Discussion in 'Math' started by Lightfire, Nov 8, 2012.

1. ### Lightfire Thread Starter Well-Known Member

Oct 5, 2010
690
21
4+4(4+4)

It seems ambiguous to me and searched that calculators have different answers with this. Either 64 or 36.

4+4(4+4)
8(4+4)
8(8)
64

4+4(8)
4+32
36

Thank you so much!

2. ### 1chance Member

Nov 26, 2011
42
185
The second is correct as according to "order of operations" one must do parentheses, thenexponents, multiplication or division as they appear left to right, and lastly addition or subtraction as they appear left to right. All calculators , to the best of my knowledge, have this preprogrammed into their "brain". To get the 1st answer, you would need to insert parentheses around the first "4 +4".

DerStrom8 likes this.

Apr 30, 2011
1,569
441
Last edited: Nov 8, 2012
4. ### amilton542 Active Member

Nov 13, 2010
496
64
A substitution in x can give you a clarity ceck.

Let $(4 + 4)$ equate to $x$, then $4 + 4x = ?$

You can see the addition cannot take place until you compute the value of the product.

Therefore, $4 +[4(4+4)] = 36$

5. ### Sparky49 Well-Known Member

Jul 16, 2011
836
422
Remember BIDMAS!!!

B - Brackets
I - Indicies (squared, cubed, etc)
D - division
M - multiplication
S - Subtraction

6. ### WBahn Moderator

Mar 31, 2012
23,069
6,920
Many simple, so called 4-function, calculators don't know about order of operations. They work with a simple single-accumulator architecture that is only capable of working with the value in the accumulator as one operand and the newly entered value as the other operand storing the result back into the accumulator.

@Lightfire: You really should try to use better, more descriptive thread titles. Not only is the one you used completely devoid of meaning, but many people would consider it downright insulting. By this I mean that it is very easy to interpret it as someone issuing a demand that everyone else drop what they are doing and answer their question as though we are all peons at their beck and call. Now, I'm sure you didn't mean it that way, but just think about how you would first react if someone came up to you with a peice of paper that had a question written on it and shouted (really shouted -- remember, you used TWO exclamation points) at you, "Answer this!!".

Last edited: Nov 8, 2012
7. ### wmodavis Well-Known Member

Oct 23, 2010
739
151
36 is correct!

8. ### Wendy Moderator

Mar 24, 2008
21,359
2,919
Actually I learned it as My Dear Aunt Sadie.

9. ### DerStrom8 Well-Known Member

Feb 20, 2011
2,424
1,355
Exactly right. The operations in the parentheses must be done first, then multiplication, and finally division.

I don't know why I just told a teacher that she was right....

I learned it as "PLease Excuse My Dear Aunt Sally", for "Parentheses Exponents Multiplication Division Addition Subtraction"

10. ### Papabravo Expert

Feb 24, 2006
11,703
2,463
With the usual precedence rules for infix notation the answer 36 is correct. What happens if you have an RPN calculator and you have to resolve the ambiguity according to some plan. In this case you must decide as there is no default behavior in this notation.

4 ENTER 4 + 4 * 4 + = 36

or you could do

4 ENTER 4 + 4 ENTER 4 + * = 64

11. ### Austin Clark Active Member

Dec 28, 2011
413
47
Odd, I was taught PEMDAS.
Parentheses, Exponents, etc;

12. ### DerStrom8 Well-Known Member

Feb 20, 2011
2,424
1,355
Same thing. PEMDAS is the American version, BIDMAS is the european version.

Lightfire likes this.
13. ### Lightfire Thread Starter Well-Known Member

Oct 5, 2010
690
21
Thank you all very much.I was taught PEMDAS.

14. ### 1chance Member

Nov 26, 2011
42
185
I think you mean "Please Excuse My Dear Aunt Sally" or PEMDAS.

DerStrom8 likes this.
15. ### 1chance Member

Nov 26, 2011
42
185
You do division BEFORE multiplication IF it appears to the left of the multiplication. Multiplication and division have the same "weight" so they are done left to right in order of appearance and the same with addition & subtraction.

DerStrom8 likes this.
16. ### Sparky49 Well-Known Member

Jul 16, 2011
836
422
Did you know you don't always round up when you have a 5?

E.g. When you have 16.5 and you round it to 2 sf, you should round it down to 16. If it is 15.5, you do round it up though.

You round to the nearest even unit.

So 245 would round down to 240. (4 is even).

Just thought you might like to know.

17. ### DerStrom8 Well-Known Member

Feb 20, 2011
2,424
1,355
Oops, I guess I worded that wrong. Yes, that's what I was always taught--M/D (left to right), A/S (left to right). Thanks for specifying for me

18. ### WBahn Moderator

Mar 31, 2012
23,069
6,920
This is the first I have every heard of either.

I guess when I was learning this stuff, we simply used it enough (at first by drill and then later just because we didn't have calculators) that we internalized it very quickly and firmly.

I always had similar feelings about "FOIL" to remember how to multiply to binomials together. It's like, "Duh! How about just applying basic arithmetic rules like, say, the distributive propery?" But now I run into students that tremble at the sight of having to multiply even a binomial and a trinomial because FOIL doesn't work and they are of the calculator generation and so they simply don't know how to use something like the distributive property. Yes, they recall hearing about it long ago in some math class at some point, but it's unfair to expect them to recall stuff from so long ago at the drop of a hat.

DerStrom8 likes this.
19. ### sby64 New Member

Sep 29, 2012
6
0
Interesting answers and comments. A great place to learn. I was taught that the following expression may not always be correct:

....6/12=5/10.......=1/2=0.5

Can you guess why or when?

20. ### WBahn Moderator

Mar 31, 2012
23,069
6,920
You need to supply some context. The thread (at least the last page of it) has been about order of operations. You are only giving a single operation unless you are using the equals sign as an operator, in which case you have to define the syntax in use.

If you are talking about the issue of integer division, then you again need to specify the context.