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And the answer is: 11!

 
 
Mathematical Order of Precedence requires that you do the multiplication  before you do the addition.  Doing it correctly:
 

1+2*3+4=

1+6+4=

11

 
The most common incorrect answers to this combination of numbers are 13 and 21.
You would get 13 if you just did the math left to right.
1+2 is 3*3 is 9+4 is 13.
You would get 21 if you remembered that you were supposed to do something first, but added before multiplying.
1+2=3 and 3+4=7 and 3*7=21.
 

Mathematical Order of Precedence

You may remember hearing the mnemonic: Please excuse my dear Aunt Sally, even if you don't remember what it was supposed to help you remember.  Here is the correct mathematical order of precedence and the symbols used to perform calculations on the computer:
 
Mnemonic Operator Symbol Example
Please Parenthesis () (1+2)*(3+4)=3*7=21
Excuse Exponentiation ^ 6^3=63=216
My Multiplication * 3*3=9
Dear Division / 21/3=21รท3=21
Aunt Addition + 1+2=3
Sally Subtraction - 3-1=2