Chapter 8 Basic Review of Mathematics

Objectives  Define all key terms.  Discuss numerical relationships.  Perform calculations involving whole numbers.  Calculate problems using fractions.  Find the lowest common denominator.  Perform calculations involving decimals.  Calculate percents, ratios, and proportions.  Solve problems for an unknown quantity.

Concepts  Whole numbers  Addition  Subtraction  Multiplication  Division

Addition  One number plus another number equals a larger number.  Used in the medical office for determining payments, time for procedures, etc.

Subtraction  A smaller number is taken away from a larger number or a larger number is decreased by a smaller number.  Used in the medical office for noting payments, determining current supplies after some are used, etc.

Multiplication  One number is repeatedly added several times.  Used in the medical office to determine total cost of several procedures, order supplies, calculate dosages, etc.

Division  One number is divided into equal parts by another number.  Used in the medical office to calculate dosages and fractions, determine use of supplies, split costs and payments, etc.

Fractions Numerator—number on top Denominator—number on bottom

Critical Thinking  What happens to the pie slices when a numerator becomes larger? When a denominator becomes larger? If you have trouble remembering this concept, ask yourself, what would happen if you and your siblings were inheriting some money: the more brothers and sisters you have, the less your share would be.

Least Common Denominators  List the multiples of each denominator.  Compare the lists. Any numbers that appear on all lists are common denominators.  The smallest number that appears on all the lists is the LCD.

Mixed Numbers and Improper Fractions  Multiply the denominator by the whole number.  Add the result from the first step to the numerator.  Keep the denominator.

Critical Thinking  Sometimes we need to teach the patient how to break certain pills. For example, if Haley Watkins takes 1½ pills per dose, how long will 30 pills last?

Fractions  Sometimes used in dosage calculations  Example: Dosage × times given per day = total dosage per day

Critical Thinking  If you give ½ tablespoon of a medication four times daily, how much of the medication do you need per day?

Reducing to Lowest Terms  Determine the largest common divisor of the two numbers.  Divide the numerator and denominator by this number to reduce to lowest terms.

Adding Fractions  Add the numerators.  Place the sum over the denominator.  Reduce to lowest terms.  If different denominators:  Change fractions to an equal fraction with the least common denominator.  Add the numerators.  Place the sum over the denominator.  Reduce to lowest terms.

Subtracting Fractions  Subtract the numerator.  Preserve the same denominator.  Reduce if necessary.  If the denominators are different, you must:  Find the lowest common denominator.  Change to equivalent fractions.  Subtract the numerators.  Place the sum over a common denominator.  Reduce if necessary.

Multiplying Fractions  Multiply the numerators.  Multiply the denominators.  Reduce if necessary.

Dividing Fractions  Invert the second fraction.  Multiply the two fractions.  Reduce if necessary.

Decimals  Rounding  Larger/smaller  Adding  Subtracting  Multiplying  Dividing

Critical Thinking  Why is it important when writing a prescription to write the leading “0” (e.g., 0.25 instead of.25)?

Decimals and Fractional Forms  Decimal-Fraction, place it over the number of the place it signifies.  Fraction-Decimal, place the decimal point one place to the left of the decimal for each 0 in the denominator.

Percentages  Numbers placed over the number 100.  Example: 20/100 = 20%

Ratios and Proportions  Expressed as fractions  Ratios as decimals  Converting decimals to ratios  Converting ratios to percents  Converting percents to ratios  Checking ratio and proportions

Critical Thinking  By what numbers did we multiply them to get to the equivalents?

Solving for an Unknown  Means and extremes  Cross-multiplication

Critical Thinking  Did you notice how similar the last two methods are? Why does cross-multiplying work?

Decimals are Fractions  Decimals are numbers that can be placed over 10, 100, 1,000 etc.  Decimals can be easily changed to fractions.  Fractions over 10, 100, 1,000 etc. can easily be converted to decimals  Example: 2/10 = 0.2

Critical Thinking  Sometimes it is easier to leave a calculation in a fractional form, and sometimes it is better to work with a decimal. When would you use a decimal rather than a fraction? When would it be easier to write a numeric equation as a fraction, and when as a ratio?

Summary  What new piece of information in this chapter were you most interested to learn?  What questions do you still have about the information in this chapter?  Return to Objectives to determine extent of learning.Objectives

Credits Publisher: Margaret Biblis Acquisitions Editor: Andy McPhee Developmental Editor: Yvonne N. Gillam Production Manager: Samuel A. Rondinelli Manager, Electronic Development: Kirk Pedrick Technical Project Manager, EP: Frank Musick Design Associate, EP: Sandra Glennie The publisher is not responsible for errors or omission or for consequences from application of information in this presentation, and makes no warranty, expressed or implied, in regards to its content. Any practice described in this presentation should be applied by the reader in accordance with professional standards of care used with regard to the unique circumstances that may apply in each situation.