Calling Math Geniuses here, I need help, pls.

[HSKLNG]

How would you simplify this problem?

 

3 squared - 2 cubic + 45/3(neg.1-2)

 

 

Need step by step if possible, thanks in advance. Oh, this is Alg I

[creekland]

Are there any "x's" in there or just numbers? If just numbers then you have 9 - 8 + ...ok, what does neg.1-2 mean? -1-2?

 

If so, then 9 - 8 + 45/3(-3)

 

Then 9 - 8 + 45/-9

 

9 - 8 - 5

 

or - 4

[jeri]

Is it: 3^2 - 2^3 + 45/3 * (-1 - 2)

 

In words: Or three squared, minus two cubed, plus 45/3, times (negative 1 - 2)

 

jeri

[HSKLNG]

We are doing Video Text and my dd just took the Cumulative Test B from Units I - IV and this problem was the last one and a "challenge problem", am quoting.

 

She solved the problem like you did, but the solutions have another way of solving the problem that my dd says does not follow the PEMDAS.

 

Are you sure this is the ONLY way to rightly solve this problem? I would vote hands up that the solution manual is wrong any time, do not get me wrong, I just want to make sure.

 

Would you confirm this? Thanks again....:D I'm so happy, she knows her stuff!

[AngieW in Texas]

I interpreted what you typed the same way that creekland did and got the same answer, -4.

[HSKLNG]

Thank you ladies, you are all awesome!:D

[kiana]

Was it written on one line, as you had it, or did the fraction bar indicate a fraction?

 

If it was written on one line, the last term should actually be simplified as 45/3(-1-2) = 15(-3) = -45, as multiplication/division have the same order of precedence in operations -- that is to say, multiplication and division should be performed from left to right, the same as addition/subtraction. If you plugged this into a calculator as written, you would get -44.

Edited April 3, 2010 by kiana

[creekland]

I agree that IF the only denominator (bottom) in the fraction is 3, then divide 45 by 3 to get 15, then multiply by -3 and you'd be back at -45 for that term. It doesn't affect the 9 or 8 from the exponents so 9 - 8 - 45 = -44.

 

IF it's all in the denominator (as I read it to be), then the answer is as I typed.

 

In general:

 

Parentheses get done first.

 

Exponents get done second.

 

Multiplication and Division get done next in order from left to right (as you read).

 

Addition and Subtraction get done last in order from left to right.

 

So 33 - 15/3 * 4 squared/2

 

= 33 - 15/3 * 16/2

 

= 33 - 5 * 16/2

 

= 33 - 80/2

 

= 33 - 40

 

= -7 (though in this case 16/2 could have been reduced to 8/1 to get the same answer a little bit easier).

[HSKLNG]

I thought this deal was over.

 

There are no fractions at all in this "sentence".

 

3 squared minus 2 cubic plus 45 divided by 3(negative one minus 2).

 

Lets try again.

 

Thank you ladies.

[AngieW in Texas]

There are several ways to interpret what you typed.

 

3^2 - 2^3 + 45

---------------

3(-1-2)

 

That would be (9-8+45)/(3 x -3) = 46/(-9) = -46/9

 

or

 

3^2 - 2^3 + 45/(3 x (-1-2))

which would be 9 - 8 + 45/(-9) = 1-5 = -4

 

or

 

3^2 - 2^3 + (45/3)(-1-2))

which would be 9 - 8 + 15(-3) = 1-45 = -44

 

or

 

(3^2 - 2^3 + 45/3) x (-1-2))

which would be (9 - 8 + 15)(-3) = 16(-3) = -48

 

There are many other possible interpretations as well.

[creekland]

I thought this deal was over.

 

There are no fractions at all in this "sentence".

 

3 squared minus 2 cubic plus 45 divided by 3(negative one minus 2).

 

Lets try again.

 

Thank you ladies.

 

 

First, anytime you have a "divided by" you have a fraction as that's what division is. For example, 10 divided by 2 can easily be written as the fraction 10/2. :)

 

However, the way you've written this now does lend it toward Angie's third interpretation due to the left --> right rule for multiplication and division. I'll do it one step at a time based on that.

 

Original as you wrote:

 

3 squared minus 2 cubic plus 45 divided by 3(negative one minus 2)

 

Step 1 --> Parentheses

 

3 squared minus 2 cubic plus 45 divided by 3(-3)

 

 

Step 2 --> Exponents

 

9 minus 8 plus 45 divided by 3(-3)

 

 

Step 3 --> Division (due to left --> right rule for multiplication and division)

 

9 minus 8 plus 15(-3)

 

 

Step 4 --> Multiplication

 

9 minus 8 plus -45

 

 

Step 5 --> Subtraction (due to left --> right rule for addition and subtraction)

 

1 plus -45

 

 

Answer = -44

 

Previously I was taking the 3(-1-2) to totally be in the bottom of the division. Since it doesn't look like a fraction to you and doesn't actually have parentheses around it showing it's supposed to be, then it's likely to be multiplication (the equivalent of being on top in a fraction or simply another term). It WOULD make sense that the book is doing this to check order of operations. Most people use PEMDAS to remember it by, but one has to remember that multiplication and division are equal steps based on left --> right (ditto addition and subtraction). Multiplication does not always come before division. This is actually another advantage of writing it all as a fraction as it would be extremely clear whether the -3 was being divided or multiplied, but I can understand their not doing so if they want a student to catch the order.

 

Hope that helps.