Basic Math Review

Boone County – ATCHealth SciencesLaura M WilliamsFMH100 Medical Math

Upon completion of this chapter, the learner will be able to:

1. Define the key terms that relate to basic mathematical computations.

2. Calculate basic addition, subtraction, multiplication, and division with 100% accuracy.

3. Perform calculations with both positive and negative integers with 100% accuracy.

4. Define and demonstrate when exponents can be used. 5. Calculate multiplication and division with exponents with 100% accuracy.

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6. Perform mathematical sentences using the order of operation theory.7. Identify greatest common factors, least common multiple, and prime

numbers.

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• Leaving a tip• Balancing a checkbook• Figuring out discounts• Estimating the cost to fill up the gas tank

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•Figuring out medication dosages•Measuring intake and output•Measuring laboratory values•Performing an inventory of office equipment•Billing services

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•Collecting deductibles or copayments at the time of service•Ordering nonreusable equipment•Preparing the office staff payroll•Billing an insurer •Formatting the budget for a company

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• The answer to an addition problem is _____.• The answer to a subtraction problem is ______.• The answer to a multiplication problem is ______.• The answer to a division problem is _____.

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The sum stays the same when the grouping of addends is changed.

(8 + 2) + 4 = 10 + 4 = 148 + (2 + 4) = 8 + 6 = 14

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The sum stays the same when the order of the addends is changed.

8 + 2 + 4 = 142 + 4 + 8 = 144 + 8 + 2 = 14

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The product stays the same when the order of the factors is changed.

10 x 3 = 30 3 x 10 = 3025 x 3 = 75 3 x 25 = 75

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The product remains the same whether the factors of the product are written as a sum or whether each addend is multiplied before the addition operation is performed.

3 x (6 + 14) = (3 x 6) + (3 x 14)

3 x 20 = 18 + 42

60 = 60

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Used to determine:

TemperatureWeight lossBody fatCash flowProfit or loss margins

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• Positive number x Positive number = Positive numbero4 x 7 = 28

•Negative number x Negative number = Positive numbero–4 x –7 = 28

• Positive number x Negative number = Negative numbero–4 x 7 = –28

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4 x 4 x 4 = 43

•Base number is 4.•Exponent is 3.

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• Do you remember what term is used instead of 2nd power?

• Do you remember what term is used instead of 3rd power?

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• Do you remember what term is used instead of 2nd power?o SQUARED

• Do you remember what term is used instead of 3rd power? o CUBED

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A positive exponent’s answer will be to the left of the decimal point.

•Example:o 43

o 4 x 4 x 4 = 43

o 64 = 64

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• Example: 5–5 (See Strategy box 1-2)

Disregard the negative symbol and find the answer to the exponent.o 55 = 5 x 5 x 5 x 5 x 5 = 3,125

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• Example, cont.:

Now address the negative symbol. o When working with a negative exponent, determine the reciprocal.o The reciprocal of 3,125 is 1 . 3125

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When multiplying exponents with like bases, add the exponents.

• Example: 33 x 36 =

o33+6 = 39 or o3 x 3 x 3 x 3 x 3 x 3 x 3

x 3 x 3 = 39

oAnswer: 19,683

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• Example: 33 x 42 =1. Compute the answer for 33 o Answer: 272. Compute the answer for 42 o Answer: 16

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•Example, cont.:o Insert the answers for steps 1 and 2 into the

equation.27 x 16 =

oSolve the equation.27 x 16 = 432

oAnswer: 432

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To multiply powers of the same base, add their exponents.

• Example: Proofo 52 x 53 = 52 x 53 = o 52+3 = 52 =

25 x 53 = 125o 55 = 3,125 25 x 125 = 3,125

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If you are dividing exponents with like bases, subtract the exponents.

• Example: 44 ÷ 42 = o 44–2 = o 42

o Answer: 16

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To divide powers of the same base, subtract the exponent of the divisor from the exponent of the dividend.

• Example: Proofo 64 ÷ 62 = 64 ÷ 62 =o 64–2 = 64 =

1,296 62 = 36o 62 = 36

1,296 ÷ 36 = 36

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The product stays the same when the grouping of factors is changed.

•Example:o (5 x 3) x 3 =

15 x 3 = 45o (3 x 3) x 5 =

9 x 5 = 45

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1. Parentheses

2. Exponents

3. Multiplication

4. Division 5. Addition 6. Subtract

ion

Please Excuse My Dear Aunt Sally

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• Example: 5(6 – 2) + 5(6 x 7) + 2(63) + 4 – 1 =

1. Parentheses: (6 – 2) = 4 (6 x 7) = 42

Problem Rewritten: 5(4) + 5(42) + 2(63) + 4 – 1 =

2. Exponents: 63 = 6 x 6 x 6 = 216Problem Rewritten: 5(4) + 5(42) = 2(216) + 4 – 1 =

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3. Multiplication or division, whichever comes first from left to right: 5 x 4 = 20 5 x 42 = 210 2 x 216 = 432Problem Rewritten: 20 + 210 + 432 + 4 – 1 =

4. Addition or subtraction, whichever comes first from left to right:Problem Rewritten: 20 + 210 + 432 + 4 – 1 = 665

5. Your answer is 665.

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Prime numbers are numbers whose only factors are 1 and that number.

• Examples: 1, 2, 3, 5, 7, 11, 23, 31, 47

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• Example:

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If the digits add up to 9, then that number has 9 as a factor.

• Example: 81

o 8 + 1 = 9 9 is a factor of 81

• Example: 126 o 1 + 2 + 6 = 9o 126 = 14 9 is a factor of 126 9

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If a number has 2 as a factor and 3 as a factor, then 6 is also a factor.

• Example: 24

o 2 is a factor 2 x 12 o 3 is a factor 3 x 8 o Since both 2 and 3 are factors, 6 is a

factor. 6 x 4 = 24

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• If the number is even: o 2 is a factor

• If the number ends in 0 or 5:o 5 is a factor

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• If the number ends in 0: o 10 is a factor

• If the sum of the number is divisible by 3:o 3 is a factor

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• Example: 435o 4 + 3 + 5 = 12o 3 x 4 = 12o 3 x 145 = 435

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• If the sum of the number is divisible by 3:o 3 is a factoro Example: 435

4 + 3 + 5 = 12 3 x 4 = 12 3 x 145 = 435

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• Example: Find the GCF for 48 and 72.Write out all the factors for 48.o 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Write out all the factors for 72. o 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

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• Example, cont.:Compare the numbers and determine the common factors. o 1, 2, 3, 4, 6, 8, 12, 24

The GCF for both 48 and 72 is 24.

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• Example: Find the LCM for 6 and 18.Multiples of 6 are: 2, 12, 18Multiples of 18 are: 18, o STOP—18 is a multiple of both 6 and 18.

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• Determining GCF:o Always write the factors in numeric order

• Determining LCM:o Always write the multiples in numeric order

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• There is more than one way to attack a math problem.• Math is used in a variety of ways in the health care professions.• Practice makes perfect.

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