# Order of Operations

How do you know what to do first in this expression? |
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2 × 3 + 3 = x |

Maybe it’s addition first, then multiplication. Adding first gets you . . . |

2 × 3 + 3 = 12 WRONG! |

Or, maybe it’s multiplication first, then addition. Multiplying first gets you . . . |

2 × 3 + 3 = 9 Right! |

And then you set fire to your math book before it gets more complicated, like . . . |

7 + (2 × 3^{2} + 3) = x |

Learn this word to help you: PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction |

Perform the operations in parentheses first. Of course, that means you have to do other operations. Start with exponents. |

7 + (2 × 3^{2} + 3) = x |

7 + (2 × 9 + 3) = x |

Then multiplication/division |

7 + (18 + 3) = x |

Then addition/subtraction |

7 + (21) = x |

Finally, add the parentheses to the remainder of the expression. |

28 = x |

Most importantly, remember **E**xponents, **M**ultiplication/**D**ivision, **A**ddition/**S**ubtraction

- 2 × 3 + 3 = ; 2 × 3 + 3 = 9
- 2 + 3 × 3 = ; 2 + 3 × 3 = 11
- 3 × 4 + 2 = ; 3 × 4 + 2 = 14
- 3 + 4 × 2 = ; 3 + 4 × 2 = 11
- 2 + 3
^{2}× 2 = ; 2 + 3^{2}× 2 = 20 - 3
^{2}× 2 - 2 = ; 3^{2}× 2 - 2 = 16

You may have heard that you should go from left to right. This is true within multiplication/division, for example. |
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12 ÷ 3 × 4 = 16 Right! |

If you go right to left, you get |

12 ÷ 3 × 4 = 1 WRONG! |