Due to the order of operations (BIDMAS - brackets, indices, division, multiplication, addition, subtraction), the operations within the parenthesis (bracket) will 'jump the queue' and be performed first. For example:
3 * 2 + 1 - 4 = 3
This is because the multiplication comes first, then the addition and then the subtraction.
3 * (2 + 1) - 4 = 5
This is because the operations inside the brackets are performed first. Therefore 3 is multiplied by (2 + 1) instead of just 2, before the subtraction at the end brings the answer to 5.
Parentheses are therefore important if you want to make a complex multi-operational problem/expression/equation more clear. For example if you wanted to multiply 9 by 4, then add 2 before dividing by 2, it is not enough to write this:
4 * 9 + 2 / 2 = 19 X
It won't produce the answer you want because by order of operations, the multiplication will occur fine, but 2 will then be divided by 2 before being added to the product of 4 and 9, giving this:
4 * 9 + 2 / 2 = 36 + 1 = 37
To express what you want, you need to use parentheses:
(4 * 9 + 2) / 2 = 19
However, it is important to be as clear as humanly possible, and for the untrained mind it may be difficult to work out which operation should be performed first within the brackets. Therefore this is the clearest answer:
((4 * 9) + 2) / 2 = 19
When you have brackets within brackets, particularly when fractions become involved, it is convention to use square brackets on the very outside:
[(4 * 9) + 2] / 2
This just helps to clarify when each set of brackets is closing.
I hope this helps
