PEMDAS Problems: Easily Simplify Equations Using PEMDAS

This article will show you how to easily simplify equations using PEMDAS problems. PEMDAS defines the order of operations or the order in which math operations are performed.

When solving math expressions such as:

18-3x4

You have to know the order in which to do the various operations. Do you subtract 3 from 18 then multiply by four?

(18-3) x4 = 60

Or do you do the multiplication first?

18-(3x4) = 6

As you can see you get vastly different results. This is where understanding PEMDAS problems and the order of operations is important, because it tells you which math operator to use first (+,-, x, /) and in which order.

The letters in PEMDAS stand for the following:
P-Parenthesis
E-Exponents
MD-Multiplication and Division
AS-Addition and Subtraction

To simplify an expression you apply PEMDAS to the expression one step at a time. First look for parenthesis, then exponents, then multiplication and division and finally addition and subtraction. Apply multiplication and division from left to right in the order of which they appear. Do the same for addition and subtraction.

Consider the following expression. (The "^" is used to indicate exponents. 4^2 means 4 squared.)

(8x4^2)-3(6+2) +9-20/5

First, work on the parenthesis. (8x4^2)
Inside the parenthesis you must again apply PEMDAS. There are no other parentheses inside the first set but there is an exponent. Apply the exponent and then do the multiplication.
8x4^2 = 8x16 = 128

The equation now reads:

128 – 3(6+2) + 9 – 20/5.

Now work on the second parenthesis.

6+2 = 8

Giving

128 – 3x8 + 9 – 20/5

There are no more parentheses. Working left to right, is there any multiplication or division? YES.

*** AT THIS POINT MANY STUDENTS WANT TO DO ADDITION AND SUBTRATION – DON’T LET THEM ***

Do all multiplication and division.

3x8 = 24
20/4 = 5

After multiplication and division you end up with 128 – 24 + 9 – 4. Just work this problem from left to right and get:

128 – 24 -> 104
+9 -> 113
-4 -> 109

Solving seemingly complex expressions becomes easy by applying PEMDAS problems to the expression one step at a time. Do not try to do multiple steps at once, this often leads to errors.

Try one yourself.

(5+ (3^3-8))/6+8(3+4) -21

Did you get 39?

Congratulations!

Related Articles