Numbers


Order of Operations

When we want to solve more complex problems such as 14 ÷ (5 + 2) + 3 we must solve these in a certain order. This is called the Order of Operations.

There are six basic math operations: addition, subtraction, multiplication, division, exponents and roots. All of these operations can be included in a single problem! When they are, we have to solve the problem in a certain order or we’ll get the wrong (incorrect) answer…so knowing the Order of Operations is very important as we progress on the math ladder…if we want to get the correct answer!

For example: the problem 7 – 1 + 4 has two different math operations in it.

It has a subtraction that looks like 7 – 1 and an addition which looks like 1 + 4… or is it 6 + 4? See what I mean?

Do we subtract 7 – 1 then take the product from that and add it to 4? Or do we add 1 + 4 first then subtract that from 7? Confusing! Naaa…and here’s why:


The Order of Operations says:

  1. We solve operations in parenthesis (1 + 2) first -level 1-
  2. Then, exponents and roots -level 2-
  3. Then, multiplications and divisions (from left to right) – level 3-
  4. Then additions and subtractions (from left to right) - level 4-

An easy way to remember this is by memorizing the word PEMDAS

P.E.M.D.A.S. means: Parenthesis, Exponents, Multiplication, Division, Addition and Subtraction.

-or-

Please Excuse My Dear Aunt Sally (see PEMDAS in that?)

Let’s check to be sure we understand this:

The P = _____________
The E = _____________
The M = _____________
The D = _____________
The A = _____________
The S = _____________

Write the sentence for remembering PEMDAS here:

____________________________________________________________________________________________

Let’s try a few problems to see if we get this right:

7 – 1 + 4 = so, 7 – 1 = 6 then add 4 = 10
23 + 10 – 6 = 23 + 10 = 33 minus 6 = 27
8 + (6 -1) – 3 = 6 – 1 = 5…8 + 5 = 13 minus 3 = 10
4 ÷ 2 + (6 – 3) = 6 – 3 = 3 and 4 ÷ 2 = 2 and 3 + 2 = 5
8 x 2 + (6 ÷ 2) – 1 = 6 ÷ 2 = 3 and 8 x 2 = 16
so, 16 + 3 = 19 minus1 = 18

Did you get all that?