**"Operations"**mean things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation.

But, when you see something like...

7 + (6 × 5

^{2}+ 3)... what part should you calculate first?

Start at the left and go to the right?

Or go from right to left?

Start at the left and go to the right?

Or go from right to left?

Calculate them in the wrong order, and you will get a wrong answer !

So, long ago people agreed to always follow certain rules when doing calculations, and they are:## Order of Operations

**Do things in Brackets First.**Example:

6 × (5 + 3) | = | 6 × 8 | = | 48 | |||

6 × (5 + 3) | = | 30 + 3 | = | 33 | (wrong) |

**Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract**. Example:

5 × 2^{2} | = | 5 × 4 | = | 20 | |||

5 × 2^{2} | = | 10^{2} | = | 100 | (wrong) |

**Multiply or Divide before you Add or Subtract**. Example:

2 + 5 × 3 | = | 2 + 15 | = | 17 | |||

2 + 5 × 3 | = | 7 × 3 | = | 21 | (wrong) |

**Otherwise just go left to right**. Example:

30 ÷ 5 × 3 | = | 6 × 3 | = | 18 | |||

30 ÷ 5 × 3 | = | 30 ÷ 15 | = | 2 | (wrong) |

## How Do I Remember ? BODMAS !

B | Brackets first |

O | Orders (ie Powers and Square Roots, etc.) |

DM | Division and Multiplication (left-to-right) |

AS | Addition and Subtraction (left-to-right) |

*The only strange name is "Orders". "Exponents" is used in Canada, and so you might prefer "BEDMAS". There is also "Indices" so that makes it "BIDMAS". In the US they say "Parenthesis" instead of Brackets, so they say "PEMDAS"*

Divide and Multiply rank equally (and go left to right).

Add and Subtract rank equally (and go left to right)

After you have done "B" and "O", just go from left to right doing any "D" "M" as you find them. orThen go from left to right doing any "A" "S" as you find them.or |

## Examples

Example: How do you work out

First

**3 + 6 × 2**?**M**ultiplication before**A**ddition:First

**6 × 2 = 12**, then**3 + 12 = 15**Example: How do you work out

First

**(3 + 6) × 2**?**B**rackets first:First

**(3 + 6) = 9**, then**9 × 2 = 18**Example: How do you work out

First

**12 / 6 × 3**?**D**ivision and**M**ultiplication rank equally, so just go left to right:First

**12 / 6 = 2**, then**2 × 3 = 6**

**Oh, yes, and what about 7 + (6 × 5**^{2}+ 3) ?7 + (6 × 5^{2} + 3) | |

7 + (6 × 25 + 3) | Start inside Brackets, and then use "Orders" First |

7 + (150 + 3) | Then Multiply |

7 + (153) | Then Add |

7 + 153 | Brackets completed, last operation is add |

160 | DONE ! |