The Order of Operations - Examples, Exercises and Solutions

The given equation is $36 - 4 \div 2$. To solve this, we must follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Step 1: Division

• Identify the division operation in the equation: $4 \div 2$.

• Perform the division: $4 \div 2 = 2$.

Now the equation becomes: $36 - 2$.

Step 2: Subtraction

• Perform the subtraction: $36 - 2 = 34$.

Therefore, the result of the equation $36 - 4 \div 2$ is $34$.

According to the order of operations, we first solve the expression in parentheses:

$5\times1=5$

Now we multiply:

$8\times5=40$

According to the order of operations rules, we first insert the multiplication exercise into parentheses:

$(7\times1)+\frac{1}{2}=$

Let's solve the exercise inside the parentheses:

$7\times1=7$

And now we get the exercise:

$7+\frac{1}{2}=7\frac{1}{2}$

According to the order of operations rules, we will solve the exercise from left to right, since there are only multiplication and division operations:

$\frac{6}{3}=2$

$2\times1=2$

$100+5-100+5=105-100+5=5+5=10$

We will use the substitution property to arrange the exercise a bit more comfortably, we will add parentheses to the addition operation:
$(3+2+1)-4=$
We first solve the addition, from left to right:
$3+2=5$

$5+1=6$
And finally, we subtract:

$6-4=2$

According to the rules of the order of operations, we will solve the exercise from left to right since it only has addition and subtraction operations:

$9-3=6$

$6+4=10$

$10-2=8$

According to the order of operations, addition and subtraction are on the same level and, therefore, must be resolved from left to right.

However, in the exercise we can use the substitution property to make solving simpler.

-5+4+1-3

4+1-5-3

5-5-3

0-3

-3

Due to the fact that the exercise only involves addition and subtraction operations, we will solve it from left to right:

$25-6=19$

$19-9=10$

$10+7=17$

$17-3=14$

Due to the fact that the exercise only involves addition and subtraction operations, we will solve it from left to right:

$14-5=9$

$9-9=0$

$0+7=7$

$7+2=9$

Due to the fact that the exercise only involves addition and subtraction operations, we will solve it from left to right:

$26-6=20$

$20+9=29$

$29+7=36$

$36-12=24$

Insofar as the exercise only involves addition and subtraction operations, we will solve it from left to right:

$30+6=36$

$36-5=31$

$31+7=38$

$38-17=21$

Due to the fact that the exercise only involves addition and subtraction operations, we will solve it from left to right:

$25+6=31$

$31-19=12$

$12+7=19$

Due to the fact that the exercise only involves addition and subtraction operations, we will solve it from left to right:

$32-4=28$

$28-19=9$

$9+3=12$

$12-7=5$

According to the rules of the order of arithmetic operations, we solve the exercise from left to right since it only has addition and subtraction operations:

$3+4=7$

$7-1=6$

$6+40=46$