Video Transcript
Today, we’re introducing evaluating
expressions with order of operations. Let’s jump right in.
Evaluate six plus four times
three.
Six plus four times three is a
numerical expression. And we need to try and evaluate
this expression. We’re actually gonna see how two
different students would evaluate this expression. We’ll start with student A who says
six plus four equals ten. So that’s the first step. And ten times three equals
thirty. Student A has concluded that this
expression is equal to thirty. Student B thinks the problem should
be solved a little differently. Student B multiplies four times
three first. And then add six plus twelve for
eighteen.
It seems as though we have a big
problem now. Because two students have evaluated
the same expression and come up with different answers. This expression, six plus four
times three, can only be equal to one of these things. It can’t be thirty and also
eighteen. And this is why learning the order
of operations is so crucial. In this case, student B was
following the order of operations. And student A was not.
So let’s just pause this example
and take a look at the order of operations. And then we’ll come back to
this.
Order of operations are rules that
ensure numerical expressions have only one value. Just like in our last example, one
student thought it was thirty. And one student thought it was
eighteen. But there’s only one correct
answer. Expressions have only one
value. These rules tell us the order that
we should operate or solve expressions. Not following the order of
operations is like driving your car the wrong way down a one-way street. So let’s keep our car going the
right direction and take a look at what the order of operations are.
We remember the order of operations
with the acronym PEMDAS. Or as I like to say “Please Excuse
My Dear Aunt Sally.” And what in the world did these
letters stand for? Well to start, the P stands for
parentheses. So here you see the parenthesis
around 𝑥 plus three. During this step, you solve
anything that is grouped together, either with parentheses or brackets. The E stands for exponents. During this step, you solve any
part of the expression that has an exponent.
The next step is a little bit
different. The M and the D stand for multiply
and divide. During this step, we will do
multiplication and division from left to right. So that doesn’t mean you do all the
multiplication first and then all the division. You look at the whole problem and
do the multiplication and division from left to right. Our last step is addition and
subtraction together. Addition and subtraction function
in the same way multiplication and division do. That means we add and subtract from
left to right. We don’t solve all the addition and
then all the subtraction. We look at the problem as a whole
and solve from left to right.
So let’s take these tools and head
back to our first example. So “Please Excuse My Dear Aunt
Sally” will help us remember how we would evaluate this problem. If we look at the expression and we
work our way down the list, we start with P, parentheses. Does this problem have any
parentheses? It does not. So we’re done with that step. We’ll also check for exponents. Are there any exponents in this
problem? There are not. Now we move on to multiplication
and division, remember from left to right. So is there multiplication or
division in this problem? And the answer to that is yes. So we must multiply four times
three first. That’s our first step here. And you can see that that’s what
student B did. And that was the mistake that
student A made. They added before they
multiplied. Once you multiply four times three,
your last step is addition and subtraction. In this problem, that means that
we’ll add six to the twelve. Following student B’s example, six
plus four times three equals eighteen. Here’s our next example.
Evaluate two minus three plus seven
divided by seven.
We’ll need the tools that we
learned in order of operations, “Please Excuse My Dear Aunt Sally.” Start this problem by checking the
first step in your order of operations, parentheses. Because there are parentheses in
this problem, we need to solve what’s inside those parentheses first. In the first step, we subtracted
three from two and found that that was negative one. Following the order of operations,
we’ll check to see if there are any exponents in our problem. There are not. So we’ll move on to multiplying and
dividing from left to right. There was no multiplication. But there was a division. And we need to divide seven by
seven. After you divide seven by seven to
equal one, there’s only one step remaining in our order of operations. And there is only one step
remaining in our expression as well. We just add and subtract from left
to right. And in this case, we’ll be adding
negative one to one. The solution to this expression
turns out to be zero.
Here’s another one.
Evaluate four cubed minus nine
divided by three squared plus five.
No matter how big the expressions
get or how many operations are inside the expression, the steps stay exactly the
same. We start with writing down our
PEMDAS, “Please Excuse My Dear Aunt Sally,” to help us remember what the order of
operations are. Then we copy down the problem and
start working our way from the beginning of the order of operations to the end. Are there any parentheses or any
other form of grouping in this problem? The answer is yes. We’re gonna solve nine divided by
three first. We divided nine by three and then
copied the rest of our problem across. So now we have four cubed minus
three squared plus five. Our next step, check for
exponents. This expression has two sets of
exponents. So we need to solve both of those
during this step. We have four cubed, which equals
64, and three squared, which equals nine. And that ends all of the exponents
in the expression.
Next we’ll check for multiplication
and division from left to right. In this case, there is none. Finally, we have addition and
subtraction from left to right. But remember that we wanna solve
this from left to right. We don’t start with all of the
addition. We just start with what’s furthest
to the left. In that case, that’s 64 minus nine,
which needs to come first. And we’ll solve addition and
subtraction from left to right. 64 minus nine equals 55. 55 plus five equals 60. And this expression equals
sixty.
To keep your car going the right
way, remember “Please Excuse My Dear Aunt Sally.” Parentheses, exponents,
multiplication, division, addition, and then subtraction.
