Order of operations
Order of Operations 1 Order of Operations
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- 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!
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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