# Order of Operations

Describe how PEMDAS is used to simplify a mathematical expression.

### Comments for Order of Operations

 Sep 16, 2011 Order of Operations by: Staff --------------------------------------------------- Part II Step 3: MULTIPLICATION PEMDAS order of evaluation: parentheses, exponents, MULTIPLICATION, division, addition, subtraction There is only one place in the expression which requires multiplication: 4 * 7 4 * 7 = 28 A step-by-step recap of the PEMDAS simplification process up to this point is shown below: 1 + 2²[3 + (22*2 - 40)] - 15/3 = 1 + 2²[3 + (44 - 40)] - 15/3 = 1 + 2²[3 + (4)] - 15/3 = 1 + 2²[3 + 4] - 15/3 = 1 + 2²[7] - 15/3 = 1 + 2² * 7 - 15/3 = 1 + 4 * 7 - 15/3 = 1 + 28 - 15/3 Step 4: DIVISION PEMDAS order of evaluation: parentheses, exponents, multiplication, DIVISION, addition, subtraction There is only one place in the expression which requires multiplication: 15/3 15/3 = 5 A step-by-step recap of the PEMDAS simplification process up to this point is shown below: 1 + 2²[3 + (22*2 - 40)] - 15/3 = 1 + 2²[3 + (44 - 40)] - 15/3 = 1 + 2²[3 + (4)] - 15/3 = 1 + 2²[3 + 4] - 15/3 = 1 + 2²[7] - 15/3 = 1 + 2² * 7 - 15/3 = 1 + 4 * 7 - 15/3 = 1 + 28 - 15/3 = 1 + 28 - 5 Step 5: evaluate ADDITION & SUBTRACTION PEMDAS order of evaluation: parentheses, exponents, multiplication, division, ADDITION, SUBTRACTION = 1 + 28 - 5 = 24 A step-by-step recap of the entire process looks like this: 1 + 2²[3 + (22*2 - 40)] - 15/3 = 1 + 2²[3 + (44 - 40)] - 15/3 = 1 + 2²[3 + (4)] - 15/3 = 1 + 2²[3 + 4] - 15/3 = 1 + 2²[7] - 15/3 = 1 + 2² * 7 - 15/3 = 1 + 4 * 7 - 15/3 = 1 + 28 - 15/3 = 1 + 28 - 5 = 24 1 + 2²[3 + (22*2 - 40)] - 15/3 = 24 ---------------------------------------------------------------------- You did not need to apply the rule requiring you to read from left to right to simplify the example just completed. It made no difference whether you read from left to right or not. You would get the correct result regardless of how you read the expression. But the following example will illustrate just how important this rule is. Simplify the expression: 50 / 2 * 10 What should you do first: divide 50 by 2, or multiply 2 * 10? To simplify this problem, read from LEFT to RIGHT: 50 / 2 = 25 25 * 10 = 250 250 is the correct answer. ---------------------------------------------------------------------- PEMDAS also applies to expressions containing variables. For example, simplify the expression: a + b²[3 + (22a - 40)] – 15a/3 A step-by-step simplification looks like this: a + b²[3 + (22a - 40)] - 15a/3 = a + b²[3 + 22a - 40] - 15a/3 = a + b²[22a + 3 - 40] - 15a/3 = a + b²[22a - 37] - 15a/3 = a + b²*22a - b²*37 - 15a/3 = a + 22ab² - 37b² - 15a/3 = a - 15a/3 + 22ab² - 37b² = a - 5a + 22ab² - 37b² = -4a + 22ab² - 37b² a + b²[3 + (22a - 40)] - 15a/3 = -4a + 22ab² - 37b² Thanks for writing. Staff www.solving-math-problems.com

 Sep 16, 2011 Order of Operations by: Staff Part IThe question:by Reggie Nardi (Wells Nv.)Describe how PEMDAS is used to simplify a mathematical expression.The answer: In the United States, the order of operations is summarized using the acronym: PEMDAS. PEMDAS stands for: parentheses, exponents, multiplication, division, addition, subtractionWhen evaluating an expression, the PEMDAS order of operations tells you what mathematical operations to complete first, second, . . . etc.Well . . . to be honest, PEMDAS “usually” tells you what mathematical operations to complete in order.In addition to PEMDAS order, you MUST ALSO READ every expression FROM LEFT TO RIGHT. When you follow both of these rules, you will arrive at the correct answer every time.----------------------------------------------------------------------As an example, let’s use PEMDAS to evaluate the expression: 1 + 2²[3 + (22*2 - 40)] - 15/3(I’ve written the example so that the issue of reading the expression from left to right will not affect the solution. I will illustrate how important it is to read from left to right using a second example.)PEMDASStep 1: you should evaluate the expression inside each set of PARENTHESESPEMDAS order of evaluation: PARENTHESES, exponents, multiplication, division, addition, subtractionIf the expression contains nested parentheses, begin with the inner parentheses first.The example contains two nested parentheses:[3 + ( …. )]And the innermost parentheses(22*2 - 40)You should begin by evaluating the innermost expression: (22*2 - 40)(PEMDAS order also applies inside every set of parentheses, so you should complete the multiplication first, and then complete the subtraction.) 22*2 - 40 = 44 - 40 = 4The nested parentheses now look like this:= [3 + (4)]= [3 + 4]Complete the evaluation of the remaining parentheses by evaluating [3 + 4][3 + 4]= [7]A step-by-step recap of the PEMDAS simplification process up to this point is shown below:1 + 2²[3 + (22*2 - 40)] - 15/3= 1 + 2²[3 + (44 - 40)] - 15/3= 1 + 2²[3 + (4)] - 15/3= 1 + 2²[3 + 4] - 15/3= 1 + 2²[7] - 15/3= 1 + 2² * 7 - 15/3Step 2: evaluate EXPONENTSPEMDAS order of evaluation: parentheses, EXPONENTS, multiplication, division, addition, subtractionThe expression contains one exponent: 2²2² = 2 * 2 = 4The entire expression has been simplified as follows:1 + 2²[3 + (22*2 - 40)] - 15/3= 1 + 2²[3 + (44 - 40)] - 15/3= 1 + 2²[3 + (4)] - 15/3= 1 + 2²[3 + 4] - 15/3= 1 + 2²[7] - 15/3= 1 + 2² * 7 - 15/3= 1 + 4 * 7 - 15/3---------------------------------------------------