What Is the Order of Operations in Evaluating Algebraic Expressions?

In evaluating algebraic expressions, the order of operations is parentheses, exponents, multiplication and division and, finally, addition and subtraction. A saying to help students remember this order is “Please excuse my dear Aunt Sally,” in which the first letter of each word corresponds to the first letter of the operation.

In evaluating an expression, work is done from left to right beginning with any calculations in parentheses and brackets. When there are double sets of brackets or parentheses, the innermost sets must be done first. When this step is completed, the next step is to solve the exponents found in the expression. The next steps involve multiplication and division. These operations are to be completed in order from left to right as they appear. Not all multiplication is done before division, but the two are done in order of appearance. Finally, operations involving addition and subtraction are done from left to right as they appear.

When the steps are not completed in the proper order, the answer differs from the correct one. For example, in the equation 4 + 8 (2+1)^2, the correct solution involves solving inside the parentheses first. The statement then reads 4 + 8(3)^2. Solving for the exponent next leaves 4 + 8(9). Completing multiplication then makes the equation read 4 + 72. Calculating the addition yields the answer 76.