PEMDAS

This tells us the order in which we need to perform the respective operations. Multiplication and division can be grouped together because they are inverses, so the order they are performed in doesn't matter. When trying to decide whether to multiply or divide first (assuming all higher priority operations have already been taken into account) compute the operations in order from left to right. The same process is used for addition and subtraction. In some cases PEMDAS is written as PE(MD)(AS), to indicate this relationship.

Also, whenever a number, or group of numbers, is next to another number or group of numbers that are in parenthesis, if there is no explicit operation written between them, the operation is multiplication.

Examples

1.	5 ÷ 2(3+7)	=	5 ÷ 2 × (10)
		=	2.5 × (10)
		=	25

This problem is slightly tricky because if we were to have multiplied the 2 × 10 instead of dividing the 5 ÷ 2, we would get an incorrect answer of 0.25.

2.		=	12 – 16 + 4
		=	0

3.
	=
	=
	=
	=
	=	27 – 3 + 9
	=	33

4.
	=
	=
	=
	=
	=
	=	-5 + 6
	=	1

Another way to practice order of operations is to construct a "maze" where progress through the maze is tied to successfully completing order of operations problems. There are many ways this can be done. Below is one example.

Solve the problem in the rectangle marked "Start," and follow the arrow for the solution that you get. If the solution that you get isn't available, that means that your solution is incorrect. However, just because the solution you acquire is available, doesn't necessarily mean that it is correct. Solve your way through the maze until you arrive at the "Finish" rectangle. Once you do, check the solution below to see if the path you followed to get to the solution was the correct one.

 

It is also possible to construct more complicated mazes. The point is just to test your understanding of order of operations since some of the solutions in the maze are possible to acquire by making certain mistakes with the order of operations.

If you progressed through the maze correctly, you would have moved from rectangle one through two, four, five, six, and then to the finish. The solutions to each of the problems in the rectangles are listed below; the numbering in the list corresponds to those in the top of each rectangle.

1. 46
2. 35
3. 74
4. 8
5. 59
6. 7
7. -1
8. 1

 

We don't use PEMDAS if there's only add. and mult. because of the commutative and associative properties.