Order of operations for beginners

The first step in the order of operations is to tackle the parentheses.
To begin we solve whatever is inside of the parentheses, regardless of the operation.
We then proceed to write the result above the parentheses with a small arc or in place of the entire expression within the parentheses.
If multiplication and division appear inside the parentheses along with addition and subtraction, multiplication and division come first, followed by addition and subtraction from left to right.
If there are parentheses within parentheses - we first solve the inner parentheses and then the outer parentheses using the solution of the inner parentheses, and then proceed to solve the rest of the exercise.

Let's practice:
$3\times(5-2)=$

Solution:
When we encounter an expression like this, the first thing that should come to mind is the parentheses!
Let's begin by solving the expression inside of the parentheses:
$5-2=3$
We write the result $3$ in a small arc above the parentheses as shown below:

and then continue to solve the exercise -
$3\times3=9$
or simply write it like this from the start.

Another exercise with parentheses:
$6-(8-2\times3)=$

Solution:
The first step is to tackle the parentheses. According to what we learned above, if both multiplication/division and addition/subtraction appear inside the parentheses, multiplication and division come first, and only then addition and subtraction from left to right.
Therefore, we first address:
$2\times3=6$
Let's write it in a small arc:

Now let's proceed to solve whatever remains inside of the parentheses:
$8-6=2$

Note - outside the parentheses there is $6$

The operations in the parentheses resulted in the value $2$
Therefore we'll solve as follows:
$6-2=4$
The final result is $4$!

Another exercise with parentheses inside of parentheses:
$4+2+(4-1\times(3-1)+5)=$

Solution:
Note – In this exercise, parentheses appear as brackets, and according to what we learned above, we first solve the inner parentheses. In our exercise $3-1=2$
We write the value in a small arc as shown below:

Now let's move to the outer parentheses - notice that there is a multiplication operation present hence we'll address it first:
$4+2+(4-1\times2+5)=$
$​​​​​​​4+2+(4-2+5)=$
Let's continue solving the parentheses:
$4+2+7=$
This is the solution:
$6+7=13$

Multiplication and division are the second step in the order of operations, directly after opening parentheses.
After opening the parentheses, if there were any present, it's advisable to rewrite the exercise in order to avoid confusion. We then proceed to solve the multiplication and division operations from left to right.
We will once again rewrite the new exercise after solving the multiplication and division operations.
Now let's practice:
$20-5\times2=$

Solution:
We have an expression that includes both multiplication and subtraction.
Notice that there are no parentheses, hence the first thing we'll address is the multiplication operation.
$5\times2=10$
Let's rewrite the expression as follows:
$20-10=10$
The final result is $10$

Another exercise:
$3\times2-4+2\div1=$

Solution:
Note that in this exercise there are no parentheses and it has multiplication and division, addition and subtraction operations. Let's start with the multiplication and division operations:
$3\times2=6$
$2\div1=2$
Let's rewrite the exercise as follows:
$6-4+2=$
$2+2=4$

Addition and subtraction are the third and final stage in the order of operations, right after multiplication and division and after opening the initial parentheses.
Let's practice:
$5-3\times1=$

Solution:
Note that addition and subtraction are the third and final step in the order of operations. Even though the subtraction operation is the leftmost one, we will instead begin with the multiplication operation.
$3\times1=3$
Let's rewrite the expression as follows:
$5-3=2$
The final result is $2$.