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Welcome to the second lesson in unit 1 on Order of Operations.
Order of operations is a rule used to clarify, unambiguously, which procedures should be
performed first in a given mathematical expression. The use of the acronym P.E.M.D.A.S. has led
to the misconception that there are six steps. There are actually four steps in order of
operations. The first step is to clean up all of the operations
that exist inside grouping symbols. Grouping symbols include but are not limited to; parentheses,
brackets, braces, and the division bar. The second step in order of operations is
to clear all exponents. Next, we will take care of all of the multiplication
and division moving from left to right. Keep in mind that multiplication does not have
priority over division, they are treated as equals and we will perform whichever comes
first when reading from left to right. The last step in our order of operations is
to add and subtract moving from left to right. Similar to the previous step, addition does
not get priority over subtraction. We simply perform the operation that comes first when
reading from left to right. We will finish our lesson with a couple of
examples. Our first example is read; twelve, divided
by the difference of four and six, squared, times five.
Beginning inside our grouping symbols, the first step is to subtract four and six. This
yields a result of negative two. The second step is to clear the exponents.
The negative two is the only item being raised to the second power which gives us a positive
four. Our third step is to perform all of the multiplication
and division moving left to right. Twelve divided by four comes first and gives us three.
Three then gets multiplied by five and we have fifteen.
Since there is no addition or subtraction in this problem, we have our answer of fifteen.
Our second example, like all problems involving order of operations, is completed using the
exact same process. The second example is read as twenty minus
two times the difference of eight and five, squared, times four divided by two.
Beginning with our parentheses, we start by subtracting eight and five leaving us with
three. Focusing on the exponent, we now have to raise
three to the second power giving us a value of nine. Be careful not to multiply the two
and the three before clearing the exponent. Next is to clean up all of the multiplication
and division. There is quite a bit of multiplication and division so your attention to detail is
valuable. We will first multiply the negative two and the nine producing negative eighteen.
Negative eighteen then gets multiplied by four yielding negative seventy-two. Lastly,
the negative seventy two is divided by two giving us a quotient of negative thirty six.
Finally, we will subtract the twenty and the thirty six giving us a result of negative
sixteen. A common mistake in this problem is to subtract
too early. The first operation that we see when looking at this problem is twenty minus
two and it is very tempting to subtract early in the problem. As I have said before, your
diligence and attention to detail will be the difference in getting the answer right
or wrong. I have provided you with ten problems for
you to practice on your own. Please check your answers when you are finished by looking
at the last slide of the PowerPoint I have provided. You are welcome to email me with
any questions. Good Luck!