How much is 3 + 4 x 5?  Some beginning algebra students will say 35 while others will say 23. Since a numerical expression can have only one value, only one of these answers can be correct.
 
 

To avoid confusion (and even conflict) mathematicians long ago agreed on a convention called the Order of Operations. The Order of Operations tells us how to evaluate an expression in the correct order:
 
 

1. Simplify all expressions inside Parentheses, brackets, braces, etc.

2. Evaluate all Exponents.

3. Multiply and Divide left to right.

4. Add and Subtract left to right.

5. Simplify fractions.
 
 

Many students use the mnemonic PEMDAS (Please Excuse My Dear Aunt Sally) to remember the order of operations.
 
 

The solution to the problem above is 23 as shown below in example 1.
 
 

Examples:
 

1.3 + 4 x 5	3 + 4 x 5 = 3 + 20                  = 23	Multiply Add
2.	= 4 - 3                           = 1	Divide (left to right!) Multiply Subtract
3. 3(3 + 7) - 16	3(3 + 7) - 16 = 3(10) - 16                         = 30 - 16                         = 14	Add inside parenthesis Multiply Subtract
4. 5(13 + 7) - (7 - 4)2	5(13 + 7) - (7 - 4)2 = 5(20) - 32                                  = 5(20) - 9                                   = 100 - 9                                   = 91	Simplify parentheses Evaluate exponent Multiply Subtract
5.		Multiply top and bottom Add and subtract Simplify fraction
6. Place parentheses in the following problem in order for it to be correct:	If you place parentheses around the 7 - 4, then apply the order  of operations, you will have a true equation.