Order of Operations

Order of Operations

Simplify: negative one times this expression in brackets

negative seven plus 2 times 3 plus 2

minus 5 in parentheses, squared.

So this is an order of operations problem,

and remember in order of operations,

you always wanna do parentheses first.

Parentheses.

Parentheses..first.

Then you do exponents. Exponents.

And there are--there is an exponent in this problem, right over here.

Then you wanna 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. Let's do the parentheses...

We have a 3+2 here in parentheses,

so we can evaluate that to be equal to 5.

And let's see we can 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 actually I should say we have some subtracting of 5 squared.

We wanna do the exponent before we worry about being subtracted,

so this 5 squared over here, we can rewrite as 25.

Let's not do too many steps at once,

so this whole thing would simplify to negative 1,

and then in brackets we have negative 7 plus 2 times 5,

plus 2 times 5, and then 2 times 5,

and close brackets, minus 25.

Minus 25.

Now, this thing we wanna do multiplication.

You could say,

"hey, we have the parentheses, why don't we do them first"

but when we just evaluate what's inside these parentheses

you just get a negative 7,

it doesn't really change anything.

So we can just leave this as negative 7.

And this expression, we do want to evaluate this whole expression

before we anything else.

I mean we could distribute this negative 1 and all 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 a 2 times 5 right over there,

2 times 5 is 10. That is 10.

So our whole expression becomes...

Normally you don't have to rewrite the expression this many times,

but what we're gonna do at this time

to make sure no one gets confused.

So is becomes negative 1 times negative 7 plus 10,

plus 10, we close our brackets, minus 25. Minus 25.

Now we can evaluate this pretty easily.

Negative 7 plus 10. You can view as starting with negative 7,

so I was gonna draw a number line there.

So we're starting - draw a number line -

so we're starting at negative 7 and then...

- so this, the length of the line is negative 7 -

... and then we're adding 10 to it.

We are 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 gonna go 7, 8, 9, 10.

So gets us to positive 3.

Another way to think about it is,

we are adding integers of different signs,

we can view this sum as going to be

the difference of the integers,

and since our larger integer is positive,

the 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, so the 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 are really just the same thing as parentheses.

So these brackets are here,

I could just literally write them like that.

And then I have a minus 25 out over here.

Now once again you wanna do multiplication or division

before we do addition and subtraction,

so it's multiplied 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 are already at negative 3,

it will become 25 more negative than that.

So you can view this as...

we are moving 25 more in the negative direction.

Or you can view this as 3 plus 25 is 28,

we're doing it in the negative direction,

so it's negative 28.

So this is equal to negative 28.

And we are done!