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Arithmetic - PEMDAS Defines How To Solve Arithmetic Problems
What Is PEMDAS?
PEMDAS
is a "MNEMONIC" ("NEW-MON-NIC"). arithmetic operations (addition, subtraction, multiplication, division, and raising number to a power) must be performed in a specific order to get the correct answer. For example, expressions enclosed in parentheses are evaluated first. Here is the order that must be followed - MNEMONIC:
P
arentheses
E
xponents
M
ultiplication and
D
ivision (left to right)
A
ddition And
S
ubtraction (left to right)
It is used to help us remember the order each operation is applied to a Arithmetic equation. Before reading this page, it is recommended the reader read the following pages for a more complete understanding of the subject:
Equality and Inequality
,
Math Symbols
.
Parentheses
( and ) are used in mathematical expressions to indicate order of math operations (precedence rules). In a math statement like (3+5)×7, the part of the expression within the parentheses, (3+5)=8, is evaluated first, and then this result is used in the rest of the expression. Nested parentheses work similarly, the inner most expression is evaluated first.
Exponents
(^) are evaluated second in equation. If an exponent is in a parentheses, it is processed first. The exponent of a number says how many times to use that number in a multiplication problem. It is written as a small number to the right and above the base number. For example: 2
^{3}
= 2 × 2 x 2 = 8, or shown another way 2^3 = 2 x 2 x 2 = 8.
Multiplication
(× or *)
Division
(÷ or /) Multiplication and Division are processed left to right after exponents are evaluated.
Addition
(+)
Subtraction
(-) Addition and Subtraction are processed last left to right after Multiplication and Division.
Let's step back for a moment. There is a easier way to remember PEMDAS. Remember its is a MNEMONIC that can be expanded into an easy to remember phase: "
P
lease
E
xcuse
M
y
D
ear
A
unt
S
ally".
Below are some examples of ....
(-1.33333333334) + 1.111111 = -1.481483
(-22 * 2^1) * -46 = 2024
(-33^1 + 38^2) * 1 = 1411
1 / 73 * 73 = 1
-37^3 * 23 * 24^3 = -16105222656
1 + 2^3 - 1 + 10 / 2 + 5 * 5 = 38
1 / --1849 = .000540
-560207 + (38^2 - 74) - 7 = -558844
1 + (2^3) - ((((1 + 10 / 2) + 5) * 5) - 12 / 3) = 51
See More About Rules Of Arithmetic