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3.1 Ratios
• Ratio – quotient of two quantities with the same units or can be converted to the same unitsExamples: a to b, a:b, or
Note: percents are ratios where the second number is always 100:
ba
10035%35
3.1 Ratios• Simplifying a ratio:
– Convert both quantities to the same units if necessary
– Convert from decimals to whole numbers if necessary
– Reduce to lowest terms
180
41
900
205
minutes90
minutes5.20
hour5.1
minutes5.20
3.1 Rates
• Rate - like a ratio except the units are different (example: 50 miles per hour)
• To simplify a rate:– Reduce as is and leave the unit names– Rates can be expressed as a decimal or fraction
b
a
3.2 Proportions
•
two rates or ratios are equal where a,d are the extremes and b,c are the means
• For a proportion to be true:
product of the means = product of the extremes
d
c
b
a - Proportion
cbdad
c
b
a
3.2 Proportions
• To solve a a proportion, use cross-multiplication
Proportion:
Cross multiplication:solve
dc
ba
bcad
3.2 Proportions
• Solve for x:
Cross multiplication:
so x = 63
7981 x
x9567x 9781
3.3 Converting Ratio Strength and Percent Strength
• Ratio Strength: fraction comparing the amount of medication by weight in a solution to the total amount of solution
• Percent Strength: amount of grams of medication in 100ml of solution
3.3 Converting Ratio Strength and Percent Strength
• To convert ratio strength to percent strength:– Ratio strength (in g/ml) is one side of
proportion– Put on the other side of the proportion– Solve the proportion– Place a percent sign after the solution
100
x
3.3 Converting Ratio Strength and Percent Strength
• Example: 24 ml of solution contains 6 grams of medication. What is the percent strength?
%25
2460010024
6
x
x
x
ml
g
3.3 Converting Ratio Strength and Percent Strength
• Converting percent strength to ratio strength:– Place the percent strength without the percent
sign over 100– Convert if necessary to a ratio of 2 whole
numbers– Reduce the fraction to lowest terms
3.3 Converting Ratio Strength and Percent Strength
• Example: Convert percent strength of 25% to a ratio.
4
1
100
25%25
4.1 Apothecaries’ System
• Apothecaries’ measures came into use by the apothecary, one who prepared and sold compounds for medicinal purposes. Some institutions and physicians still use apothecaries’ measures. The Pharmaceutical Association “went metric” in 1959 – so this system is for the most part obsolete.
4.1 Apothecaries’ System
• Apothecaries’ measures: weights – 1 grain = weight of a drop of water
poundounces
ouncedrams
dramgrains
dramscruples
scruplegrains
112
18
160
13
120
4.1 Apothecaries’ System
• Apothecaries’ measures: volume – 1 minim = volume of a drop of water; the abbreviation for drop is gtt.
quartounces
gallonquarts
quart
ounces
ouncedrams
dram
132
14
1pints2
pint116
18
1minims60
4.2 Household System• Household measures: volume – liquid
medications (again a drop is abbreviated gtt.)
quartounces
gallonquarts
quart
cups
cupounces
ouncestablespoon
tablespoonteaspoons
teaspoontt
132
14
1pints2
pint12
18
12
13
1s.g75
4.3 Abbreviations and SymbolsUnit Abbreviation Symbol
gallon gal. C.
quart qt.
pint pt. O.
ounce oz. See book
dram dr. See book
grain gr.
minim min. See book
4.3 Abbreviations and SymbolsUnit Abbreviation Symbol
drops gtts.
pound lb. #
teaspoon tsp. t
tablespoon Tbl. or Tbs. or Tbsp. T
cup c. c
4.3 Abbreviations and Symbols – Roman Numerals
Vorv5
IVoriv4
IIIoriii3
IIorii2
Iori121
ss
Xorx10
IXorix9
VIIIorviii8
VIIorvii7
VIorvi6
Lorl50
XLorxl40
XXorxx20
XVorxv15
XIIorxii12
XIorxi11
4.4 Charted Dosages
• Charting in Apothecaries’ SystemMain rule: symbol or abbreviation – then amount in Roman numerals
Exceptions:Fractions – fraction in Arabic (not Roman)Amount > 40 – amount in Arabic & reverse orderHousehold – amount in Arabic & reverse order using abbr.
4.4 Charted Dosages
• Example: what is the meaning of the charted dosages: dr. v t.i.d. – 5 drams 3 times a day
oz. iii q. 4h. – 3 ounces every 4 hours
min. viss b.i.d. - minims 2 times a day216
4.5 Converting Units within Apothecaries’ System
• Using Factor-label Method to convert.
Example: express 3 yards in feet
inchesfoot
inchesfeet 36
1
123
4.5 Converting Units within Apothecaries’ System
• To convert from one unit to another1. Write down amount from which you are
converting
2. Put an “X” and draw a fraction bar
3. Put “old units” on bottom and “new units” on top
4. Find the conversion from the table
5. Solve:unitsnew
unitsold
unitsnewamount
4.5 Converting Units within Apothecaries’ System
• Example: Convert 5 gallons to pints
Notice how the units “cancel”
pints40
1
pints2
1
45
quartgallon
quartsgallons
Supplement 2.1 Using Formulas
• A = lw• I = prt• A = ½bh• d = rt• •
• Area of rectangle• Interest• Area of triangle• Distance formula• C-F Temperature Conversion• F-C Temperature Conversion
3259 CF
)32(95 FC
Supplement 2.1 Using Formulas
• Example: d = rt; (d = 252, r = 45)
then 252 = 45tdivide both sides by 45:
5
35
45
275 t
Supplement 2.2 Solving a Formula for a Specified Variable
• Example: Solve the formula for B
multiply both sides by 2:
divide both sides by h:
subtract b from both sides:
)(2 BbhA
)(21 BbhA
Bbh
A2
bh
AB 2