How many laws does vector addition obey

Point before line calculation, calculation with brackets

Point calculation before line calculation

The point calculation includes multiplication, division and powers (which are an abbreviation for multiplying several equal numbers). Examples: 9 x 5 (multiplication), 72: 9 (division), 4³ (power, corresponds to: 4 x 4 x 4).

The addition and subtraction are part of the line calculation. Examples: 15 + 23 (addition), 64 - 54 (subtraction).

If we now have a larger term, we must first calculate all multiplications, divisions and powers and then add or subtract. We consider the following example: 23 + 14: 2 - 2³ - 2 + 5 · 2.

So we have to think about what to calculate first. We see three point calculations, which we calculate first, i.e. 14: 2 = 7, 2³ = 2 · 2 · 2 = 8 and 5 · 2 = 10, then we calculate the additions and subtractions from left to right.

Calculate with brackets

However, the rule “point before line” can also be overridden using parentheses. Because before the point calculation, i.e. multiplications, divisions and powers, brackets are calculated. Within brackets, however, “point before line” applies again. Usually (…) is used as brackets, but for reasons of clarity one can also use […]. Brackets that belong together should not be different, i.e. not […).

However, you can also just use round brackets. So instead of 5 · [14 - (1 + 3)] one can also use 5 · (14 - (1 + 3)).

As already said, brackets are counted before scoring. If you have several brackets, start with the innermost brackets.

Here is an example: 5 · [14 - (29 + 3): (2² + 8: 2)] - 10

We take it step by step. First we look for the innermost brackets and calculate them according to the "point before line" rule. Then a new term is created, in which we first calculate the brackets again until there are no more brackets left and the term is simplified step by step until you can finally calculate the term after "dot before dash" and get the result.

Note: It is important to be able to write an equal sign in front of each line, all factors and summands must be "dragged along". If you do not want to "drag everything along", you must not write an equal sign between unequal lines:

Whereby the part outlined in orange is to be understood as a subsidiary calculation. Even if this notation is clearer for understanding, the above style should be preferred.