Transcript 3.1 Ratios • Ratio – quotient of two quantities with the same units or can be converted to the same units a Examples: a to.

3.1 Ratios
• Ratio – quotient of two quantities with the
same units or can be converted to the same
units
a
Examples: a to b, a:b, or
b
Note: percents are ratios where the second
number is always 100:
35
35%  100
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
20.5 minut es 20.5 minut es

1.5 hour
90 minut es
205 41


900 180
3.1 Rates
a
b like a ratio except the units are
• Rate 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
3.2 Proportions
•
a c
Proportion - 
b d
two rates or ratios are equal
where a,d are the extremes and b,c are the means
a
c
• For a proportion to be true:
  ad  bc
b d
product of the means = product of the extremes
3.2 Proportions
• To solve a a proportion, use crossmultiplication
a
Proportion: b

Cross multiplication:
solve
ad  bc
c
d
3.2 Proportions
• Solve for x:
81
x

Cross multiplication:
81  7  9  x
567  9  x
so x = 63
9
7
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
x
– Solve the proportion
100
– Place a percent sign after the solution
3.3 Converting Ratio Strength
and Percent Strength
• Example: 24 ml of solution contains 6
grams of medication. What is the percent
strength?
6g
x

24m l 100
600  24x
x  25%
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.
25 1
25% 

100 4
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
20 grains  1 scruple
3 scruples  1 dram
60 grains  1 dram
8 dram s 1 ounce
12 ounces 1 pound
4.1 Apothecaries’ System
• Apothecaries’ measures: volume – 1 minim =
volume of a drop of water; the abbreviation for
drop is gtt. 60 minims 1 dram
8 dram s 1 ounce
16 ounces 1 pint
2 pint s 1 quart
4 quarts  1 gallon
32 ounces 1 quart
4.2 Household System
• Household measures: volume – liquid
medications (again a drop is abbreviated gtt.)
75 gtts.  1 teaspoon
3 teaspoons 1 tablespoon
2 tablespoons  1 ounce
8 ounces 1 cup
2 cups  1 pint
2 pints 1 quart
4 quarts  1 gallon
32 ounces 1 quart
4.3 Abbreviations and Symbols
Unit
gallon
quart
pint
ounce
dram
grain
minim
Abbreviation
gal.
qt.
pt.
oz.
dr.
gr.
min.
Symbol
C.
O.
See book
See book
See book
4.3 Abbreviations and Symbols
Unit
drops
pound
teaspoon
tablespoon
cup
Abbreviation
gtts.
lb.
tsp.
Tbl. or Tbs. or Tbsp.
c.
Symbol
#
t
T
c
4.3 Abbreviations and Symbols
– Roman Numerals
1
2
 ss
1  i or I
2  ii or II
6  vi or VI
7  vii or VII
11  xi or XI
12  xii or XII
8  viii or VIII 15  xv or XV
3  iii or III 9  ix or IX
20  xx or XX
4  iv or IV 10  x or X
40  xl or XL
5  v or V
50  l or L
4.4 Charted Dosages
• Charting in Apothecaries’ System
Main rule: symbol or abbreviation – then amount
in Roman numerals
Exceptions:
Fractions – fraction in Arabic (not Roman)
Amount > 40 – amount in Arabic & reverse order
Household – 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. - 6 12 minims 2 times a day
4.5 Converting Units within
Apothecaries’ System
• Using Factor-label Method to convert.
Example: express 3 yards in feet
12 inches
3 feet 
 36 inches
1 foot
4.5 Converting Units within
Apothecaries’ System
•
To convert from one unit to another
1. 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:
new units
am ount
old units
 new units
4.5 Converting Units within
Apothecaries’ System
•
Example: Convert 5 gallons to pints
4 quarts 2 pints
5 gallons

1 gallon 1 quart
 40 pints
Notice how the units “cancel”
Supplement 2.1 Using Formulas
•
•
•
•
•
•
A = lw
I = prt
A = ½bh
d = rt
F  95 C  32
C  95 ( F  32)
•
•
•
•
•
•
Area of rectangle
Interest
Area of triangle
Distance formula
C-F Temperature Conversion
F-C Temperature Conversion
Supplement 2.1 Using Formulas
• Example: d = rt; (d = 252, r = 45)
then 252 = 45t
divide both sides by 45:
27
3
t 5
5
45
5
Supplement 2.2 Solving a Formula
for a Specified Variable
• Example: Solve the formula for B
A  12 h(b  B)
multiply both sides by 2:
2 A  h(b  B)
divide both sides by h: A
2
h
subtract b from both sides:
bB
A
B  2 b
h