Order of Operations

By kylemarx86

  • Parentheses

    Parentheses, or grouping symbols, are the first step in our order of operations for simplifying expressions. We will use up all of the operators on the inside of any parentheses before moving on to any operations outside of the parentheses. Note that this entire order of operations could happen inside of another set of parentheses; we would work inside out, then. ex 1: (2+3) / 5 = (5) / 5 ex 2: 2 + (6 * 8) = 2 + (48) continuing ex: 2 * (5+3)^2 + 4 / 2 - 1 = 2 * (8)^2 + 4 / 2 - 1
  • Period: to

    Order of Operations

    PEMDAS
    or
    Please Excuse My Dear Aunt Sally

  • Exponents

    Exponents come next. Exponents show that a number is being repeatedly being multiplied by itself. The symbol ^ will denote an exponent in this slide show. The number before the ^ symbol is called the base, and the number after the ^ symbols is the exponent. An example of their use would be, 5 ^ 3 = 5 * 5 * 5 which equals 125. The book we use will use superscripted numbers instead of ^. ex 1: 5 ^ 2 + 3 = 25 + 3 ex 2: 2 ^ 4 / 4 = 16 / 4 cont ex: 2 * (8)^2 + 4 / 2 - 1 = 2 * 64 + 4 / 2 - 1

  • Multiplication

    Multiplication is the next step in the order of operations. This is the same multiplication you should be used to. Just remember that this step comes after exponents are taken care of. ex 1: 8 * 4 + 6 / 2 = 32 + 6 / 2 ex 2: 2 - 9 * 2 = 2 - 18 cont ex: 2 * 64 + 4 / 2 - 1 = 128 + 4 / 2 - 1

  • Division

    Division is the next step in simplifying expressions. Division actaully has the same presedence as multiplication; it is just usually easier to take care of division after multiplication. ex 1: 6 / 2 - 1 = 3 - 1 ex 2: 6 + 33 / 11 = 6 + 3 cont ex: 128 + 4 / 2 - 1 = 128 + 2 - 1

  • Addition

    Almost to the end. Addition comes next. Usually we take care of addition from left to right, but it is also important to note that with addition we can look for things that might add up easier. ex 1: 2 + 5 - 2 = 7 - 2 ex 2 : 5 + 4 + 3 = 9 + 3 cont ex: 128 + 2 - 1 = 130 - 1

  • Subtraction

    The final step of the order of operations is subtraction. This subtraction could happen inside of parentheses, so as I mentioned earlier, we would have to start over again with parentheses once we finished with the subtraction. ex 1: -7 - 6 = -13 ex 2: 2 * (6 - 2) + 5 = 2 * (4) + 5 cont ex: 130 - 1 = 129

  • Example 1

    3 * (5 + 3 - 2)^2 + 3
    3 * (5 + 3 - 2)^2 + 3 (parentheses)
    (within parentheses there are no parentheses, exponenents, multiplication, or division)
    3 * (8 - 2)^2 + 3 (parentheses add)
    3 * (6)^2 + 3 (parentheses sub)
    3 * 36 + 3 (exponents)
    108 + 3 (mult)
    111 (addition)

  • Example 2

    4 * (2 * 6 + 1 - 8)^3 / 2 - 5
    4 * (2 * 6 + 1 - 8)^3 / 2 - 5 (parentheses)
    (within parentheses there are no parentheses, exponenents, or division)
    4 * (12 + 1 - 8)^3 / 2 - 5 (parentheses mult)
    4 * (13 - 8)^3 / 2 - 5 (parentheses add)
    4 * (5)^3 / 2 - 5 (parentheses subt)
    4 * 125 / 2 - 5 (exponents)
    500 / 2 - 5 (multiplication)
    250 - 5 (division)
    245 (subtraction)

  • Try it yourself

    Name each of the steps taken in simplifying the expression
    6 + (1 + 3 * 6 - 21)^3 / 2 - 5
    6 + (1 + 3 * 6 - 21)^3 / 2 - 5 _________
    6 + (1 + 18 - 21)^3 / 2 - 5 _________
    6 + (19 - 21)^3 / 2 - 5 _________
    6 + (-2)^3 / 2 - 5 _________
    6 + (-8) / 2 - 5 _________
    6 + (-4) - 5 _________
    2 - 5 _________
    -3 _________

  • Try It Yourself (answers)

    6 + (1 + 3 * 6 - 21)^3 / 2 - 5
    6 + (1 + 3 * 6 - 21)^3 / 2 - 5 (parentheses)
    6 + (1 + 18 - 21)^3 / 2 - 5 (parentheses mult)
    6 + (19 - 21)^3 / 2 - 5 (parentheses add)
    6 + (-2)^3 / 2 - 5 (parentheses subt)
    6 + (-8) / 2 - 5 (exponents)
    6 + (-4) - 5 (division)
    2 - 5 (addition)
    -3 (subtraction)