# Grade 7

### Order of Operations – PEMDAS

“Operations” means 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?

**….. So, long ago people agreed to follow rules when doing calculations, and they are:**

**Order of Operations**

**Do things in Parentheses First**.

Example:

**Then Exponents (Powers, Roots)**

Example:

**Then Multiply or Divide which comes first**.

Example 1:

Example 2:

How Do I Remember It All … ? **PEMDAS** !

P |
Parentheses first |

E |
Exponents (ie Powers and Square Roots, etc.) |

MD |
Multiplication and Division (which comes first) |

AS |
Addition and Subtraction (which comes first) |

You can remember by saying “Please Excuse My Dear Aunt Sally”. |

**Note:** in the UK they say **BODMAS** (Brackets,Orders,Divide,Multiply,Add,Subtract),

and in Canada they say **BEDMAS** (Brackets,Exponents,Divide,Multiply,Add,Subtract).

It all means the same thing! It doesn’t really matter how you remember it, just so long as you get it right.

**Example:**** How do you work out 3 + 6 × 2 ?**

Multiplication before Addition:

First 6 × 2 = 12, then 3 + 12 = 15

**Example: How do you work out (3 + 6) × 2 ?**

Parentheses first:

First (3 + 6) = 9, then 9 × 2 = 18

**Example: How do you work out 12 / 6 × 3 / 2 ?**

Multiplication and Division rank equally, so just go left to right:

First 12 / 6 = 2, then 2 × 3 = 6, then 6 / 2 = 3

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

7 + (6 × 5^{2} + 3) |
Start inside Parentheses, and then use Exponents First |

7 + (6 × 25 + 3) | Then Multiply |

7 + (150 + 3) | Then Add |

7 + 153 | Parentheses completed, last operation is an Add |

160 | DONE ! |

### Commutative, Associative and Distributive Laws

**Commutative Laws**

The “Commutative Laws” say you can **swap numbers** over and still get the same answer …

**… when you add:**