Addition and Subtraction

The order of operations teaches us the correct way to solve an expression with multiple different operations.
When solving such an expression, we will follow these steps:

Let's only solve what's inside the parentheses - we can also call this stage opening the parentheses.
If there are no parentheses at all in the exercise, we'll move on to the next stage.

Multiplication and division in order.
After opening the parentheses ,if there were any present, we rewrite the exercise in order to avoid confusion. We then proceed to solve the multiplication and division operations from left to right.

Addition and subtraction in order.
We add and subtract from left to right.

Pay attention!
After each step, we rewrite the expression. In doing so the exercise will be shorter meaning that we can solve it more easily.
Note - regardless of which expression appears inside of the parentheses, we will solve it first.
If multiplication and division appear along with addition and subtraction, multiplication and division come first, and only then do we address the addition and subtraction from left to right.

And now? Let's practice!!

Solve the following exercise:
$10-(5+3):2=$

Solution:
First, we look at the exercise and notice that it contains parentheses. Therefore, we will open the parentheses (solve the expression inside the parentheses) and continue.
$5+3=8$
We will then rewrite the exercise as shown below:
$10-8:2=$

Once we obtain the result of the parentheses, there's no need to keep them in the exercise.
Now for the second step - multiplication and division before addition and subtraction.
$8:2=4$
We'll rewrite the exercise as follows:
$10-4=6$
The result is $6$.

Let's move on to the next exercise:
$10-5+3:2=$

Solution:
Pay attention! It seems identical...
However there are no parentheses, hence the order of operations will be multiplication and division first, and only then addition and subtraction in order.
Start solving the problem:
$3:2=1.5$
Let's rewrite the exercise:
$10-5+1.5=$
Continue solving the exercise.
$5+1.5=6.5$
The result is $6.5$

Another exercise:
$10+3\cdot(2+4)+6=$

Solution:
In this exercise we have parentheses, hence we'll always start with them.
We obtain the following:
$2+4=6$
Let's rewrite the exercise:
$10+3\cdot6+6=$

Now we notice that we have multiplication, so we need to solve it first.
Let's solve it as follows:
$3\cdot6=18$
Proceed to rewrite the exercise
We obtain the following:
$10+18+6=$
We'll solve in order and obtain the following:
$28+6=34$
The result is $34$.

Now let's move on to a similar but different exercise without parentheses and see if the result changes:
$10+3\cdot2+4+6=$

Solution:
Since there are no parentheses, we'll start with the multiplication operation in the expression and solve it first.
We obtain
$3\cdot2=5$
Let's rewrite the expression:
$10+6+4+6=$
Now let's continue solving the expression:
$16+4+6=$
$20+6=26$
The result is $26$

Another exercise!
$40:(10-5)+9=$

Solution:
First, we'll check if there are parentheses in the exercise, the answer is yes, so we'll address them first and solve them.
$10-5=5$
We'll rewrite the exercise without parentheses:
$40:5+9=$
Now we have an exercise with division and subtraction operations, so we'll start with division according to the order of operations.
We obtain the following:
$40:5=8$
Proceed to rewrite the exercise:
$8+9=17$
The result is $17$

Another exercise:
$(5+8:2)+6\cdot0=$

Solution:
Note that we have parentheses here, so we'll always start with them.
Within the parentheses, it's important to follow the correct order of operations. That is, we'll perform division first and then continue to addition.
Let's start
$8:2=4$
Let's write the expression with the new parentheses:
$(5+4)+6\cdot0=$
Now let's add according to the parentheses:
$5+4=9$
Let's rewrite the expression without any parentheses and we should obtain the following
$9+6\cdot0=$
Proceed to the multiplication
$6\cdot0=0$
Let's rewrite the expression as shown below
$9+0=0$
The result is $9$