```Question 604681
There is an order for doing mathematical operations involving expressions such as these. That order says:
.
First step, do the operations within parentheses. Within the parentheses follow these rules in the order as below. Once you get through with the contents of the parentheses, move on to the second step directly below
Second step, do exponents
Third step, read the resulting expression from left to right and do the multiplications and divisions as you encounter them
Fourth step, again read the resulting expression from left to right and do the additions and subtractions in the order that you encounter them
.
You can use the acronym PE(MD)(AS) or just PEMDAS as a way of remembering the order. P means parentheses, E means exponents, MD means multiplications and divisions, and AS means additions and subtractions. (A memory trigger is "Please Excuse My Dear Aunt Sally" with the first letters being PEMDAS.)
.
Let's now work these problems following the PEMDAS rules.
.
First problem: 6+8/2+3
.
There are no parentheses or exponents, so we can skip those. Next we read the problem from left to right looking for multiplications and divisions and we do them as we encounter them. We only encounter the division 8/2 and that division results in 4. When we substitute 4 for 8/2, the problem simplifies to 6 + 4 + 3. Finally, we re-read the problem from left to right and do the additions and subtractions as we encounter them. (There are no subtractions.) So the first addition we find is 6 + 4 which equals 10 and we substitute 10 for that addition resulting in the problem then being 10 + 3. Of course, this addition results in 13 and that is the answer to this first problem.
.
Second problem: [17-(-4)]/7-3
.
In this problem the pair of brackets are also considered to be a set of parentheses. We begin by considering the most nested set of parentheses which enclose the -4. There are no mathematical operations (exponents, multiplications, divisions, additions, subtractions) within those parentheses so we can move on to the next higher set of parentheses which are the brackets. Within the brackets, the only mathematical operation we encounter is the subtraction of -4 from 17. Subtracting -4 from 17 results in 21. Therefore we can replace the contents of the brackets with 21. This makes the problem simplify to:
.
21/7 - 3
.
No more parentheses or exponents to consider so we read the problem from right to left and do any multiplications or divisions as we encounter them. Obviously there is just the single division of 21/7 and this results in an answer of 3. When we replace the 21/7 with 3, the problem is then reduced to:
.
3 - 3
.
And we do this single subtraction to get the answer to the problem. It is 0 (or zero, if you prefer).
.
Final problem: ((-4)^3-1)/5+4+3*3
.
Look inside the most nested set of parentheses. This set encloses the -4 and there are no mathematical operations to consider within that set of parentheses. So go to the next higher set of parentheses and this set encloses an exponential operation (the exponent 3) and a subtraction of 1 (the minus 1). According to the order rules, we do the exponent first by cubing the -4 to get -64. Then we substitute the -64 for the exponential and the problem becomes:
.
(-64 - 1)/5+4+3*3
.
We are still working inside the parentheses and we have just the single operation of subtracting 1 from -64 to get -65. So we replace the parentheses and its contents with -65 to simplify the expression to:
.
-65/5+4+3*3
.
There are no more parentheses or exponents to consider so we read the problem from left to right and do the multiplications or divisions as we encounter them. The first such sign we encounter is the division operation between the -65 and 5. We divide -65 by 5 and get -13. Then we replace the -65/5 with -13 and the problem then reads:
.
-13+4+3*3
.
We continue reading from left to right looking for multiplications and divisions. The only one is 3*3 so we get that product as 9 and we substitute 9 for 3*3 to make the expression now read:
.
-13+4+9
.
Finally we re-read the expression from left to right and do the additions and subtractions as we encounter them. The first one is the addition of -13 and +4 to get -9. Substitute that and the expression becomes:
.
-9 +9 and this addition results in 0 (or if you again prefer "zero")
.
If you follow these three problems all the way through to a solution, you should get a reasonable understanding of the order in which you do mathematical operations when they are written in this form.  A little more practice and it will become fairly easy to work problems such as these.
.
I hope this helps you understand these problems and the way they are solved.Good luck with your study of mathematics (or maths, if you prefer).
. ```