Transcript order of operations

MM212 Unit 1 Seminar Agenda
•
•
•
•
•
•
•
Welcome and Syllabus Review
Classifying Numbers
Operations with Real Numbers
Division and ZERO
Exponents
Order of Operations
Distributive Property
Syllabus Review
• Located under Course Home Page and under
DocSharing
• Familiarize yourself with Rubrics for grading
Discussion Board
• Familiarize yourself with policies on Late Assignment
Policy
Terminology
• Begin your own mathematics “dictionary”
• Include all new terms, a definition, and an
example for each term
• You will find it invaluable as we progress
from unit to unit!
Examples
• Variables: x, y, z, a
• Algebraic Expression:
–a+b
– 4x – 7
– 6y
– x/4
– They can be longer, like these:
3x2 – 7y3 + 12z – 2
–a+b+c+d+e+f+g
Numbers
•
•
•
•
•
•
Natural Numbers: 1, 2, 3, 4, …
Whole Numbers: 0, 1, 2,3, …
Integers: …-3, -2, -1, 0, 1, 2, 3, …
Rational Numbers: ½, 0.5, -6, .333…
Irrational Numbers: pi, √[2], √[3]
Real Numbers: all rational and irrational
numbers
RATIONAL NUMBERS:
• To test if a number is a rational number,
there are three things that must be true
(not one or two of the things BUT ALL
THREE).
– The number must be able to written as a
fraction (whose denominator ≠ 0)
– This fraction must be able to be converted to
a decimal number
– This decimal number TERMINATES or
REPEATS
IRRATIONAL NUMBERS:
• The definition of an irrational number is a
number that is NOT RATIONAL. Another
way to put this is
– The number must be able to written as a
fraction (whose denominator ≠ 0)
– This fraction must be able to be converted to
a decimal number
– This decimal number is NONTERMINATION
or NONREPEATING
Operations with Real Numbers
• Additive Inverse means opposite
The additive inverse of-10x is 10x
• Absolute Value is the distance from zero I-4I = 4 and I5I = 5
• Sign Rules for Addition/Subtraction
Same sign: add and take that sign -5 + -5 = -10
Different sign: subtract and take the sign of the larger
-10 + 5 = -5
[if subtracting, change the – to + (-)]: -5 - 2 = -5 + (-2) = -7
• Sign Rules for Multiplication/Division
Same sign: positive Different sign: negative
Division and the number ZERO
• THREE TYPES
– 0 in the numerator (dividend) only = 0
• Example: 0/6 = 0
– 0 in the denominator (divisor) only =
UNDEFINED
• Example: 4/0 = undefined
– 0 in both the numerator and denominator =
INDETERMINATE (or cannot be determined)
• Example: 0/0 = indeterminate
EXPONENTS
• How many times you multiply a number
times itself …
– Example: 24 = 2*2*2*2 = 16
– Example: x6 = x*x*x*x*x*x
SQUARE ROOTS
• The square root of a number is the value
that you can multiply times itself to get the
original number
• It is the opposite arithmetic of exponents
(specifically of squaring a number)
– Example: √9 = 3
– Example: √100 = 10
ORDER OF OPERATIONS
• PEMDAS
P: Grouping Symbols
– ( ), { }, fraction bars, radicals (like the square
root symbol, absolute value | |.
– We will ALWAYS do the arithmetic inside the
grouping symbol first
ORDER OF OPERATIONS
• PEMDAS
E: Exponents: We will always perform
arithmetic of exponents next.
ORDER OF OPERATIONS
• PEMDAS
MD: Multiplication/Division
– Perform these as they occur from left to right.
Do not first do all multiplication and then come
back for division. They are equal-level
operations
ORDER OF OPERATIONS
• PEMDAS
AS: Addition/Subtraction
– By now, this is all you have left to do.
– Perform these as they occur from left to right.
(JUST LIKE multiplication/division)
• Order of Operations Mneumonic Device:
Please Excuse My Dear Aunt Sally
(Parenthesis, Exponents, Multiplication, Division, Addition,
Subtraction)
**Note be careful because multiplication and division
are together, and addition and subtraction are together.
2(3 – 5 + 6) + 5
= 2(-2 + 6) + 5
= 2(4) + 5
=8+5
= 13
in parentheses, 3 – 5 = -2
in parentheses, -2 + 6 = 4
got rid of parentheses by multiplying
addition is all that’s left: 8 + 5 = 13
You try it!
1. 6 – 4 * 2 =
2. 52 - 3(4+1) =
3. 5 – 23 + 8*3 – 1 =
Distributive Property
Examples:
• a(b+c) = ab + ac
• -2(x+2) = -2x-4
• 4(2x-3y) =
• -10(6a-5) =
• (1/2 – 2t+u)(-3/4) =
Virtual Field Trip to the
Math Center
Link: http://khe2.acrobat.com/kumcfieldtrip
Login using the “Enter as a Guest” option.
Type your name in the guest box and click “Enter Room.”