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Basic Math Review Boone County – ATC Health Sciences Laura M Williams FMH100 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. 4. 5. Perform calculations with both positive and negative integers with 100% accuracy. Define and demonstrate when exponents can be used. Calculate multiplication and division with exponents with 100% accuracy. Saundes,anmn fElseveInc.. 3 6. 7. Perform mathematical sentences using the order of operation theory. Identify greatest common factors, least common multiple, and prime numbers. Saundes,anmn fElseveInc.. 4 • Leaving a tip • Balancing a checkbook • Figuring out discounts • Estimating the cost to fill up the gas tank Saundes,anmn fElseveInc.. 5 • Figuring out medication dosages • Measuring intake and output • Measuring laboratory values • Performing an inventory of office equipment • Billing services Saundes,anmn fElseveInc.. 6 • 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 Saundes,anmn fElseveInc.. 7 Saundes,anmn fElseveInc.. 8 • 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 _____. Saundes,anmn fElseveInc.. 9 The sum stays the same when the grouping of addends is changed. (8 + 2) + 4 = 10 + 4 = 14 8 + (2 + 4) = 8 + 6 = 14 Saundes,anmn fElseveInc.. The sum stays the same when the order of the addends is changed. 8 + 2 + 4 = 14 2 + 4 + 8 = 14 4 + 8 + 2 = 14 Saundes,anmn fElseveInc.. The product stays the same when the order of the factors is changed. 10 x 3 = 30 25 x 3 = 75 3 x 10 = 30 3 x 25 = 75 Saundes,anmn fElseveInc.. 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) 6) + (3 x 14) 3 x 20 42 60 = 60 = (3 x = 18 + Saundes,anmn fElseveInc.. 3 Saundes,anmn fElseveInc.. 4 Used to determine: Temperature Weight loss Body fat Cash flow Profit or loss margins Saundes,anmn fElseveInc.. 5 • Positive number x Positive number = Positive number o 4 x 7 = 28 • Negative number x Negative number = Positive number o –4 x –7 = 28 • Positive number x Negative number = Negative number o –4 x 7 = –28 Saundes,anmn fElseveInc.. 6 4 x 4 x 4 = 43 • Base number is 4. • Exponent is 3. Saundes,anmn fElseveInc.. 7 • Do you remember what term is used instead of 2nd power? • Do you remember what term is used instead of 3rd power? Saundes,anmn fElseveInc.. 8 • 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 Saundes,anmn fElseveInc.. 9 A positive exponent’s answer will be to the left of the decimal point. • Example: 43 o 4 x 4 x 4 = 43 o 64 = 64 o Saundes,anmn fElseveInc.. • 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 Saundes,anmn fElseveInc.. • 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 Saundes,anmn fElseveInc.. When multiplying exponents with like bases, add the exponents. • Example: 33 x 36 = o 33+6 = 39 or o3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 39 o Answer: 19,683 Saundes,anmn fElseveInc.. 3 • Example: 33 x 42 = Compute the answer for 33 o Answer: 27 2. Compute the answer for 42 o Answer: 16 1. Saundes,anmn fElseveInc.. 4 • Example, cont.: o Insert the answers for steps 1 and 2 into the equation. 27 x 16 = o Solve the equation. 27 x 16 = 432 o Answer: 432 Saundes,anmn fElseveInc.. 5 To multiply powers of the same base, add their exponents. • Example: Proof o 52 x 53 = o 52+3 = 53 = 125 o 55 = 3,125 = 3,125 52 x 53 = 52 = 25 x 25 x 125 Saundes,anmn fElseveInc.. 6 If you are dividing exponents with like bases, subtract the exponents. • Example: 44 ÷ 42 = o 44–2 = o 42 o Answer: 16 Saundes,anmn fElseveInc.. 7 To divide powers of the same base, subtract the exponent of the divisor from the exponent of the dividend. • Example: o 64 ÷ 62 = o 64–2 = 62 = 36 o 62 = 36 36 = 36 Proof 64 ÷ 62 = 64 = 1,296 1,296 ÷ Saundes,anmn fElseveInc.. 8 The product stays the same when the grouping of factors is changed. • Example: o (5 x 3) x 3 = 15 x 3 = 45 o (3 x 3) x 5 = 9 x 5 = 45 Saundes,anmn fElseveInc.. 9 1. Parenth eses 2. Expone nts 3. Multipli cation 4. Division 5. Addition 6. Subtract ion Please Excuse My Dear Aunt Sally Saundes,anmn fElseveInc.. 3 • 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 = 216 Problem Rewritten: 5(4) + 5(42) = 2(216) + 4 – 1 = Saundes,anmn fElseveInc.. 3 3. Multiplication or division, whichever comes first from left to right: 5 x 4 = 20 5 x 42 = 210 2 x 216 = 432 Problem 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. Saundes,anmn fElseveInc.. 3 Prime numbers are numbers whose only factors are 1 and that number. • Examples: 1, 2, 3, 5, 7, 11, 23, 31, 47 Saundes,anmn fElseveInc.. 33 • Example: Saundes,anmn fElseveInc.. 34 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=9 o 126 = 14 9 9 is a factor of 126 Saundes,anmn fElseveInc.. 35 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 3x8 o Since both 2 and 3 are factors, 6 is a factor. 6 x 4 = 24 Saundes,anmn fElseveInc.. 36 • If the number is even: o 2 is a factor • If the number ends in 0 or 5: o 5 is a factor Saundes,anmn fElseveInc.. 37 • 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 Saundes,anmn fElseveInc.. 38 • Example: 435 o 4 + 3 + 5 = 12 o 3 x 4 = 12 o 3 x 145 = 435 Saundes,anmn fElseveInc.. 39 • If the sum of the number is divisible by 3: o 3 is a factor o Example: 435 4 + 3 + 5 = 12 3 x 4 = 12 3 x 145 = 435 Saundes,anmn fElseveInc.. 4 • 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 Saundes,anmn fElseveInc.. 4 • 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. Saundes,anmn fElseveInc.. 4 • Example: Find the LCM for 6 and 18. Multiples of 6 are: 2, 12, 18 Multiples of 18 are: 18, o STOP—18 is a multiple of both 6 and 18. Saundes,anmn fElseveInc.. 43 • Determining GCF: o Always write the factors in numeric order • Determining LCM: o Always write the multiples in numeric order Saundes,anmn fElseveInc.. 44 • 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. Saundes,anmn fElseveInc.. 45