Basic Mathematics

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Basic Mathematics
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Ensuring Proper Doses

• It is the health-care professionals
  responsibility to ensure that the patient
  receives the proper dose of medication, and to
  educate the patients about the proper measurement
  of doses.

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Essentials of Math

• Basic math uses
• Arabic numbers
• Roman numerals
• Fractions
• Decimals
• Percents
• Ratios
• Proportions

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Arabic and Roman Numeral Systems

• The Arabic system is based on the numbers 0
  through 9.
• Arabic numbers can be written as whole numbers,
  fractions, and decimals.
• Roman numerals consist of letters that represent
  numbers.
• Roman numerals are commonly used to represent
  units of the apothecary system.

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Reading Roman Numerals

• Roman numerals are read by adding or subtracting
  the value of the letters.
• I 1 V 5 X 10 L 50 C 100
• When a lower valued letter follows a larger
  valued letter, add the letters.
• When a lower valued letter precedes a larger
  valued letter, subtract the lower valued letter
  from the larger.

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Reading Roman Numerals

• IX 10 1 9
• IV 5 1 4
• XIII 10 3 13
• XL 50 10 40
• XXXIV 10 10 10 (5 1) 30
  4 34

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Table 5-1 The Most Common Roman Numerals and
Their Arabic Values
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Fractions

• A fraction is one or more equal parts of a unit.
• The fraction below means 3 parts out of 4 total
  parts.
• Also means 3 4

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Top number numerator Bottom number denominator
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Classification of Fractions

• A common fraction represents equal parts of a
  whole (e.g., 1/2, 2/5, 3/7, 4/9).
• A decimal fraction is commonly referred to as a
  decimal (e.g., 0.5, 1.7, 5.25, 10.79).

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Classification of Fractions

• The numerator of a proper fraction is less than
  its denominator and its value is less than 1
  (e.g., 1/2, 2/3, 3/4, 10/24).

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Classification of Fractions

• The numerator of an improper fraction is greater
  than, or the same as, its denominator its value
  is equal to or greater than 1 (e.g., 5/3, 8/4,
  12/9, 75/25).
• A mixed fraction is a whole number and a fraction
  combined its value is always greater than 1
  (e.g., 1-1/2, 2-1/4, 3-1/2).

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Complex Fractions

• A complex fraction consists of at least 1
  fraction and no more than 1 whole number its
  value may be less than, equal to, or greater than
  1.

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Adding Fractions

• When fractions have the same denominators, add
  the numerators and keep the value of the
  denominators the same then reduce to lowest
  terms.
• 1/10 3/10 4/10 2/5

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Subtracting Fractions

• If fractions have the same denominator, subtract
  the smaller numerator from the larger numerator
  and keep the denominator the same then reduce to
  lowest terms.
• 6/8 2/8 4/8 1/2

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Dissimilar Denominators

• If fractions do not have the same denominator,
  change them so they have the smallest common
  denominator then subtract the numerators and
  leave the denominator the same.

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Subtracting/Adding Fractions With Dissimilar
Denominators

• Since 12 is a multiple of 24 (24 2 12),
  divide both numerator and denominator of the
  fraction with the larger denominator by 2 to
  reach the smallest common denominator.
• Note that 24 and 12 can also be divided by 4 or
  3, but 5 cannot be divided by either 4 or 3.

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Multiplying Fractions

• To multiply fractions, first multiply the
  numerators, then multiply the denominators and
  then reduce to lowest terms.
• 3/5 2/4 6/20 3/10

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Dividing Fractions

• The dividend is the number being divided, and the
  divisor is the number that is dividing.
• To divide, you must invert the divisor (3/4
  becomes 4/3) then multiply the fractions and
  reduce to lowest terms.
• 4/8 2/8 4/8 8/2 32/16 2

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Decimals

• Decimals are used within the metric system, and
  their denominators are understood to be 10 or a
  multiple of 10.
• The denominator is not written instead a decimal
  point is added to the numerator to signify the
  multiple of 10.

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Decimals

• For decimals that are less than 1, always place a
  zero to the left of the decimal point to avoid
  confusion (2/10 0.2 19/100 0.19).

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Values of Decimals

• Decimals decrease in value from left to right.
• Decimals increase in value from right to left.
• Each column in a decimal has its own value
  depending on where it is situated compared to the
  decimal point.

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Decimal Values
Hundreds Tens Decimal point Tenths Hundredths
100 10 . 0.1 0.01
? Increasing value ? Increasing value ? Decreasing value ? Decreasing value
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Figure 5-1 Decimal values as they relate to the
location of the decimal point.
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Adding Decimal Fractions

• To add decimals, write the decimals in a column,
  aligning the decimal points directly under each
  other.

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Subtracting Decimals

• To subtract decimals, write the decimals in
  columns, aligning the decimal points zeros may
  be added after the decimal point without changing
  the values.

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Multiplying Decimal Fractions

• Multiply the numbers count the number of places
  to the right of the decimal points in both
  numbers then, place the decimal point in the
  answer at that position.

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Dividing Decimals

• Convert decimals to whole numbers by moving the
  decimal point in the divisor to the right then
  move the decimal point in the dividend the same
  number of places to the right.

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Dividing Decimals

• 4.75 0.5 X Move the divisors decimal 1 place
  to the right to make a whole number then move
  the dividends decimal 1 place too.
• Now the equation is 47.5 5 9.5.

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Ratios

• A ratio is a mathematical expression that
  compares one number to another number, or
  expresses a part of a whole number.
• The expression 34 means 3 out of 4 parts or 3
  4.
• 2/5 25
• 2/100 2100

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Proportions

• A proportion expresses the relationship of
  equality between two ratios.
• The two inside terms (means) when multiplied,
  must equal the two outside terms (extremes) when
  multiplied.
• 14 312
• To verify, 4 3 12, and 1 12 12.

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Figure 5-2 The means and extremes of a
proportion.
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Percents

• The term percent, or the symbol , means
  hundredths.
• Percentages may be expressed as fractions,
  decimals, or ratios.
• 60 60/100 0.60 60100

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Decimal Conversions

• To change a percent to a decimal, move the
  decimal point 2 places to the left.
• 60 0.60
• To change a fraction to a percent, divide the
  numerator by the denominator, then multiply the
  results by 100 and add the percent sign.
• 1/5 1 5 0.2 then, 0.2 100 20