PEMDAS

PEMDAS is a mnemonic that stands for "Please excuse my dear aunt sally." It is known as the order of operations:

Please - parentheses

Excuse - exponents

My - multiplication

Dear - division

Aunt - addition

Sally - subtraction

This tells us which order we need to perform the respective operation in. Multiplication and division can be grouped together because they are inverses so the order they are performed in doesn't matter with respect to each other, and we perform either operation as we read from left to right. The same is true of addition and subtraction. So, in some cases you may see PEMDAS 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