What does "Order of Operations" mean?

This is the order in which you should go about solving a math problem.

It is a fairly simple rule that applies to all of maths. Without this information you will often get the wrong answer and wonder why.

BODMAS

B(rackets), O(ther), (D)ivision, (M)ultiplication, (A)ddition, (S)ubtraction

This is a helpful mnemonic to help you remember this important rule. Whenever working on a math problem start with the stuff in the brackets, then work further until you end up with only subtractions.

Brackets do not mean anything except from "Prioritize these first!".

For example:

$9 * 3 + 6 = 27 + 6 = 33$ We start with the multiplication first here as it takes priority over subtraction. Here is a much harder problem which we have slowly worked on:

$(9 + 3) * 5 + 3 \div 2 - 5 = 12 * 5 + 3 \div 2 - 5 = 12 * 5 + 1.5 - 5 = 60 + 1.5 - 5 = 61.5 - 5 = 56.5$

O(ther) means roots and powers. For example: $(5+7)^2 * 3 + 10 \div 2 = 12^2 * 3 + 10 = 144 * 3 + 10 = 432 + 10 = 442$

Operations with negative numbers

$+ -$ makes $-$ $- +$ makes $-$ $+ +$ makes $+$ $- -$ makes $+$

In practice:

$-3 + -4 = - 3 - 4 = -7$ $-3 + -4 = - 3 - 4 = -7$

Balancing the force

This is the most powerful and important fact about the whole of maths:

$\text{This side} = \text{This side}$

This means that you can change each side, provided you do the same to both sides.