Order of Operations

•What are the four math operations?•Addition•Subtraction•Multiplication•Division

Order of Operations

• Math has rules that we all have to follow so we will all come up with the same (correct) solution!

• One of the rules or procedures we follow is the “Order of Operations.”

• The “Order of Operations” is just that—the order in which we perform an operation in a math problem.

Order of Operations

• We may use a simple sentence to help us remember the Order of Operations.

• Please• Excuse• My• Dear• Aunt• Sally

Order of Operations

• Please Excuse My Dear Aunt Sally stands for• Parentheses• Exponents• Multiplication and Division

in order, from left to right• Addition and Subtraction

in order, from left to right• Another way to remember is PEMDAS

Order of Operations• IMPORTANT!!!• Multiplication and division are equal operations.• Addition and subtraction are equal operations• That means if we have both multiplication and

division in a problem, we work straight across (left to right) as we perform those two operations.

• That means if we have both addition and subtraction in a problem, we work straight across (left to right)as we perform those two operations.

Order of Operations

• Just because “multiplication” comes before “division” in PEMDAS, that does not mean we perform the the multiplication operations before the division operations.

• Just because “addition” comes before “subtraction” in PEMDAS, that does not mean we perform the addition operations before the subtraction operations.

Order of Operations

• REMEMBER!!!• Multiplication and division are equal

operations—we perform them left to right, in the order they are in the problem.

• Addition and subtraction are equal operations—we perform them left to right, in the order they are in the problem.

Order of Operations

• So, let’s work a few problems using the Order of Operations (PEMDAS)

• First, we look to see if there are any parentheses in the problem. – If so, we do what is inside the parentheses first.

• Second, we look to see if there are any exponents in the problem. – If so, we work that out second.

Order of Operations

• Next, we look for multiplication or division.-- If we have either, or both, we work those out,

going straight across from left to right.• Last, we look for addition or subtraction.

-- If we have either, or both, we work those out, going straight across from left to right.

• We always show our work!!

Order of Operations

• Example• 40 ÷ 2 · 4 – 2=

• 20 · 4 – 2 =

• 80 – 2 = 78

Order of Operations

• Let’s try another problem• 15 + 5 – 14 + 6 =

20 – 14 + 6 =

6 + 6 = 12

Order of Operations

• 74 + (17 – 6) · (6 ÷ 2) = 74 + 11 · 3 =

74 + 33 = 107 74 + 33 = 107

Order of Operations

• To multiply powers of the same base, add the exponents:

• 2⁴ · 2⁶ = 2⁴⁺⁶ = 2¹⁰

• 3 · 3⁵ · 3² = 3¹⁺⁵⁺² = 3⁸ – Don’t forget 3 = 3¹

Order of Operations

• To multiply different bases with the same exponents:

• Write down the exponent.• Multiply the bases.• 3² · 5² · 2² = 30²• Solve the equation to check your work.• 9 · 25 · 4 = 900• 9 · 100 = 900• 900 = 900

Order of Operations

• Sheila Stueve• Capital City School• Fall 2009