MATHEMATICS All slides.pdf

Fundamentals of
Mathematics for Nurses
Iftikhar Ul Haq
Demonstrator
INS-KMU
1
ZIUDDIN ZEB COLLEGE OF NURSING DIR LOWER TIMERGARA

Conversion
• There are three measurement systems commonly
used in health care facilities: The matric,
household, and apothecary system.
• In order to compare measured amounts in the
system, approximate equivalents have been
developed.
 1 Teaspoon is approximately equivalent to 5
millilitres.
2

Rule for Conversion
 Always convert from one unit of measure to
another by the shortest number of steps possible.
System of measurement and approximate equivalents
Volume
Matric Apothecaries Household
1 millilitre (ml)/(cc) - 15-16 gtts
5 millilitres (ml) - 1 teaspoon (t)
60 drops (gtts)
15 millilitres (ml) - 1 tablespoon (T)
3 teaspoons (t) 3

Volume
30 millilitres (ml)/(cc) 1 ounce (oz) 2 Tablespoons (T)
240 millilitres (ml) 8 ounce (oz) 1 cup ©
1000 millilitres (ml) 1 quart 1 quart
4

Weight
60 milligrams (mg) 1 grain (gr) -
- 16 ounces (oz) 1 pound (lb)
1 Killogram (Kg)
1000 grams
- 2.2 pounds (lb)
5

Rule for Conversion
 Units and milliequivalents (meq) cannot be
converted to units in other systems. They have their
value given and will never need to be converted.
 1 unit = 1000 milliunits
 Cubic centimeters (cc’s) and millimetres (ml’s) are
the same equivalents.
o However, ml is the preferred usage.
6

Matric Weight
1 milligram (mg) = 1000 microgram (mcg)
1 gram (g) = 1000 milligrams (mg)
1 kilogram (Kg) = 1000 grams (gm)
Matric Weight to Volume
1 gram (gm) = 1 millilitre (ml) (approximately)
7

Common Pharmacologic
Abbreviations
 To transcribe medication orders and document
drug administration accurately, review the
following commonly used abbreviations for drug
measurement, dosage forms, routes and times of
administration, and related terms.
8

Drug and Solution Measurement
Oz. Ounce
G, gm Gram
gr Grain
gtt Drop
Kg Kilogram
L Liter
mcg Micrograms
mEq Milliequivalent
mg Milligram
ml Milliliter
pt Pint
qt Quart
Tbs, T Tablespoon
Tsp, t Teaspoon 9

Drug Dosage Forms
cap Capsule
DS Double strength
EC Enteric coated
Elix Elixir
Liq Liquid
Sol Solution
Supp Suppository
Susp Suspension
Syr Syrup
Tab Tablet
10

Routes of Drug Administration
IM Intramuscular
IV Intravenous
IVPB Intravenous piggyback
V, PV Vaginally
PO By mouth
R, PR By rectum
Subcutt Subcutaneous
S&S Swish and Swallow
11

Times of Drug Administration
ac Before meals
Ad lib As desired
Bid Twice a day
Tid Three times a day
Qid Four times a day
pc After meals
Prn As needed
Daily Every day
Qh (hr) Every hour
Q2h (hr) Every 2 hours
Q3h (hr) Every 3 hours
STAT immediately 12

Basic Math Review
1. Roman Numerals
i. I = 1
ii. V = 5
iii. X = 10
 The basic form is to place the larger numerals to
the left and add other numerals.
xxxiii = 33 ( 30 + 3 = 33)
13

Roman Numerals
 There is an exception to the basic form.
 If smaller numeral precedes a larger numeral, the smaller
should be subtracted from the larger.
• ix = 9 (10 – 1 = 9)
 If there seems to be several ways of writing a number –
use the shorter form.
• xvvi – incorrect
• xxi – correct (10 + 10 + 1 = 21)
14

Roman Numerals
 Only one smaller numeral is allowed to precede a
larger numeral.
• viii = 8 – correct
• iix = 10 - incorrect
15

Fractions
 The term fraction means a type of division.
 A fraction is a part or piece of a whole number that
indicates division of that number into equal units or
parts.
 A fraction is written with one number over another,
for example ¼.
 The line between the numbers is a division sign.
16

Denominator of a Fraction
 The denominator of a fraction refers to the total
number of equal parts into which the whole has
been divided.
 It is also called as a divisor.
 Rule:
 The larger the number in the denominator, the
smaller the value of the equal parts (or fraction) of
the whole.
17

Numerator of a Fraction
 The numerator of a fraction tells how many parts of the whole are being
considered.
 If you divide a circle into four equal parts, each part (1) that you are
considering is the top number of the fraction and is called the numerator.
 The numerator is also called the dividend.
 Rule:
 The larger the number in the numerator, the more parts of the whole are
being considered.
18

Fractions
 The number above the line (Nomirator) is divided by the
number under the line (Deniminator).
 Numerator/Denominator
i. 2/3 = Proper fraction = numerator is smaller than
denominator.
ii.3/2 = Improper fraction = numerator is larger than
denominator.
iii.1 ½ = Mixed fraction = Whole number and a fraction.
19

Fractions
 To change an improper fraction to a mixed number:
a. Divide the numerator by the denominator
b. Place remainder over denominator
 (13/5 = 2 3/5)
 To change a mixed number to an improper fraction:
a. Multiply denominator by the whole number
b. Add numerator
c. Place sum over the denominator
 3 ½ = 7/2
20

Fractions
 To reduce a fraction to its lowest denominator:
a. Divide numerator and denominator by the greatest common
divisor
b.The value of the fraction does not change.
 Example: Reduce 12/60
 12 divides evenly into both numerator and denominator
 (12/12 = 1) , (60/12 = 5) >>>>> ( 12/60 = 1/5)
21

Fractions
 3 divides evenly into both
 (9/3 = 3) , (12/3 = 4) >>>>> (9/12 = ¾)
 15 divides evenly into both
 (30/15 = 2), (45/15 = 3) >>>> (30/45 = 2/3)
22

Addition of Fractions
 Rule: You cannot add or subtract a fraction unless the
fractions have the same denominator, however you can
multiply or divide when denominators are not alike.
 Addition of fractions:
a. Must have common denominator
b.Add numerators
 Example:
 ¼ + 2/8 = (change 2/8 to ¼) = ¼ + ¼ = 2/4 = ½
23

Subtraction of Fractions
 Subtraction of fraction:
a. Must have common denominators
b.Subtract numerators
 Example:
 6/8 – ¾ = (change 6/8 to ¾) = ¾ - ¾ = 0
24

Multiplication of Fractions
a. To multiply a fraction by a whole number, multiply
numerator by the whole number and place product
over denominator.
 4 * 3/8 = 12/8 = 1 4/8 = 1 ½
b. To multiply a fraction by another fraction, multiply
numerators and denominators.
 5/6 * ¾ = 15/24 = 5/8
25

Division of Fractions
a. Invert terms of divisor
b. Then multiply
 Example 1:
 (2/3) / (4/5) = (2/3) * (5/4) = 10/12 = 5/6
 Example 2:
 (4) / (5/6) = (4) * (6/5) = 24/5 = 4_4/5
26

Decimals
• In the next slide, reading from right to left, each
place is 10 times larger in value.
 For example, 100 is 10 times larger than 10 and 1.0
is 10 times larger than 0.1.
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-------------------------------------------------------------------------------Decimal----------------------------------------------------------------------------
To the left Point To the right
28

Changing Decimals to Fractions
a. Express the decimal in words
b. Write the words as a fraction
c. Reduce to lowest terms
 Example 1: 0.3
a. Three tenths
b. 3/10
c. Already reduced to lowest terms
29

Changing Decimals to Fractions
 Example 2: 0.84
a. Eighty-four hundredths
b.84/100
c. 21/25
30

Changing Fractions to Decimals
• Divide the numerator by the denominator
 Example 1: ¾
 Example 2: 8/40
31

Addition and Subtraction of
Decimals
 Use the decimal point as a guide and line up the
numbers by their decimal place so that all the ones
places are lined up under each other, all the tens
places lined up and so on.
• Addition example 1: (7.4 + 12.39)
• Addition example 2: (0.003 + 2.4 + 0.15 + 0.02157)
• Subtraction example 1: (86.4 – 3.817)
• Subtraction example 2: (6.079 – 0.85)
32

Multiplication of Decimals
a. Multiply the numbers as if they were whole numbers
b. Count the total number of decimal places to the right
of the decimal point for each of the numbers
c. Use that total to count decimal places in the answer
i. (17.3 * 0.45)
33

Division of Decimals
• To divide a decimal by a whole number, the decimal
is placed directly above the decimal in the dividend.
Quotient
• Divisor  Dividend
• Example 1: 3.0 ÷ 0.6
• Example 2: 22.36 ÷ 1.3
34

Rounding off Decimals
• Decide how far the number is to be rounded, such as
to the tenths place or the hundredths place. Mark
that palace by putting a line under it.
• If the digit is to the right of that place is less than 5,
drop that digit and any others to the right.
• If the digit to the right of the place to be rounded to
is 5 or grater, increase the number in the place by 1
and drop the digits to the right.
35

Rounding off Decimals
• Example 1: 7.423957 = 7.42
(rounded to nearest hundredths)
• Example 2: 87.852 = 87.9
(rounded to nearest tenths)
36

Practice-1
 Roman Numerals
i. xvi = -------------
ii.xxi = --------------
iii.29 = ---------------
iv.19 = ---------------
v.3 = -----------------
37

Practice-2
(Fractions)
1. 15/2 = -----------
2. 13/6 = ----------
3. 7/4 = ------------
4. 11/3 = -----------
5. 15/8 = -----------
6. 37/5 = -------------
7. 4/6 = --------------
8. 3/9 = --------------
9. 15/60 = -----------
10. 6/12 = ------------
38

Practice-2
(Fractions)
11. 1/16 + 4/5 + ¾ =-------
12. 5/9 + 2/5 = -------
13. 2/7 + ½ + 9/14 = -----
14. ½ - 1/3 = ------
15. 9/12 – ¾ = ------
16.6/7 – 2/3 = -----
17.7/8 × 2/3 = ----
18. 1 ½ × ¾ = -----
19. 12/25 × 1/100 = ----
20. 2/8 ÷ ½ = ----
21. 1 ½ ÷ 1/3 = -----
22. 2 ½ ÷ 1/6 = ----
23. 2/9 ÷ ½ = ----
39

Practice-3
Decimals
• Change fractions to
decimals:
1. 6/8 = -----
2. 5/10 = ----
3. 3/8 = -----
4. 2/3 = -----
• Change decimals to
fractions:
1. 0.54 = -----
2. 0.0154 = ----
3. 0.60 = ------
4. 0.2 = -----
40

Practice-3
Decimals
• Add decimals:
1. 1.64 + 0.6 = ----
2. 0.02 + 1.0 = -----
3. 2.63 + 0.01 = -----
4. 1.54 + 0.3 = -----
5.0.008 + 2.002 = ---
• Subtract decimals:
1. 1.23 – 0.6 = -----
2. 0.02 – 0.01 = ----
3. 2.45 – 0.03 = -----
4. 0.45 – 0.02 = ----
5. 2.002 – 0.008 = ---
41

Practice-3
Decimals
• Multiply decimals:
1. 0.23 × 1.63 = -----
2. 0.03 × 0.123 = ----
3. 1.45 × 1.63 = -----
4. 0.2 × 0.03 = -----
• Divide decimals:
1. 3.2 ÷ 4 = ----
2. 1.86 ÷ 3.0 = ---
3. 1.00 ÷ 25 = -----
4. 68.8 ÷ 2.15 = ----
42

Practice-3
Decimals
• Round to hundredths:
1. 0.4537 = -----
2. 0.00584 = ------
• Round to tenths:
1. 9.888 = ------
2. 50.09186 = -----
• Round to tens:
1. 5619.94 = -----
2. 79.13 = -------
43

44

Measurement Systems
Iftikhar Ul Haq
Demonstratot
INS-KMU
45

Ratios and Proportions
 A ratio compares 2 quantities and can be
written as a fraction, 3 to 4 or ¾ .
 4 quarters to 1 dollar is a ratio and can be
written 4/1 or 4:1.
 Other familiar ratios are 60 minutes to 1
hour; 2 cups to 1 pint; 16 ounces to 1
pound.
46

Ratios and Proportions
 A proportion is 2 ratios equal to each other.
4 quarters 8 quarters
1 dollar 2 dollars
 This proportion can be read 4 quarters are to 1
dollar as 8 quarters are to 2 dollars.
o In a proportion, the products of cross
multiplication are equal.
47

Basic Steps
• There are 4 basic steps to solving proportion problems.
i. Set up a known ratio.
ii. Set up a proportion with known and desired units.
Use x for the quantity that is desired or unknown.
 Be sure the units are the same horizontally.
 Example: ounces ounces
pounds pounds
48

Basic Steps
iii. Cross multiply.
iv. Solve for x.
 To solve a proportion problem such as 3 lbs. = ?
Ounces:
a. Set up a known ration of pounds to ounces.
 1 lb. : 16 oz.
49

Cont.
b. Make a proportion using the known ratio on one
side and the desired ration on the other.
16 oz. X oz.
1 lb. 3 lbs.
c. Cross multiply. ( 1 × X = 16 × 3 )
d. Solve for x: 1 (x) = 16 × 3 >> X = 48
 Therefore, 3 lbs. = 48 ounces.
50

Cont.
 Another name for a ratio with numerator and
denominator of approximately the same value is a
conversion factor.
 The ratios 4 quarters to 1 dollar and 2 pints to 1
quart are conversion factors.
 Systems of measure use conversion factors to
change from one unit to another.
51

Matric System
 The basic unit of weight in the matric system is the
gram (G or gm.).
 The basic length is the meter (m) and,
 The basic volume is the liter (l or L).
 Matric measurement uses the decimal system as
the basis for its units.
 The prefix of the unit identifies its decimal
location and value. 52

Micro (mc) = millionth
Milli (m) = thousandths
Centi (c) = hundredths
Deci (d) = tenths
Deka (da) = tens
Hecto (h) = hundreds
Killo (k) = thousands
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Larger Decimal P. Smaller
53

Conversion Examples .01
 0.5 G = -------mg.
Solve: 1000mg x mg
1 G 0.5 G
Cross Multiply: 1 × x = 1000 × 0.5
x = 500 mg
54

 2000 mcg = ----------mg.
Solve: 1000 mcg 2000 mcg
1 mg x mg
Cross Multiply: 1000 × x = 1 × 2000
x = 2000/1000
x = 2 mg
55

Conversion in Household System
• Household system:
• The units of volume include drop (gtts), teaspoon
(tsp or t.), tablespoon (tbsp. or T) and ounces (oz.)
i. 1 tsp = 60 gtts
ii. 1 tbsp. = 3 tsp.
iii. 1 oz. = 2 tbsp.
56

 4 tsp. = ----------x gtts.
 Solve: 60 gtts x gtts
1 tsp. 4 tsp.
Cross Multiply: 60 × 4 = 1 × x
240 = x
4 tsp. = 240 gtts
57

Practice Problems
i. 7 kg = --------mg.
ii. 2.5 gm = ------mg.
iii. 0.5 ml = ------- L.
iv. 1.34 kg = ------- mg.
v. 0.05 L = -------- ml.
vi. 5.07 kg = ------ gm.
vii. 00193 L = ----- ml.
viii. 3.7 mg = ------- gm.
58

Practice Problems
i. 2 tsp. = --------- gtt.
ii. 1 ½ tbsp. = ------ tsp.
iii. 45 gtts = -------- tsp.
iv. 5 tbsp. = ----- oz.
v. 8 oz. = ------- tbsp.
vi. 12 tsp = -------- tbsp.
59

60

DOSAGE
CALCULATIONS
IFTIKHAR UL HAQ
DEMONSTRATOR
INS-KMU
61

Single-Step Calculation
 Medication may be ordered in a form or amount
different from what is available.
o Proportion may be used to calculate the right
dosage.
 Steps:
a. Set up proportion.
b. Check to be sure units are the same horizontally.
c. Cross multiply and solve for x.
62

Example 1
 60 mg of medication is ordered. Tablets are
available which have 30 mg of medication in each
of them. How many tablets are needed to give 60
mg ?
a. Set up the problem as a proportion. 30 mg are to 1
tablet as 60 mg are to x tablets.
30 mg 60 mg
1 tab x tab
63

Cont.
b. Remember to have the same units horizontally
(mg to mg and tab. To tab.).
c. Cross multiply and solve for x.
30x = 60
x = 60/30 = 2
 2 tablets = 60 mg = the amount of medication
ordered.
64

Example 2
• Ordered : 15 mEq
• Available : 10 mEq/5 ml
 How many ml’s needed ?
 Solve:
10 mEq 15 mEq 10 x = 75
5 ml x ml x = 7.5 ml
65

Example 3
• Ordered : gr 1/800
• Available : gr 1/200 per ml
 How many mls ?
Solve: 1 1
200 gr 800 gr 1 (x) 1 (1)
1 ml x ml 200 800
x = 2/800 = ¼ = 0.25 ml
66

Multiple-Step Calculations
• It may be necessary to convert from one unit to
another first before solving a dosage problem.
 Steps:
a. Set up proportions
b. Convert to like units
c. Substitute converted unit into the proportion
d. Cross multiply and solve for x
67

Example 1
• 240 mg are ordered. Medication is available in 2
grains/1 tablet. How many tablets should be given.
• Solve: 2 gr 240 mg
1 tab x tab
(units do not match. Convert to like units)
1 gr = 60 mg 1 gr x gr x = 4 gr
60 mg 240 mg
68

Cont.
2 gr 4 gr
1 tab. X tab.
x = 2 tablets
69

Example 2
• Ordered : 0.016 gm
• Available : 4 mg/ 1ml
 How many ml should be given ?
 Solve:
4 mg 0.016 gm
1 ml x ml
(units do not match)
70

Cont.
• Convert to like units:
1 gm 0.016 gm
1000 mg x mg
• Cross Multiply: 1 × x = 1000 × 0.016 x = 16 mg
• Substitute converted units into proportions.
4 mg 16 mg 4 x = 16
1 ml x ml x = 4 ml
71

Example 3
• Ordered : 10.5 grans
• Available : 300 mg / 5 ml
 How many ml’s should be given ?
a. Set up proportion
300 mg 10.5 gr
5 ml x ml 1 gr x gr
b. Convert to like unit: 60 mg 300 mg
72

Cont.
• 60 x = 300 × 1
x = 300/60 = 5 gr
c) Substitute converted units into the proportion
5 gr 10.5 gr
5 ml x ml
d) Cross multiply and solve for x
5 x = 52.5 x = 10.5 ml
73

Example 4 & 5
 Two tablespoon of a liquid every 2 hours for 12
hours. How many ml’s of the drug will the client
receive over the 12 hours period ?
 A client is to receive 2 gm of a drug. The drug
comes 500 mg/ 5 ml. Each vial contains 10 ml’s.
How many vials would you need ?
74

Drop Factor (Drops/ml)
 The size of the drop entering the drip chamber based
on the size of the IV tubing.
 Drop factors range from 10 gtt per mL to 60 gtt per
mL.
 1 ml = 1 cc
 Normal I/V set : 15 (drops) gtt/ml (micro drop)
 Blood transfusion set : 10 (drops) gtt/ml
 Buretrol : 60 (drops) gtt/ml
75

Guide lines for Drug Calculation
 Simple Calculation:
 Formula: Required dose ÷ stock dose × dilution
 Example : Order is to give Inj. Lasix 5 mg stat
I/V. Pharmacy provides Inj. Lasix 20 mg/2ml.
 5 mg ÷ 20 mg × 2 ml = 0.5 ml
76

Drops/Min
 Stat order normal saline 1 liter @ 200 cc/hr. How many
drops per minute ?
 Formula :
 Drops/min = Rate × D.F ÷ 60 (mins)
 = 200 × 15 ÷ 60 = 50 gtt/min
o 200 cc = 50 gtt/min
o 250 cc = 62 gtt/min
77

Example. 06
 If a patient is receiving 1 Litre of D/Water with 120 mEq
of kcl at 40 cc/hr, how much kcl the patient is receiving per
hour ?
1000 cc 40 cc
120 mEq x mEq
1000 × x = 120 × 40
> X = 4800 ÷ 1000 = 4.8 mEq/hr
78

Example. 07
 Inj. Solumedrol 125 mg in 2 cc is available. You need to
give 60 mg to a patient. How many cc you will give ?
 Solve:
• Set proportion
125 mg 60 mg
2 cc x cc
Cross multiply : 125 × x = 2 × 60 => x = 120/125 = 0.96 cc
79

Example. 08
 Three years old baby came to ED for Inj. Claforan 350 mg
I/V. The vail is 500 mg and you have to dilute with 5 cc of
sterile water. How many cc you will give to the child ?
 Solve:
500 mg 350 mg
5 cc x cc
500 × x = 5 × 350 .> x = 1750 ÷ 500 = 3.5 cc
80

Criteria for Grading Dosage
Calculation Exams
1. Each problem must be set up in the fractional format.
2. Must show fractional format for each step in multiple
step problems.
3. Must show units in formulas.
4. Must solve for x in each formula.
5. Always convert from one unit of measure to another by
the shortest number of steps.
81

Practice Exam
1. Ordered : 40 units
Available : 100 U/ml
 How many ml’s should
be given ?
2. Ordered : 3 mg
Available : 1.5 mg/ tab.
 How many tablets
should be given ?
3. Ordered : 1.5 gr
Available : ½ gr / tablet
should be given ?
4. Ordered : 100 mg
Available : 250mg /tab.
should be given ?
82

Cont.
5. Ordered : 5 mg
Available : 10 mg/2 ml
 How many ml’s
should be given ?
6. Ordered : 0.125 mg
Available : 0.25mg/tab.
should be given ?
7. Ordered : 1/200 gr
Available : 1/100gr/tab.
should be given ?
8. Ordered : 0.5 mg
Available : 2mg/ml
be given ?
83

Cont.
9. Ordered : 0.3 gm
Available : 300mg/tab.
should be given ?
10. Ordered : 150 mg
Available : 1 gr/ tab.
should be given ?
11. Ordered : 0.03 gm
Available : 6mg/8ml
be given ?
12. Ordered : 2 gr
Available : 60mg/tab.
should be given ?
84

Cont.
13. Ordered : 0.75 gm
Available : 250 mg/tab.
should be given ?
Available : 60 mg/ml
 How many tsp should
be given ?
15. Ordered : 0.25 Gm
Available : 125 mg/ml
be given ?
Available : 0.5 gm/tab.
should be given ?
85

Cont.
17. Ordered : 1/6 gr
Available : 5 mg/ml
 How many ml’s
should be given ?
18. Ordered : 2 Tbs. Q2h
for 12 hours.
 How many ml’s of
the drug will the pt.
receive over 12 hours
period ?
86

Cont.
19. Ordered: 800,000 units
Available : 2,000,000
units/10 ml
be given ?
20. Ordered : 60 mg
be given ?
21. Ordered : 2 mg
 How many ml’s
should be given ?
87

88

DOSAGE
CALCULATION
IFTIKHAR UL HAQ
DEMONSTRATOR
INS-KMU
89

Dosage by Weight
• Order : 25 mg/kg of body wt.
• Available : 5 gm/20 ml
 How many ml’s do you give to a 30 lb. child ?
 The order first needs to be clarified to establish
exactly what has been ordered.
90

Steps
• Step 1 :
1. Clarify the order (How much medicine is 25
mg/kg for a 30 lb. patient)
a. Set up proportions.
25 mg x mg
1 kg 30 lbs.
(Units don’t match so they must be converted)
91

Cont.
b. Convert to like units.
2.2 lbs. 30 lbs.
1 kg x kg
2.2 x = 30 x = 13.64 kg
(Note : Remember to round the kg to hundredths
place before continuing with the problem)
92

Cont.
c. Substitute converted units into the original
proportion.
25 mg x mg
1 kg 13.64 kg
Cross Multiply: 25 × 13.64 = 1 × x x = 341
mg
(Total desired dose for a 30 lbs. child is 341 mg)
93

Cont.
• Step 2:
a. Set up proportion
5 gm 341 mg
20 ml x ml
b. Convert to like units
1 gm x gm
1000 mg 341 mg
94

Cont.
• Cross Multiply
1000 x = 341 x = 0.341 gm
d. Substitute converted units and solve for x.
5 gm 0.34 gm
20 ml x ml
Cross Multiply: 5 x = 20 × 0.34 x = 1.364 ml
Round off the final answer = 1.4 ml
Give 1.4 ml to 30 lbs. child ordered to have 25mg/kg of B.W
95

Exam Practice
1. A twenty-two pound infant is to receive 2 mg/kg
of a drug. The drug is available in 10 mg/0.5 ml.
How many ml’s will be given ?
2. A client weighing 110 lbs. is to receive a drug at
the dosage of 2.5 mg/kg of body weight. How
many mg of the drug will the client receive ?
3. A client is to receive 0.2 ml/kg of a drug every 2
hours. The client weighs 110 lbs. How many ml’s
of drug will the client receive in 24 hours ?
96

Exam Practice
4. A 66 lbs. child is to receive a drug 2.5 mg/kg of
body weight. How many mg’s will the child
receive ?
5. A sixty-six pound child is to receive 0.4 mEq/kg
of a drug. The drug is available in 2 mEq/4 ml.
How many ml’s will be given ?
97

98

PEDIATRIC
MEDICATIONS
IFTIKHAR UL HAQ
DEMONSTRATOR
INS-KMU
99

Steps
1. Convert pounds to kilograms.
2. If weight is in ounces, convert ounces to nearest
hundredths of a pound and add this to total
pounds.
3. Since 16 oz. = 1 lb., change oz. to part of a pound
by dividing by 16.
4. Convert total pounds to kilograms to nearest
hundredths.
100

Example 1
• Order : Lasix 15 mg. Per Oral B.D
• Desired Dose : 2 mg/kg/day
• The infant weighs 16 lbs. 10 oz., How many mg will
you give ? Single dose? & BID dose ?
 Solve:
o Convert oz. to lbs.
16 oz. 10 oz.
1lb x lb x = 0.63 lb.
101

Cont.
• Child’s total weight is : 16 lb + 0.63 lb = 16.63 lbs.
• Convert lbs. to kgs.
2.2 lb 16.63 lbs.
1 kg x kg
x = 7.56 kg
2 mg x mg
1 kg 7.56 kg x = 15.12 mg
102

Cont.
• The total desired dose for the infant is 15.12
mg/day
• So, OD or once daily dose (Single dose) would be
15.12 or 15 mg
• B.D or twice daily (10:00 AM & 10:00 PM) dose
would be 15/2 = 7.5 mg
103

Example 2
• Order : 115 mg/ml tid. (TDS)
• Desired dose : 30 mg/kg/day in divided doses.
• Infant weighs 25 lbs. 4 oz., How many mg will you
give in 1 day ?
 Solve :
o Convert oz. to lb.
4 oz./16 lbs. = ¼ or 0.25
So, infant’s weight is : 25 lbs. + 0.25 lb. = 25.25 lbs.
104

Cont.
• Now convert lbs. into kgs.
2.2 lbs 25.25 lbs
1 kg x kg
x = 11.48 kgs
• Calculate total dose in mgs:
30 mg x mg
1 kg 11.48 kg
x = 344.4 mg
105

Cont.
• Now calculate total ml’s for 344.4 mgs
115 mg 344.4 mg
1 ml x mls
• 115 × x = 1 × 344.4
• x = 2.99 0r 03 mls
• so, you can give only 3 ml of the medicine in a day
• As the order is in TDS dose, hence you will give 01
ml of the medicine every 8 hourly. 106

Practice Exam
1. A 20 pound, 8 ounce child is to receive cosmegen
20 mcg/kg of body weight. How many
micrograms should the child receive ?
2. Ordered : Phenergan 1 mg/kg of body weight.
How many mgs should you give to a 45 pound
post-op child ?
107

Cont.
3. Ordered : 30 mEq per kg. Client weighs 8 lb. 8 oz.
 How many mEq should you give ?
4. Ordered : 40 mg per kg of body wt.
Available : 100 mg per 1 ml
 How many ml’s should you give to a 8 lb. 4 oz. infant ?
5. Ordered : 40 mEq /kg of body weight. Pt. weighs 8 lbs. 6 oz.
 How many mEq should you give ?
108

109

PARENTERAL
MEDICATIONS
IFTIKHAR UL HAQ
DEMONSTRATOR
INS-KMU
110

Directions for Calculating IV
Problems
A. To find flow rate stated in ml’s per hour (If not given in
the order) :
• Divide the total volume of the solution in ml by the total
number of hours to run.
 Example 1: 1000 ml IV solution ordered to infuse over
8 hours.
1000 ml x ml
8 hrs 1 hr 8 x = 1000 >> x = 125 ml/hr 111

Example 2
• 1000 ml solution to infuse over 6 hours.
• Solve: 1000 ml
6 hrs = 166.6 ml/hr = 167 ml/hr
112

B. To find flow rate stated in
drops per minute :
 Drop factor is the number of drops it takes to equal
1 ml with a specific type of IV tubing. The drop
factor is stated on the tubing package.
ml/hr. × drop factor
60 min/hr gtts/min
 (60 minutes/hr is a constant in this formula)
113

Example 3
 The drop factor is a 15 gtts/ml and the flow rate is
120 ml/hr. Find gtts./min or drops per minute.
 Solve :
120 ml/hr × 15 gtts/ml
60 mins/hr
= 1800/60 = 30 gtts/min.
114

Example 4
 The drop factor is 20 gtts/ml and the flow rate is
100 ml/hr. Find gtts/min.
 Solve:
100 ml/hr × 20 gtts/ml
60 mins/hr
= 2000/60
= 33 gtts/min
115

Example 5
C. To find how much drug is in 1 ml of fluid:
 Keflin 500 mg is available in 1000 ml of fluid.
Find out how much of medicine is in 1 ml of the
mentioned fluid.
 Solve:
500 mg x mg
1000 ml 1 ml
Cross Multiply: 1000 x = 500 --- > x = 0.5 mg/ml 116

Example 6
D. How much drug in hour?
 500 mg/1000 ml of keflin was infused in 10
hours. Find mg/hr.
 Solve :
500 mg x mg
10 hrs 1 hr
• Cross Multiply: 500 = 10 x  x = 50 mg/hr
117

Example 7
• Order: 5 mg
• Available : 2 mg/ml
 How many ml do you give ?
 Solve:
2 mg 5 mg
1 ml x ml
• Cross multiply: 2 x = 5  x = 2.5 ml
118

Example 8
• IV order : D5W with 20 mEq Kcl per liter to infuse
at 50 ml/hr. Available dose is inj. Kcl 10 mEq/5 ml.
Solve the problem.
 To find out how many ml of Kcl will contain 20
mEq.
10 mEq 20 mEq
5 ml x ml
Cross Multiply: 10 x = 100  x = 10 ml 119

Cont.
 The drop factor is 60 gtts/ml. How many gtts/min
will IV run?
50 ml/hr × 60 (DF)
60 min./hr  = 50 gtts/min
 How much fluid will the patient receive in 24 hrs ?
50 ml/1 hr × 24 hrs = 1200 ml.
120

Cont.
• How many mEq of Kcl will the patient receive in
one hour ?
20 mEq x mEq
1000 ml 50 ml
Cross Multiply:
20 × 50 = x × 1000  x = 1 mEq
121

Practice Exam
1. Ordered : 2mg/kg. Client weighs 44 lbs. How
many mg will client receive ?
2. Ordered : D5 ½ N/S to infuse 2 liters over 16
hours. How many ml’s/hr will be infused per hr ?
3. Ordered: IV of D5 ½ N/S at 100 ml/hr. ( DF: 20
gtt/ml ). How many drops per minute ? 122

Cont.
4. Order : 500 ml of LR with 20 mEq Kcl over 8
hours. (DF: 15 gtts/min) How many drops/min ?
5. Order: 1.5 Gm P.O. Available is 500 mg/tab. ,
How many tablets will you give ?
6. Order : gr/ 1/6 IM. Available is 30 mg/ml. How
many ml’s will you give ? 123

Cont.
7. Order : 0.5 gm p.o., Availaable is 250 mg/ml.
How many ml’s will you give ?
8. Order : 200,000 units IM. Available is 500,000
units/5 ml. How many ml’s will you give ?
9. Order : 200 mg IM. Available is 500 mg/ml. How
many ml’s will you give ? 124

Cont.
10. Order : 750 mcg p.o., Available is 0.5 mg/tab.,
How many tablets will you give ?
11. Order : 250 mcg IM. Available is 1 mg per 2 ml.
How many ml’s will you give ?
12. Order : 1000 ml of D5W to infuse over 12 hours
(DF: 20 gtts/min).
• How many ml per hour ?
• How many drops per minute ? 125

Cont.
13. Order : 1000 ml of D5 NS to infuse at 125 ml/hr
(DF: 60 gtts/min). How many drops per minute ?
14. Order : 1000 ml of D5W with 2 gm of keflin to
infuse in 1 hour (DF: 15 gtts/min).
• How many drops per minute?
• How many mg of keflin in 1 ml ?
126

Cont.
15. 500 ml LR to infuse over 10 hours (DF: 60
gtts/min).
• How many drops per minute ?
16. 500 ml D5W with 500 mg Aminophylin to infuse
at 150 ml/hr (DF: 20 gtts/min).
127

Cont.
17. 1000 ml LR to infuse over 10 hours (DF: 60
gtts/min).
18. Order : 2 gm p.o. , Available is 500 mg/tab.
• How many tablets will you give ?
128

129

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