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Math Questions - Order of Operations

# Math Questions - Order of Operations

by Reggie Nardi
(Wells Nv.)

Explain how the order of operations determines how you evaluate an algebraic expression. Be sure to explain the rules for addition, subtraction, multiplication, division, and the use of grouping symbols. Use examples to illustrate your points

### Comments for Math Questions - 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