The ordering of algebraic operations

When both writing down and reading the algebraic expressions, the binary operation (including addition+, subtraction-, multiply*, divide/, exponential^) follow a conventional order:

0) Parenthesis, including {}, [], ()
1) Exponent, multiply and divide
2) Addition and subtraction

The ordering is 0)>1)>2). Then there is no ordering within each group, eg multiply and divide are at the same level of priority except that 0) comes in such as a parenthesis.

Let's take a look at one quick example: 3+(8-2)*6.
First compute (8-2)=6;
Then compute (8-2)*6=6*6=36;
Finally compute 3+(8-2)*6=3+36=39.

Another example: 3^2+3/(5-2)
First compute (5-2)=3;
Then do 3/(5-3)=3/3=1;
Next compute 3^2=3*3=9;
Finally add 3^2+3/(5-2)=9+1=10.

Hope it helps!


This blog puts exponentiation in the same group as multiplication and division, as though any of these three operations could be done in any order. However, exponentiation should ALWAYS be done BEFORE multiplication and division, except as modified using parentheses. For example, 2*3^2 should be computed as 2*3^2 = 2*9 = 18 (i.e., do the exponentiation first) and NOT as 2*3^2 = 6^2 = 36 (i.e., multiplication before exponentiation).


Yingda Z.

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