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Math K-Plus

Arithmetic - PEMDAS Defines How To Solve Arithmetic Problems

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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:
  • Parentheses
  • Exponents
  • Multiplication and Division (left to right)
  • Addition And Subtraction (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: 23 = 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: "Please Excuse My Dear Aunt Sally". 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