Order of Operations MD|AS
Imagine that you are faced with the problem 16 + 9 ÷ 3 - 11.
If we were to just work from left to right, we would actually get the wrong answer. Instead, we need to complete all of the multiplying and dividing first, from left to right.
16 + 9 ÷ 3 - 11
16 + 3 - 11
Next, we will complete the adding and subtracting from left to right.
16 + 3 - 11
19 - 11
8
Some people like to use MDAS, or other acronyms to help them remember the steps. These can be helpful, as long as you don't follow it letter for letter. You might even want to split it up. MD|AS
This may help you to remember to do all of the multiplying and dividing together. Instead of doing the multiplying and then the dividing, you actually look for both together at the same time.
Check this example to see what this means: 16 ÷ 8 x 3 + 2 - 5
In this example, we survey the problem for any multiplication or division. We should see that the division shows up before the multiplication. So we must work from left to right.
16 ÷ 8 x 3 + 2 - 5
2 x 3 + 2 - 5
6 + 2 - 5
Now that we are left with adding and subtracting, we again, move from left to right.
6 + 2 - 5
8 - 5
3
If we had followed the letters exactly, we would have gotten a different answer.
This is NOT CORRECT! You need to look for the operations in their pairs and work from left to right.
Hopefully, you have also noticed that the solutions to order of operation questions for a V shape. Take your time and show one step on each line of your solution. This will help you organize your mathematical thoughts. And, if you do happen to make an error, it will be easier to locate.
Let's solve one more final example: 18 + 30 ÷ 5 - 2 x 4
Here is the solution:
18 + 30 ÷ 5 - 2 x 4
18 + 6 - 2 x 4
18 + 6 - 8
24 - 8
16
Related Links:
Order of Operations PE|MD|AS
Order of Operations
Math
Fractions
Factors