# Order Of Operations

## What Is PEMDAS?

**PEMDAS**is a "MNEMONIC" ("NEW-MON-NIC"). of

**Order Of 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 - PEMDAS:

**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".

(-22 * 2^1) * -46 = 2024 |

(-33^1 + 38^2) * 1 = 1411 |

1 / 73 * 73 = 1 |

1 / --1849 = .000540 |

-37^3 * 23 * 24^3 = -16105222656 |

(-1.33333333334) + 1.111111 = -1.481483 |

1 + 2^3 - 1 + 10 / 2 + 5 * 5 = 38 |

-560207 + (38^2 - 74) - 7 = -558844 |

1 + (2^3) - ((((1 + 10 / 2) + 5) * 5) - 12 / 3) = 51 |