So what is the deal with PEMDAS? It is called the order of operations,
but why the PEMDAS acronym? This acronym stands for Parenthesis, Exponents,
Multiplication, Division, Addition, and Subtraction. It is typically
remembered by using the mnemonic "Please Excuse My Dear Aunt Sallie."
The order of operations is used for every math problem. All math problems
are designed to find answers using different ways to solve the problem.
However, they all follow the order of operations.
Let's take a look at simple problem: a( b + c - d )
The first thing you do is look at PEMDAS at determine which gets
answered first. Sine we read from left to right we will solve for
parenthesis first. Then try to solve for exponents, there is nothing
to solve because there are no exponents. Next try to solve for Multiplication,
however we need to solve the inside the parentheses first.
Let's plug in some numbers: 2( 3 + 6 - 1 )
Using the method described above it would be 2(3 + 6 - 1) = 2(9 -
1) = 2(8) = 16 or it can be solved this way 2(3 + 6 - 1) = 2(3 + 5)
= 2(8) = 16. Either way you will come out with the same answer because
it does not matter which you do first Addition or Subtraction.
Many students will try to solve it this way 2(3 + 6 - 1) = 2 x 3
+ 6 - 1 = 6 + 6 - 1 = 12 - 1 = 11 (which is incorrect). This is caused
by trying to follow the left to right operations typical of many problems
that do not have parentheses. Anytime you see parentheses in a problem
solve everything inside the parentheses first.
Let's try one with exponents:
using PEMDAS. First we solve everything inside parentheses, followed
by exponents, and then multiplication.
Following the order operations or PEMDAS is a critical step that
must be completed in every math problem once an expression can be
written. Even when completing written problems, you need to always
determine the expression that is derived from the story and use PEMDAS
to complete the problem.
Lets take another look at order operations using are more challenging
problem, see if you can pick out each step that follows the PEMDAS
Let's look at another problem and explain it a different way:
|3 (2 + 5) + 5 (2 + 6) / 4
|3(7) + 5(8) / 4
||Parentheses - addition
|21 + 40 / 4
|21 + 10
As you can see there is really nothing mystical or complicated when
solving a problem when using PEMDAS - Order of Operations. It does
not so let's try another expression:
|3(5 + 6) + 4(4 + 3) / 3 + 6 - 12
|3(11) + 4 (7) / 3 + 6 - 12
||Parentheses - addition
|33 + 28 / 3 + 6 - 12
|33 + 9.33 + 6 - 12
|48.33 - 12
There order operations needs to be completely understood by you,
because when you move into Algebra knowing the order of operations
is critical. PEMDAS was developed as a mnemonic that was designed
to help you remember the order of operations. A recommendation is
to write PEMDAS on your problem sheets when work the problems so that
you can learn to integrate it into your logical mathematical skills.