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# Order of operations example

Video transcript

Simplify negative 1
times this expression in brackets, negative 7 plus
2 times 3 plus 2 minus 5, in parentheses, squared. So this is an order
of operations problem. And remember, order
of operations, you always want to
do parentheses first. Parentheses first. Then you do exponents. Exponents. And there is an exponent in
this problem right over here. Then you want to
do multiplication. Multiplication and division. And then finally, you do
addition and subtraction. So let's just try to
tackle this as best we can. So first, let's do
the parentheses. We have a 3 plus 2
here in parentheses, so we can evaluate
that to be equal to 5. And let's see, we
could do other things in other parts of
this expression that won't affect what's going on
right here in the parentheses. We have this negative 5 squared. Or I should just, we're
subtracting a 5 squared. We want to do the
exponent before we worry about it being subtracted. So this 5 squared over
here we can rewrite as 25. And so let's not do
too many steps at once. So this whole thing will
simplify to negative 1. And then in brackets, we have
negative 7 plus 2 times 5. And then, 2 times 5. And then close brackets. Minus 25. Now, this thing-- we want
to do multiplication. You could say, hey, wait. I still have a parentheses here. Why don't I do that first? But when you just
evaluate what's inside of this parentheses,
you just get a negative 7. It doesn't really
change anything. So we can just leave this
here as a negative 7. And this expression. We do want to evaluate this
whole expression before we do anything else. I mean, we could distribute
this negative 1 and all of that, but let's just do straight
up order of operations here. So let's evaluate
this expression. We want to do multiplication
before we add anything. So we get 2 times
5 right over there. 2 times 5 is 10. That is 10. So our whole
expression becomes-- and normally, you wouldn't
have to rewrite the expression this many times. But we're going
to do it this time just to make sure no
one gets confused. So it becomes negative 1
times negative 7 plus 10. Plus 10. And we close our brackets. Minus 25. Now, we can evaluate
this pretty easily. Negative 7 plus 10. We're starting at negative 7. So I was going to draw
a number line there. So we're starting-- let
me draw a number line. So we're starting at negative 7. So the length of this
line is negative 7. And then, we're adding 10 to it. We're adding 10 to it. So we're going to
move 10 to the right. If we move 7 to the
right, we get back to 0. And then we're going to
go another 3 after that. So we're going to
go 7, 8, 9, 10. So that gets us to positive 3. Another way to
think about it is we are adding integers
of different signs. We can view the
sum as going to be the difference of the integers. And since the larger
integer is positive, our answer will be positive. So you could literally just
view this as 10 minus 7. 10 minus 7 is 3. So this becomes a 3. And so our entire expression
becomes negative 1. Negative 1 times. And just to be clear,
brackets and parentheses are really the same thing. Sometimes people
will write brackets around a lot of
parentheses just to make it a little bit easier to read. But they're really just the
same thing as parentheses. So these brackets out here,
I could just literally write them like that. And then I have a
minus 25 out over here. Now, once again, you want to
do multiplication or division before we do addition
and subtraction. So let's multiply the negative
1 times 3 is negative 3. And now we need to
subtract our 25. So negative 3 minus 25. We are adding two
integers of the same sign. We're already at
negative 3 and we're going to become 25 more
negative than that. So you can view
this as we're moving 25 more in the
negative direction. Or you could view it
as 3 plus 25 is 28. But we're doing it in
the negative direction, so it's negative 28. So this is equal to negative 28. And we are done.