16 Basic Math Skills

State Standard 22) Calculate correct doses required when given a simulated prescription for a pediatric dose, adult dose, and geriatric dose based on weight (if applicable), length of administration, times per day of administration, and presence of other diseases/disorders.

Objectives Students will be able to… Describe the use of decimals in pharmacology Correctly use decimals in dosage calculations Identify Roman Numerals commonly used in pharmacology

Decimals Every digit in a decimal has a place value. Decimals as fractions Decimals are fractions with a denominator that is a multiple of 10. Denominator's value determined by number of digits to the right of the decimal point

Figure 16-1 Place value.

Decimals Decimals as fractions Examples 8/10 represents the decimal 0.8 8/100 represents the decimal 0.08 8/1000 is equivalent to the decimal 0.008

Decimals Decimal fractions Fractions written as a whole number with a zero and a decimal point in front of the value

Decimals Zeros placed before or after a decimal number do not change the value of the number. Examples: 00.8 is the same as 0.8, which is the same as .8 0.800 is the same as 0.80, which is the same as 0.8

Decimals Health care professionals always place a zero before the decimal point to avoid misreading of a number (a decimal point not preceded by a zero is easily missed). Example: write 0.8 (not .8)

Decimals Key points for working with decimals Moving decimal point one place to the right multiplies the number by 10. Moving decimal point one place to the left divides the number by 10. When calculating dosages, only need to go three places to the right of the decimal (1000ths).

Decimals Rounding Round to the nearest thousandth (third decimal place to the right). Determine appropriate decimal place to round to. Look at number to the right of that decimal place.

Decimals Rounding Round to the nearest thousandth (3rd decimal place to the right) If number is 4 or less, round down. 1.8123 rounds to 1.812 If number is 5 or more, round up. 4.465948 rounds to 4.466

Decimals Adding and subtracting decimals Write the numbers vertically and line up the decimal points. Add zeroes as placeholders, if necessary. Add/subtract from right to left.

Decimals Multiplying decimals Same process as for whole numbers, with one additional step at the end Multiply the numbers, ignoring the decimal points. Add the total number of decimal places from the original numbers.

Decimals Multiplying decimals Same process as for whole numbers, with one additional step at the end Place a decimal point that number of places by moving from the right to the left of the answer. If there are not enough numbers for the correct placement of the decimal point, add as many zeroes as necessary.

Decimals Dividing decimals Place the dividend, or number to be divided, inside the division bracket. Place the divisor, or number you are dividing by, outside the division bracket. Change the divisor to a whole number by moving the decimal point all the way to the right.

Decimals Dividing decimals Move the decimal point in the dividend the same number of places to the right as you did for the divisor. Place a decimal point directly above the decimal in the dividend and divide as normal.

Table 16-2 Roman Numerals.

Roman Numerals Used in health care to designate drug quantities Letters or symbols used to represent numbers Symbols and their position critical to understanding and deciphering them

Roman Numerals Rules for Roman Numerals Rule 1: Roman numerals are never repeated more than three times in a row. Rule 2: When a Roman numeral is repeated, or when a smaller numeral follows a larger numeral, their values are added together.

Roman Numerals Rules for Roman Numerals Rule 3: When a smaller numeral comes before a larger numeral, the one of lesser value is subtracted from the larger value. Ones (I) may only be subtracted from fives (V) and tens (X). Tens (X) may only be subtracted from fifties (L) and hundreds (C).

Roman Numerals Rules for Roman Numerals Rule 3: When a smaller numeral comes before a larger numeral, the one of lesser value is subtracted from the larger value. Hundreds (C) may only be subtracted from five hundreds (D) and thousands (M).

Roman Numerals Rules for Roman Numerals Rule 4: When a numeral of smaller value comes between two numerals of larger value, the subtraction rule is always applied first, then the addition rule.

Activity Complete Drug cards for the following… Levofloxacin (Levaquin) Donepezil (Aricept) Celecoxib (Celebrex) Complete the Roman Numeral Activity on the class website

Fractions Ratios and Proportions

State Standard 22) Calculate correct doses required when given a simulated prescription for a pediatric dose, adult dose, and geriatric dose based on weight (if applicable), length of administration, times per day of administration, and presence of other diseases/disorders.

Objectives Students will be able to… Correctly use fractions in pharmacy dosage calculations Correctly use ratios and proportions in pharmacy dosage calculations

Fractions Common fraction Can be expressed as one number that is set on a fraction line above another number

Fractions Common fraction Four categories of common fractions Proper fractions: value of the numerator is smaller than the value of the denominator. Improper fractions: value of the numerator is larger than the value of the denominator.

Fractions Common fraction Four categories of common fractions Simple fractions: cannot be reduced to any lower terms Complex fractions: both the numerator and the denominator are themselves fractions.

Fractions Rules for calculating with fractions Reducing Fractions to Lowest Terms To reduce a fraction to its lowest terms (making it a simple fraction) simply divide both the numerator and the denominator by the largest whole number that will go evenly into them both.

Fractions Rules for calculating with fractions Converting Improper Fractions Convert to equivalent whole number or mixed number by dividing the numerator by the denominator; express remainder as a proper fraction reduced to lowest terms.

Fractions Rules for calculating with fractions Adding and Subtracting Fractions All fractions must have the same denominator. If necessary, each fraction can be converted to a fraction with the least common denominator; then you can add or subtract the numerators.

Fractions Rules for calculating with fractions Multiplying Fractions Multiply the numerators by the numerators and then the denominators by the denominators. Reduce to lowest terms.

Fractions Rules for calculating with fractions Dividing Fractions Invert (flip upside down) the divisor, and then multiply the two fractions. Reduce to lowest terms.

Ratios and Proportions Basic math skills effective in solving majority of pharmacy calculations

Ratios and Proportions Express the relationship of two numbers Numbers are separated by a colon (:) The ratio x:y indicates that for every "x" amount, there is a "y" amount of something else Ratios can be rewritten as fractions x:y = x/y

Ratios and Proportions Two or more equivalent ratios or fractions that both represent the same value Example: if you need 2x of an ingredient in ratio x:y, you will also need 2y; 2x:2y is a proportion of x:y

Ratios and Proportions Solving for X Critical principle for solving pharmacy calculations Once you have set up two ratios or fractions in relationship to each other as a proportion, you can cross-multiply to solve for the unknown (X).

Ratios and Proportions Solving for X There are two approaches to using cross-multiplication to solve for X. Set the proportion up as fractions, making sure to keep units of measurement the same across from one another. Cross-multiply along the diagonal with two numbers and divide that value by the remaining number to solve for X.

Ratios and Proportions Solving for X Two approaches solving for X. Set the proportion up as fractions, making sure to keep units of measurement the same across from one another. This time, however, you cross-multiply along both diagonals to establish an equation, which you can solve for X.

Summary None of this material should be new to you. Solid, basic math review Calculations used in pharmacy based on these skills

Activity Complete drug cards for the following… Codeine/APAP (Tylenol #2) Mometasone (Nasonex) Ciprofloxacin (Cipro) Complete pages 15-21 on the Pharmacy technician Study Guide with review questions. Make sure to read the explanations and examples.