Clinical Medical Assisting Chapter 2: Mathematical Calculations and Conversions

Objectives Identify whole numbers Perform basic calculations using addition and subtraction Perform basic calculations using multiplication and division Set up problems using fractions

Objectives (con’t) Compare fractions, express them as decimals, and find common denominators. Perform basic mathematical calculations that use fractions and decimals. Perform basic mathematical calculations using percentages

Chapter Overview Medical Assistants perform calculations in the clinical setting that require a basic understanding of addition, subtraction, division, multiplication, fractions, percentages, and decimals.

Numbers A number is a value expressed by a word or symbol that represents a particular quantity.

Whole Numbers Whole numbers are counting numbers and is a base 10 number system.

Addition Increases the quantity by a given number to obtain a sum, which is the amount obtained.

Subtraction Reduces the quantity by a given number and the difference is the amount obtained.

Multiplication The product is the amount obtained by multiplying numbers.

Division The quotient is the amount obtained by dividing one number by another number.

Fractions Fractions are part of a whole number and is also called a ratio.

Ratio Compares two numbers or quantities.

Numerator Is the number above the fraction line.

Numerator (con’t) Is how many parts of the whole that is being expressed.

Denominator Is the number below the fraction line.

Denominator Is how many equal parts are in the whole.

Always has a value less than 1 Proper Fraction Always has a value less than 1

Improper Fraction Has a value equal to, or greater than 1.

Mixed Number Has whole numbers and fractions.

Factor A number that is multiplied by another number (also a factor) to make another number.

Comparing Fractions Fractions can be compared when the denominators are the same or different, as well as when the numerators are the same or different.

Fractions with Like Denominators When the denominator is the same, the smaller the numerator, the smaller the value of the fraction.

Fractions with Like Numerators When two fractions have the same numerator, the fraction with the smaller denominator has the larger value.

Adding and Subtracting Fractions Find the lowest common denominator when adding and subtracting fractions.

Common Denominator The number into which both denominators can divide evenly.

Adding Fractions with Like Denominators When adding fractions with like denominators, add the numerators and keep the denominator the same.

Adding Fractions with Different Denominators When adding fractions that have different denominators, find the lowest common denominator and convert the fractions using this lowest common denominator.

Subtracting Fractions with Like Denominators When subtracting fractions that have the same denominator, subtract the numerators and keep the denominator the same.

Subtracting Fractions with Different Denominators Find the lowest number that all denominators divided evenly into and convert the fractions.

Multiplying Fractions Step One Convert mixed numbers into improper fractions.

Multiplying Fractions Step Two Multiply the numerators together; then multiply the denominators together.

Multiplying Fractions Step Three Reduce the resulting fraction to its simplest form.

For Example [3/2] × [3/5] 3 × 3 = 9 2 × 5 = 10 Answer: [9/10]

Dividing Fractions Step One Like multiplying fractions, convert mixed numbers into improper fractions.

Dividing Fractions Step Two Invert or reverse the numbers of the second fraction.

Dividing Fractions Step Three Multiply the numerators of each fraction and the denominators of each fraction.

Dividing Fractions Step Four Reduce the resulting fraction to its simplest form.

For Example [1/3] ÷ [1/7] Step 1: Multiply the dividend by the reciprocal of the divisor. [1/3] × [7/1] [1/3] × 7 = [7/3] Step 2: Write the product in simplest form. Answer: [7/3], which simplifies to 2[1/3]

Decimals Decimal numbers are numbers that are written using place value.

Adding and Subtracting Decimals The numbers should be placed in columns so that the decimal points are all aligned.

For Example 4.7 +2.32 +1.789 8.809

Multiplying Decimals Step One Multiply them as whole numbers

Multiplying Decimals Step Two Move the decimal the total number of places that were in the two numbers being multiplied.

For Example 29.24 × 43.67 = 1,276.9108

Dividing Decimals Step One Change each decimal to a whole number by multiplying each number by the same factor of 10.

Dividing Decimals Step Two Divide whole numbers as usual.

Percentages Are used to express a value that is part of 100, and represents the same number as a fraction whose denominator is 100.

For Example 0.9% = [0.9/100] 5% = [5/100] [10/100] = 10%

Converting Decimals to Percentages Simply move the decimal point over two places to the right Write [1/4] as a percent First , find the equivalent fraction with a denominator of 100 [1/4] = [?/100] Then [1/4] × [25/25] = [25/100] Answer: [1/4] = 25%

Summary Numbers can be represented as whole numbers, fractions, and decimals Addition and subtraction involve adding numbers to each other or taking numbers away from each other, respectively Multiplication involves changing the quantity of a number by multiplying a number by another number Division involves changing the quantity of a number to determine a part or portion of a quantity needed Fractions are used to express a portion that is a part of a whole number Decimals are numbers that are written using place value