# Mathematic Foundations 002 by 7akgJz52

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```									                                    Mathematic Foundations
Order of Operations – PEMDAS
A way to remember PEMDAS: “Please Excuse My Dear Aunt Sally.”

Mathematical operations are things like addition, subtraction, multiplication, division, square roots, etc.
So an operation is an action that is applied to number(s) or letter(s). For example, in the expression 9 ,
the operation/action is to take the square root of nine. Another example is the expression x  17x ;
here the operation/action is to add the two terms. A term is a number or variable, or a product
(multiplication) or quotient (division) of numbers and variables.
1 2         w                   x
Examples of 1-term expressions: x, 3q, 1, 923zxwy,           ,    x,     , 2 x  3x  x  .
2 5         4                   2
1
Examples of 2-term expressions: x 2  17 x, 2  q, 3 y  3x,     w  2 y, y  3  3 y  5  y .
2
2
Examples of 3-term expressions: x 2  17 x  3, x   4, y 2  6 y  7  y  3  4 y 2 .
y
A mathematical expression is a mathematical phrase that uses letters and/or numbers, and
mathematical operation symbols; expressions do NOT have equal signs. An equation is a mathematical
sentence that says the left side equals the right side. You can think of an equation as being made up of
more than one mathematical expression; for example, x  3  17x  5 .

Back to Order of Operations
P Parentheses first (some operations imply parentheses without writing them; see examples below)
E    Exponents (i.e. Powers and Square Roots, etc.)
MD Multiplication and Division (left-to-right); multiplication and division are of equal rank
AS Addition and Subtraction (left-to-right); addition and subtraction are of equal rank

In short
First do P and E. Then go from left to right and do M or D as you find them (first come first do). Then go
from left to right and do A or S as you find them (first come first do).

Examples of situations where parentheses are implied
3 4                                (3  4)                           (7 )                      1
1.          is the same thing as saying           so first do parentheses       then division to get
6  15                             (6  15 )                         ( 21)                      3

2.   4 8  1 is the same thing as saying 4 (8  1) so first do parentheses 4 (9) then the square
root because it comes before multiplication 4  3 then multiplication to get 12

3. Since operations are done from left to right, 30  5  3 is the same thing as saying (30  5)  3
so first do parentheses (6)  3 then multiplication to get 18

4. Since multiplication (or division) come before addition (or subtraction), 2  5  3 is the same
thing as saying 2  (5  3) so first do parentheses 2  (15) then addition to get 17

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