#PreAlgebra - The Order of Operations

Question

What's the Order of Operations? And why does it matter?

Answer

It's akin to grammar for math - it helps to make sure that what is being written by one person is understood the same way by someone else reading it.

Analysis

When we write a sentence, we use grammar to help make sense of what's being written. One of my favourite examples of this is on my son's T-shirt

It's time to eat grandma

It's time to eat, grandma

Commas save lives

That little bit of grammar tells us that we don't intend to eat grandma but rather that we're letting her know it's time to eat.

The Order of Operations is like grammar for math. It tells us in what order we're supposed to do operations. For instance, with the following:

5 + 3 X 6

is the answer 23 (= 5 + 18)? is it 48 (= 8 X 6)? The Order of Operations helps the person reading the math and the person writing it to both see the same meaning (and answer).

The Order is sometimes called PEMDAS (or PEDMAS or BEMDAS or some other acronym like that. It refers to:

P or B = Parentheses (or Brackets)
E = Exponentials
M = Multiplicaton
D = Division
A = Addition
S = Subtraction

M and D have the same weight so we do those in order from left to right. The same is true for A and S.

In 5 + 3 X 6, using PEMDAS, we can see one addition and one multiplication. We do the multiplication first, so that gives

5 + 18 = 23

Let's do something a little harder:

(6 + 3^2) / 3 + 2

We do the bracket first. Within the bracket there is an addition and an exponential - we do the exponential first:

(6 + 9) / 3 + 2

Now we have division and addition. Division comes first:

15 / 3 + 2

5 + 2 = 7

~~~~~

Questions and comments always welcome!