adding  25 + 275 must be 300, so that CphT does not make mistake in calculation.

 

phT calculation no. 6:

How many Sodium Bicarbonate in grams to make 500 ml of 1:1000 w/v solution? [think that "w" weight is a question, and "v" volume is known/given
(a) 0.5 (b) 0.2 (c) 2.0 (d) 500000

1st, CC Normality is CC Normality;

2nd, CC Normality = 500 ml x 1/1000 w/v;

3rd, CC Normality = 500 ml x 1/1000 g/ml = 0.5 g.

 

phT calculation no. 7:

During 4 hours, 0.5 liter is infused. What is its infusion rate in ml/hr?
(a) 2000 (b) 8 (c) 2 (d) 125;   Also see: CphT Measurement conversion Liquid Metric;

1st, 1L = 1000 ml, therefore 500 ml is infused over 4 hours; so 4 hr = 500 ml;

2nd, 1 hr = ?  

Remark:   IFF 1hr < 4hr, so (1hr/4hr);

If question is infusion rate in ml/day, and then 24hr > 4hr, so (24hr/4hr); Answer would be 3L/d;

3rd, 500 ml x (1 hr / 4 hr) = 125 ml for 1 hr = 125 ml/hr.

 

phT calculation no. 8:

Patient XYZ's weight is 180 pounds. Solution's strength % is in kilograms. What is patient XYZ's weight in kilogram?
(a) 82 (b) 28 (c) 18 (d) 180;   Also see: CphT Measurement conversion systems;

1st, 2.2 lb = 1 Kg;  

2nd, 180 lb = ?

3rd, 1 Kg x (185 lb / 2.2 lb) = 81.81 Kg = 82 Kg.

 

phT calculation no. 9:

Prescription Rx is: Amoxicillin 375 mg tid x 5d; dispense 150 ml;

250 mg / 5 ml is in stock; What is the dose in teaspoon?
(a) 1.5 tbsp (b) 1.5 tsp (c) 3 tbsp (d) 3 tsp;   Also see: CphT Measurement conversion household;

1st, 250 mg = 5 ml [weight per volume solution]; 375 mg = ?; 5 ml x (375 mg / 250 mg) = 7.5 ml;

2nd, 5 ml = 1 tsp; 7.5 ml = ?; 1 tsp x (7.5 ml / 5 ml) = 1.5 tsp;

3rd, tid is three times a day, so 3 doses per day; 1 dose is 1.5 teaspoonful; 5d is 5 days; CphT dispenses 150 ml, accordance with prescription, even though exact volume is (7.5 ml x 3 times a day x 5 days) = 112.5 ml in 5 days; CphT labels "Take 1.5 teaspoonful orally, 3 times a day for 5 days".

 

phT calculation no. 10:

What is % strength of 1:100 solution?
(a) 1% (b) 0.1% (c) 10% (d) 0.01%

1st, ratio 1:100 is 0.01;

2nd, % is based on 100;

3rd, 1 ratio solution = 0.01; for 100 = %?; 0.01 x (100/1) = 1% strength.

 

phT calculation no. 11:

A vial which contains 500 mg of drug in 2 ml solution [aka w/v solution]; What is % strength of the drug?
(a) 0.25% (b) 2.5% (c) 25% (d) 0.025%


1st, in ratio concentration, CphT must memorize and write

1:1000 is 1 mg/ml;

1:100  is 10 mg/ml;

1:10   is 100 mg/ml;

2nd, 500 mg in 2 ml = (500/2) mg/ml = 250 mg in 1 ml; so 250 mg/ml;

3rd, since 1:100 is 1% strength [also see: phT calculation no. 10], 1:10 is 10% strength, for 250mg/ml becomes 25% strength; Otherwise, wrong answer would be 2.5% if CphT does NOT memorize ratio concentration.

 

phT calculation no. 26:

How many milligrams NaCl is in 20 ml of NS?
(a) 180 mg (b) 18.0 mg (c) 1.8 mg (d) 0.18 mg
 

1st, NS is Normal Saline; Normal Saline is 0.9% NaCl aka 0.9% sodium chloride;

2nd, in common, 0.9%; so, 900mg/100ml;

3rd, cc normality is cc normality, so (900mg/100ml) = X/20ml = 180 mg.

 

phT calculation no. 12:

A patient was injected 2.3ml of (epinephrine) Injection, USP 1:1000. How many mg of drug did the patient receive?
(a) 2.3 mg (b) 23 mg (c) 230 mg (d) 2300 mg
 

1st, CphT must memorize ratio concentration; so 1:1000 = 1mg/ml;

2nd, w/v is w/v aka weight per volume is weight per volume; i.e. mg/ml = X/2.3ml;

3rd, ml/ml is 1; so X = 2.3 mg.

 

phT calculation no. 13:

Rx would have been written as: Hydrocortisone 2.5% in skin moisturizer cream; Dispense 60 gm; apply bid prn; How many grams of hydrocortisone, and how many grams of skin moisturizer cream should be weighted to do a compound?

1st, Total weight to dispense is 60 gm; Total dispense wt = Hydrocortisone's wt + Skin moisturizer cream's wt;

2nd, HC 2.5% means 2.5 gm HC by 100 gm HC, so (2.5 gm / 100 gm) of total dispense weight 60 gm; thus, (2.5/100) x 60 gram = 1.5 gm of hydrocortisone;

3rd, Skin moisturizer cream's wt = (total dispense weight 60 gm) - (HC 1.5 gm) = 60 - 1.5 = 58.5 gm of skin moisturizer cream; CphT dispenses 60 gm of mixed compound (1.5 gm of hydrocortisone thoroughly mixed with 58.5 gm of skin moisturizer cream); CphT labels "apply 2 times a day, as needed"

Assume that a health insurance company will pay the bill. Above compound took 20 minutes to prepare, and current pharmacy's dispensing fees is $5.00. How much the bill is going to be?

Assume that 10 gm of HC cost to pharmacy is $30.

so, 10 gm = $30

1.5 gm = ?

30 $ x (1.5 gm / 10 gm) = $4.5;

Assume that 1lb of skin moisturizer cream cost to pharmacy is $10.

so, 454 gm [also see: CphT Measurement Conversion's Systems] = $10

58.5 gm = ?

10 $ x (58.5 gm / 454 gm) = $1.28;

Bill = Ingredients cost + Dispensing fees + compound preparation time period cost;

Assume that HR cost [Human Resources cost] $20/hr for preparing Rx prescription.

so, 60 minutes = $20

20 minutes = ?

20 $ x (20 minutes / 60 minutes) = $6.66;

Therefore, bill = (4.500 + 1.280) + 5.000 + 6.666 = 17.000.

 

phT calculation no. 14:

Available iodine tincture is 5% Iodine solution. How many grams of iodine contains in 50 ml of tincture?

1st, 5g per 100ml is 5%, because % is in wt per vol;

2nd, set ratio & proportion as 5g/100ml = X/50ml

3rd, X = (5g x 50) / 100 = 2.5g.

 

phT calculation no. 15:

Amoxicillin 500 mg / 10 ml is in stock, so available. Rx is amoxicillin 75 mg QID x 10d. How many ml of the amoxicillin should CphT dispense?
(a) 40 ml (b) 50 ml (c) 60 ml (d) 400 ml
 

1st, therefore 500 mg / 10ml = 75 mg / X;

2nd, X = ( 75 mg x 10 ml ) / 500 mg = 1.5 ml;

3rd, QID is 4 times a day; 10d is 10 days; Thus, 1.5 ml x 4 x 10 = 60 ml.

 

 

 

 

TPN Concentration: your direction is:

IFF necessary to do manually, tic-tac-toe to solve TPN order, however high risk in calculation due to mEq/ml, several % of concentration in different ml, step-by-step procedure of mixing [concerning drug-drug interaction]... ; In common, ready made packages are used; In common, many hospitals set formulary only; 

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