Fraction
Something divided into equal parts, and each part together represent a whole.
Top = Numerator
Bottom =Denominator
Types of fractions:
1. Proper fraction 1/4
3. Improper fraction 5/4
Converting fractions:
1. Improper fraction to a mixed number
7/4 = 4/4 + 3/4 = 1 3/4
2. Mixed number to Improper fraction
1 3/4 = 4/4 + 3/4 = 7/4
Reducing fractions
Tips:
Even # = divide by 2
# ends with 0 = divide by 2,5,10
example:
32/24 = 8/6 = 4/3
Multiplying Fractions
Proper fraction
7/8 x 3/5 x 9/16 = 189/640
3/8 x 4/5 = 12/40= 6/20 = 3/10
Mixed numbers
2 7/8 x 1 3/5 = ?
23/8 x 8/5 = 184/40 = 23/5
2 2/3 x 5/6= ?
8/3 x 5/6= 40/18 = 20/9
Dividing fractions
Turn the fraction around and multiply
Example:
3/8 : 9/18 = 3/8 x 14/19 = 21/36 = 7/12
Decimals
Rules:
1. if # is less than 1 put a o in front of the decimal
.5 = 0.5
2. if there are 0's after decimal point, ignore them
15.5000000 = 15.5
3. 0's in the middle are NOT ignored
15.00001 = 15.0001
Fraction to decimal
Divide numerator by denominator
Example:
1/10 = .1
2 73/100 = 273/100 = 2.73
30/100= 0.030
72/10000 = .0072
833/10 = 83.8
Decimals to fraction
0.01 = 01/100
0.2 = 2/10 = 1/5
1.1 = 1 1/10
0.25 = 25/100 = 5/20
10.50 = 10 + 0.50 = 10 50/100 = 10 5/10
5.7 = 5 7/10
7.45 = 7 + 0.45 = 7 45/100 = 7 9/20
0.76 = 76%
0.19 = 19%
20%= .20
0.9% = 0.009
5/8 = 625%
Multiplying decimals
Multiply and move decimal point the total # places
15.503 x 12.1 = 187.5863
1.706 X 6.23 = 10.628
Percentages
per cent = per 100
50% = 50/100 = 1/2 = 0.50
%= g/100 ml
2% = 2g/100 ml
20mg/ml
4/5 = 0.80 = 80%
Percentages calculation
Multiply % Convert one of the % to a decimal
80% x 30% = 80% x 0.30 = 24%
25% x 80% = 25% x .8= 20% = 0.2
Dividing % 3 ways:
1. Convert % to decimal
10% : 20% = 0.1 : 0.2= 0.5 = 50%
2. Convert % to fraction
10% : 20% = 1/10 : 2/10
1/10 x 10/2 = 1/2= 50%
3
% Calculation examples
27% + 33% = 0.27 + 0.33 = 0.6
100% - 71% = 29% or 0.29
25% x 80% = 25% x 0.8 = 0.2 or 20%
75% : 3 = 25 % or 25
75% : 3% - 75% : 0.03 = 2500 or 0.25 or 2500%
Lola's food is 35% protein. If its a 20-pound bag of dog food how many pounds of protein are in this bag?
7 pounds protein
20lbs bag x 0.35 % protein= 7
you were given 100 tablets to give your dog. you are to give 5 tablets a day for 20 days. After day 5, what % of tablets have you given?
25%
100 total
5/day ( 5 days) = 25
25/100 = .25 = 25%
Lili originally weighed 15 lbs. Now she weighs 10 lbs. What % of body weight did she lose?
33%
was: 15
now: 10
5
5/15 = 0.3333333 = 33%
Ratio
relationship between 2 #s
Each tablet is 250mg = 1 tab:250mg
1 kilogram= 2.2 pounds = 2.2#/1 kg or 1kg/2.2#
A dog requires 400 mg of a drug. Each tablet has 50mg. How many tablets do you give?
8 tablets
400mg x 50mg = 8 tab
X tab 1 tab
You are asked to give 1.2 ml of Albon liquid to a patient. Te concentration of Albon is 50mg/ml. How many mg of Albon will you give?
60mg
50 mg x * mg = 60mg
1 ml 1.2 ml
Procaine penicillin is available in a concentration of 300,000 IU/ml and a dosage of 20,000 IU/kg
1. How much do you give a 45kg dog?
2. How much do you give a 1500 lb cow?
1. 3ml
45 kg x 20,000 IU x ml = 3ml
kg 300,000IU
2. 45.24 ml
1500 lb x kg x 20,000 IU x ml = 45.45 ml
2.2 lb kg 300,000 IU
A 9.8 lb cat needs 1.5 IU/Kg of insulin BID.
U-40 Insulin is 40 units/ml
1. How many ml of U-40 insulin does the ca need in one dose?
2. how much in one day?
3. one week?
4. How long will a 10 ml bottle of U-40 insulin last? (days)
1. 0.17 ml
9.8 lb x kg x 1.5 U x ml = 0.17 ml
2.2lb kg 40 IU
2. 0.33 ml
0.17 ml x 2 times = 0.22 ml
time day
3. 2.34 ml
0.33 ml x 7 days = 2.34 ml
day
4. 30 days
10/ 0.33 = 30.30
3 systems of measurement used in Veterinary pharmacology:
Metric
Apothecary
Household
Metric
3 measurements:
Weight: gram (g)
Volume: Liter (L)
Lenght: meter (m)
King Henry Died Drinking Chocolate Milk
K-Kilo
H-Hecti
D-Deca
----BASE
D-Deci
C- Centi
M-Milli
M-Micro
*
*
*
UG-Micro
Metric system practice
Convert:
1) 1.732 L - mL
2) 0.003kg - g
3) 9324m - km
4) 100.9 dg - kg
5) 0.032mg-ug
6. 3.4kg-g
1)L- 1732 mL
2) kg- 3g
3) m- 9.324 km
4) dg- 0.01009 kg
5) mg- 32 ug
6) kg- 3400g
Apothecary
...
Household
...
Conversions
1 mile = 1.6 km
1 tsp = 5 ml
1 tbs= 3 tsp = 15 ml
1 oz = 2 tbs
1 kg= 2.2 #
1 inch = 2.54 cm
1 ounce = 30ml
Coversions Practice:
1. A subcutaneous mass on a dog is 2.5
inches in diameter. How many cm is it ?
2. A client reports he's been giving his dog 2
tablespoons of Kaopectate for diarrhea.
how many ml is this?
3. A client reports her cat drinks 1/2 cup of
w
1. 6.35 cm
2.5 in x 2.54 cm = 6.35
1 inch
2. 30 mL
2 tbs x 15 mL = 30 mL
1 tb
3. 4 ounces, 120 mL
0.5 cup x 8 ounces = 4 ounces 30 ml = 120 mL
1 cup 1 ounce
4. 4 km
25miles x 1.6 km = 4 km
1 mile
Abbreviations
SID : Once a Day
BID : 2 x day
q : Every
q8h: Every 8 hours
PO : By mouth
SQ : Subcutaneous
IM : Intramuscular
IV : intravenous
Oral Medication comes as
Tab: Tablets
Cap: Capsules
Liquid
Powder
What is Parenteral?
Not given orally
Given as : IV, IM, SQ
Needle
Anatomy (pic)
Bevel - Shaft- Hub
Tip metal plastic
Lenght:
1/2" , 5/8", 3/4", 1", 1 1/2"
Diameter:
measured as a gauge
16g, 18g, 20g, 22g, 25g, 26g, 30g
bigger # = smaller needle
Syringes
measure in units ( not mL)
1 cc = ones
3 cc = tenths
6 cc = 2 tenths
12cc = hundreths
Dose
Weight x Dose / Concentration
Example:
a 15 kg terrier requires a drug at a dosage of 10mg/kg. The concentration of the drug is 100mg/ml. How many ml should you give?
15kg x 10mg x 1 ml = 1.5 ml
kg 100 mg
% to mg/ml
% -> mg/ml x10
60% = 600 mg/ml
1.2% = 12 mg/ml
0.9% = 9 mg/ml
5% = 50 mg/ml
mg/ml -> % : 10
500 mg/ml = 50%
15mg/ml = 1.5%
35 mg/ml= 3.5%
1.5 mg/ml = 0.15%
.0007 mg/ml = .00007%
Solution/ Dilution
C1 X V1 = C2 X V2
C = Concentration = %
V = Volume = ml
Practice: solutions
Drug A comes as a powder in 1g packets. How many mL of diluent is needed to achieve a final concentration of:
1. 15%
2. 20%
3. 50%
1. 15% = 150mg x ml = 6.67 mL
ml 10000mg
2. 20% = 200 mg x ml = 5mL
ml 10000mg
3. 50% = 500 mg x ml = 2 ml
ml 10000mg
Dilutions
1 part substance being diluted / 100 part solution
1/100 = 0.01 = 1%
5/100 = 0.05 - 5%
10/80 = 0.125 = 12.5%
2/300 = 0.0067 = 0.67%
Dilution as a fraction: as a percent
1:9 = 1/10 = 10%
Concentration
OC x D = FC
OC= Original Concentration
D = Dilution
FC= Final Concentration
Example:
If we have 15% iodine solution. If we dilute it by 1/5, what is our final concentration?
15% x 1/5 = 3%
Practice:
You have a 10mg bottle of 2% Selemectin. How many mg of Selemectin are in this bottle?
10 ml 20mg = 200 mg
ml
Practice:
A 2.4 kg rabbit needs 0.40 mg/kg of 1% Ivermectin to treat sarcoptic mange. How many mL would you draw up?
2.4 kg x 0.40 mg x ml = 0.96 mL
kg 10mg
Practice:
Lidocaine of 2% is prescribed to a 13 lb beagle at a dose of 2 mg/kg IV. How many mL will you give?
13 lb x kg x 2 mg x ml = 0.59 mL
2.2 lb kg 20 mg
Military time
based on a 24 hour scale
Midnight: 0000
Noon : 1200
11:00 am = 1100
11:00 pm = 2300
5:00 am = 0500
5:00 pm = 1700
Temperature
Vet techs use 2 temperature scales:
Fahrenheit
Celsius
Normal room tempt: 72 degrees F
22 degrees C
Wate freezes at: 32 degrees F
0 degrees C
Water boils at 212 degrees F
100 degrees C
Normal human body temp: 98.6 degrees F
37 degrees C
F= ( 1.8 x *C) + 3
Practice:
The cats temperature is 40C. What would it be in Fahrenheit ?
F= ( 1.8 x *C) + 32
F= (1.8 x 40) + 32
F= 72 +32
F= 104
Scientific Notation
1.2 x 10^3 = 1200
1 x 10^ -3 = 0.001
(2.7 x 10^3) + ( 3.3 x 10^3) = 6 x 10^3
5600000000 = 5.6 x 10^8
0.0003 = 3 x 10^-4
(4.1 x 10^4) x ( 2 x 10^3) = 8.2 x 10^7
(6 x 10^-3) : (2 x 10 ^-3) = 3 x 10^-6
(7.5 x 10^7) : (1.5 x 10^-3) = 5 x 10^10
(6 x 10^9) - (4
Drip set
IV fluids are administered through a plastic tubing with a drip chamber and a roller clamp.
ggt = drips
drip sets come as:
60 ggt/ ml
15 ggt/ ml
Practice:
1.
Dog needs 1.73 mL/min.
How many drops does this animal need:
Per minute? (use 60ggt)
Per second?
2.
Administer 220 ml of fluids to a 60lb dog over a 4 hr period using a 15 ggt/ml set.
How many drops will the animal need:
Per second?
Problem 1:
1.73 ml x 60 ggt = 103 ggt
ml min
103 ggt x min = 1.71 ggt
60 sec 60 sec
Problem 2:
220 ml x 1hr x 1 min x 15 ggt = 0.229 ggt
4 hr 60 min 60 sec mL sec
convert 0.23 ggt/sec to 1 ggt/ x sec
0.23 ggt = 1 ggt x= 4.3
sec x sec
Practice:
You're making a cleaning solution at work. You are asked to make a 1: 54 solution. The bottles are 278 mL. How many mls of the solution do you put in the bottle? how many mls of water?
278 ml = 5.05 ml solution
55
278 ml - 5.05 =272.96 mL water
Whats the fluid deficit for a 50lb dog to be about 8% dehydrated?
1.82L ( 1820 ml)
0.08 x 22.72 = 1.82 L
8:10= 0.08
50 : 2.2 = 22.72 kg
Citations
Dr. Peterson VT 103 Veterinary Calculation Powerpoints.