Transcript Chapter 1 - Basic Math Review

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.

Saundes,anmn
fElseveInc..
3
6.
7.
Perform mathematical sentences using the order of operation theory.
Identify greatest common factors, least common multiple, and prime
numbers.

Saundes,anmn
fElseveInc..
4
• Leaving a tip
• Balancing a checkbook
• Figuring out discounts
• Estimating the cost to fill up the gas tank

Saundes,anmn
fElseveInc..
5
• Figuring out medication dosages
• Measuring intake and output
• Measuring laboratory values
• Performing an inventory of office equipment
• Billing services

Saundes,anmn
fElseveInc..
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

Saundes,anmn
fElseveInc..
7

Saundes,anmn
fElseveInc..
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 _____.

Saundes,anmn
fElseveInc..
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

Saundes,anmn
fElseveInc..

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

Saundes,anmn
fElseveInc..

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

Saundes,anmn
fElseveInc..

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 +

Saundes,anmn
fElseveInc..
3

Saundes,anmn
fElseveInc..
4
Used to determine:
Temperature
Weight loss
Body fat
Cash flow
Profit or loss margins

Saundes,anmn
fElseveInc..
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

Saundes,anmn
fElseveInc..
6
4 x 4 x 4 = 43
• Base number is 4.
• Exponent is 3.

Saundes,anmn
fElseveInc..
7
• Do you remember what term is used instead of 2nd power?
• Do you remember what term is used instead of 3rd power?

Saundes,anmn
fElseveInc..
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

Saundes,anmn
fElseveInc..
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

Saundes,anmn
fElseveInc..

• 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

Saundes,anmn
fElseveInc..

• 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

Saundes,anmn
fElseveInc..

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

Saundes,anmn
fElseveInc..
3
• Example: 33 x 42 =
Compute the answer for 33
o Answer: 27
2.
Compute the answer for 42
o Answer: 16
1.

Saundes,anmn
fElseveInc..
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

Saundes,anmn
fElseveInc..
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

Saundes,anmn
fElseveInc..
6
If you are dividing exponents with
like bases, subtract the exponents.
• Example: 44 ÷ 42 =
o 44–2 =
o 42
o Answer: 16

Saundes,anmn
fElseveInc..
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 ÷

Saundes,anmn
fElseveInc..
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

Saundes,anmn
fElseveInc..
9
1. Parenth
eses
2. Expone
nts
3. Multipli
cation
4. Division
5. Addition
6. Subtract
ion
Please Excuse My Dear Aunt Sally

Saundes,anmn
fElseveInc..
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
=

Saundes,anmn
fElseveInc..
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.

Saundes,anmn
fElseveInc..
3
Prime numbers are numbers whose
only factors are 1 and that number.
• Examples: 1, 2, 3, 5, 7, 11, 23, 31,
47

Saundes,anmn
fElseveInc..
33
• Example:

Saundes,anmn
fElseveInc..
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

Saundes,anmn
fElseveInc..
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

Saundes,anmn
fElseveInc..
36
• If the number is even:
o 2 is a factor
• If the number ends in 0 or 5:
o 5 is a factor

Saundes,anmn
fElseveInc..
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

Saundes,anmn
fElseveInc..
38
• Example: 435
o 4 + 3 + 5 = 12
o 3 x 4 = 12
o 3 x 145 = 435

Saundes,anmn
fElseveInc..
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

Saundes,anmn
fElseveInc..
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

Saundes,anmn
fElseveInc..
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.

Saundes,anmn
fElseveInc..
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.

Saundes,anmn
fElseveInc..
43
• Determining GCF:
o Always write the factors in numeric order
• Determining LCM:
o Always write the multiples in numeric order

Saundes,anmn
fElseveInc..
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.

Saundes,anmn
fElseveInc..
45