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## Algebra basics

### Course: Algebra basics > Unit 1

Lesson 5: Order of operations# Order of operations example

Simplify this tricky expression using the order of operations. Expression include negative numbers and exponents. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- How Would one do 10 to the hundredth power?(7 votes)
- If n is any whole number, then 10^n is a 1 followed by n zeros.

So 10^100 is a 1 followed by a hundred zeros. This number is called a googol.

Have a blessed, wonderful day!(12 votes)

- So is 5 to the 2nd power 25?(6 votes)
- yes. if you square (A.K.A to the power of 2) a number, you multiply the number by itself twice.(7 votes)

- why do you multiply 2x(3+2) I don't see a times symbol(4 votes)
- Putting a number next to parenthesis, like 2x next to (3+2), counts as multiplication. The parenthesis is technically the multiplication question.
**Example**

3(5+ 7)*Start with the parenthesis first (PEMDAS)*

3(12)

=**36**(14 votes)

- How would you solve -(2)squared minus -54(6 votes)
- Exponents come before subtraction.

-(2)^2 - (-54) = -4 -(-54)

Next, clean up the signs on the 54 to get: -4 + 54

Now add to get: 50

Hope this helps.(7 votes)

- I didn't understand that can you make another video explaining better.Plz(5 votes)
- Order of Operations is often called PEMDAS. This helps you remember which parts of a math problem to do first. It works like this:

5 + 2 / ((8-7)x2) x (5 x 2)

You do anything inside the parentheses first. That's the P in PEMDAS. If you have parenthese INSIDE a set of parentheses, you do the inner set first.

5 + 2 / (1 x 2) x (5 x 2) We solved the inner (8-7) first. 8 - 7 is 1.

5 + 2 / 2 x (5 x 2) When you have more that one operation to do at a step, you work left to right. So we solved (1 x 2) before we solve (5 x 2).

5 + 2 / 2 x 10

We don't have any exponents in this problem so we skip the E in PEMDAS.

5 + 1 x 10 Now we've reached the MD part of PEMDAS. We do all the multiplication AND division, starting at the left and working to the right. So we solve 2 / 2 first.

5 + 10 Still working on the MD part, solving the multiplication problem 1 x 10

15 The last part of PEMDAS is the AS step. We do all of the addition AND subtraction, starting at the left and working to the right.(7 votes)

- Wait so if we need to multiply a negative number with positive, it'll be a negative number?(5 votes)
- Yes. Ex: If someone owes you $5, they have $-5. If you decide that they need to pay you back double, they now owe you $10. This means that they have $-10. (The math is: -5*2=-10.)(5 votes)

- What is the property that says (-28)-(-2) is just like 28 + 2 but then you put a negative sign on the answer and to say something else i misspell "sign" as "sing" a lot.(6 votes)
- Why do we have to do so much just to solve this problem?(6 votes)
- If you don't do PEMDAS, you may get a different answer (this only applies for some questions). It is just "safer" to try and do PEMDAS or PEDMAS or (you get the idea) in problems with multiple operations. Just saying, this is what I got out of your question. I may have got the wording wrong but I hope this helps anyway!(2 votes)

- This is great I learned exactly like this in my grade, so this was easy for me.

I always have to remember though that if there are to -- then you add them to a positive

- - = +

+ += +

- += -(5 votes) - A plane figure can be rotated about a point. A solid figure can be rotated about a line. So could we rotate a 4-dimensional shape about a plane?(3 votes)
- Nice thinking! Probably would work too but I do not know.(2 votes)

## 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.