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