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Chapter 7
Review of Mathematical Principles
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
1
Arabic Numerals
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Number system we are most familiar with
Includes fractions, decimals, and whole
numbers
Examples include numbers 1, 2, 3, etc.
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Basic Rules of Roman Numerals
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1. Whenever a Roman numeral is
repeated or a smaller Roman numeral
follows a larger number, the values are
added together.

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For example: VIII
(5 + 1 + 1 + 1 = 8)
2. Whenever a smaller Roman numeral
appears before a larger Roman numeral,
the smaller number is subtracted.

For example: IX (1 subtracted from 10 = 9)
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Basic Rules of Roman Numerals
(cont.)
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3. The same numeral is never repeated
more than three times in a sequence.

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For example: I, II, III, IV
4. Whenever a smaller Roman numeral
comes between two larger Roman
numerals, subtract the smaller number
from the numeral following it.

For example: XIX = 10 + (10-1) = 19
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
4
Fractions
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One or more equal parts of a unit
Part over whole, separated by a line:
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3 parts of 4 = ¾
3 is the top number, 4 is the bottom number
The “numerator,” or top number, identifies
how many parts of the whole are
discussed
The “denominator,” or lower number,
identifies how many equal parts are in the
whole
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Fractions (cont.)

Fractions may be raised to higher terms by
multiplying the numerator and denominator
by the same number:

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Fractions can be reduced to lowest terms
by dividing the numerator and denominator
by the same number:


¾ x 3/3 = 9/12
9/12 ÷ 3/3 = 3/4
A fraction is easiest to work with when it
has been reduced to its lowest term.
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
6
Adding Fractions
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You must find the common denominator first.
EX: 1/3 and 1/5 (multiply the 2 denominators)
The common denominator is 15
1/3 … (3 into 15 = 5 so… 5x1=5) 1/3 = 5/15
1/5…(5 into 15 = 3 so… 3x1=3) 1/5 = 3/15
5/15
+3/15 equals
8/15
Are you able to reduce this fraction to its lowest
terms?
Fractions (cont.)

Proper fraction: numerator is smaller than
denominator


For example: ¾ is a proper fraction, 3 is less
than 4
Improper fraction: numerator is larger
than denominator
For example: 8/6 is an improper fraction, 8 is
greater than 6


Mixed number: whole number is
combined with a proper fraction

For example: 1 ⅔ is a mixed number
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
8
Question 2
The number 9 5/8 is a(n):
1.
2.
3.
4.
Proper fraction.
Improper fraction.
Mixed number.
Complex fraction.
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
9
Fractions (cont.)

Multiplying fractions; multiply the numerators
together and the denominators together



For example: 2/4 × 3/9 = 2 × 3 (6)/ 4 × 9 (36)
Tip: it is easier to reduce the fractions to lowest
terms before multiplying.
Therefore: ½ × 1/3 = 1/6
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
10
Fractions (cont.)

To divide two fractions, invert (or turn upside
down) the fraction that is the divisor and then
multiply.
For example: ¾ ÷ ½ =
¾ × 2/1 =
3 × 2 / 4 × 1 or 6/4
*** 6/4 can be reduced to 3/2 or 1 ½.
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
11
Decimal Fractions (less than 1)
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To the left of the decimal, numbers are whole
numbers.
To the right of a decimal, numbers are fractions of
a whole in denominations of 10.
Tenths, hundredths, thousandths…… The th is
cueing you the value is less than 1
Think Money when you use decimals!
Adding and subtracting decimals, line up the
decimal place and do the math
This is just like managing your checkbook
[assuming you do so ;) ]
Decimals

All fractions can be converted to a decimal
fraction by dividing the numerator into the
denominator.


To add two decimal fractions, first line up
the decimal points.

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For example: ¾ is 3 ÷ 4 = 0.75
For example: 0.345 + 2.456 = 2.801
To subtract two decimal fractions, first line
up the decimal points.

For example: 1.6 − 0.567 = 1.033
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
13
Decimals (cont.)

Multiplying decimals
1.467 (3 decimal places)
× 0.234 (3 decimal places)
________
0.343278 (6 decimal places in answer)
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
14
Decimals (cont.)

To divide two decimals, first move the
decimal point in the divisor enough places to
the right to make it a whole number.


6 ÷ 0.23 (the decimal must be moved two places
to the right to change 0.23 into “23”)
600 ÷ 23 (move the decimal two places to the
right in the dividend) = 26.09 (rounded)
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
15
Ratios and Percents
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A ratio is a way of expressing the relationship
of one number to another or expressing a
part of a whole number. The relationship is
reflected by separating the numbers with a
colon (e.g., 2:1).
Percent (%) means parts per hundred; can
be written as fractions or decimals
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Proportions
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A way of expressing a relationship between two
ratios
The two ratios are separated by a double colon (::)
which means “as.”
If three variables are known, the fourth can be
determined.
When solving for “x,” the numerators must be the
same measurement and the denominators the
same measurement.
The numerators and denominators in the proportion
must be written in the same units of measure.
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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EX: ½:: 3/6 or 1:2 :: 3:6 these two
expressions mean the same thing
Some people work with fractions better,
Others work with linear aspects better
Let’s see which you prefer…..
Chapter 8
Mathematical Calculations
Used in Pharmacology
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
19
Apothecary System
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Grains: gr (solids)
Lowercase Roman numerals
Common fractions
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
20
Metric System
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Decimal system
Meter: m (length)
Liter: L (volume)
Gram: g (weight)
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
21
Metric Measure
Kilogram
0
Gram
.
8
8
Milligram
5
3
,
.
5
3
.
mcg
,
.
Each group has three place values, just like money does.
So ones, tens, and hundreds would be in the microgram section.
Thousands would be like the miligrams; millions would be like the grams and
billions would be like the kilograms.
Grains of sand belong
in the clock!!
60 mg
Gr 1
45 mg
Gr 3/4
Gr 1/4
Gr 1/2
30 mg
15 mg
Converting Temperature Readings
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Fahrenheit
Celsius
Formulas to convert
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
24
Conversion of temperatures
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Celsius
100 ͦ
Cold scale
0ͦ
boiling
212 ͦ Fahrenheit
hot scale
freezing
32 ͦ
Celsius to Fahrenheit
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(C ° x 9/5) +32 = F °
OR
(C ° x 1.8) + 32 = F °
C is a cold scale. Transitioning up the hot scale needs
you to Multiply by a fraction greater than one then
add the 32 to finish the calculation.
EX: 36.8 C x 9/5 = 66.2 + 32 = 98.2 F °
Fahrenheit to Celsius
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
C = (F ͦ - 32) x 5/9
OR
C= (F ͦ - 32) ÷ 1.8
 You started with the hottest scale, so you need to
subtract 32 and then multiply by a fraction (less
than 1) or divide to lower the number toward the
cold scale.
 C = 101.2 – 32 = 69.2 x 5/9 = 38.4 ° C
 Normal Celsius body temp is 37 °

Question 1
50 mcg = __________ mg.
1.
2.
3.
4.
500
5000
0.05
0.005
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
28
Question 3
A patient weighs 198 pounds. How much
is this in kilograms?
1.
2.
3.
4.
98 kg
90 kg
108 kg
88 kg
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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
Questions?