Posted on 04/12/2011 1:32:09 PM PDT by grundle
Texas Instruments TI-85 says:
48÷2(9+3) = 2
But Texas Instruments TI-86 says:
48÷2(9+3) = 288
The way the problem was stated initially was ambiguous.
Actually I think age is the problem. The TI-85 is over 15 years old. The expression is poorly written and can be two calculated two different ways, using two different interpretations of the rules. Modern rules result 288 and old school rules result 2.
Well, let’s see.
I wrote my first “Hello World” program in Forgo (a stripped down Fortran) on an IBM 1620 in 1963.
And I think the correct answer is 288.
“Notice the 288 crowd always seperates the 2 from the (9+3) without any reason other than to say the / following the 48 should go first.”
The ‘crowd’ doesn’t say it should go first. The rules of math say so. Operations in parens are first, followed by div and mult, followed by add and subt. If 2 operators have same precedence, the leftmost operation is evaluated first.
The original poster's question concerned a programmable calculator. Therefore other such calculators are worthy of examination, such as the well-known bc, "an arbitrary precision calculator" which yields the following:
That is not the problem; it is 48/2(9+3).
Showing all the work:
48/(2x9 + 2x3) Distributive property =
48/(18 + 6) Simple multiplication =
48/24 Simple addition
48/24 = 2
Please tell me where this is faulty? Do you even know about the distributive property?
Here is a link that even a third-grader can understand:
http://www.freemathhelp.com/distributive-property.html
The only thing worse than being wrong is to maintain ones ignorance in the face of an undisputable fact.
The correct answer is 2.
“Can you cite a rule anywhere that says any calculation that looks like the distributive property of multiplication voids the normal precedence of operations in an algebraic equation?”
The Order of Operations which is 4 rules, NOT 6.
P: Simplify inside parentheses first.
E: Then apply Laws of Exponents
MD: Then multiply OR divide from left to right as it occurs
AS: Then add OR subtract from left to right as it occurs
(Too bad math textbook writers seldom know laws of arithmetic.)
The Distributive Law doesn’t apply for this expression because of the Order of Operations. The Distributive Law would apply if there was a + or - before the 2(9 + 3).
So, 48/2(9 + 3) = 48/2(12) = (48/2)(12) = 24(12) = 288
48/2(9+3) + ???????
=
(48/2) * 48/(9+3) =???????
24 * 48/12 = ?????????
24 * 4 = 96
easy!
No, we understand that.
They even acknowledge that the parentheses needs to be solved first, but somehow don’t understand or won’t admit that solving the parentheses yields an answer of 24.
9 + 3 is 24?
When I solve the parentheses, I solve what is inside the parentheses. What do you do?
They ignore the distributive rule.
No, we follow the order of operations. Division and multiplication have the same precedence, so you go left to right.
Can you cite a rule anywhere that says the distributive property means you can ignore the order of precedence and do multiplication first? Can you cite a rule that says when multiplication is implied rather than explicit that you have to do that multiplication first?
You have the whole internet. Should be easy to find.
2(9+3) IS the same 2*(9+3)... the problem is... you forgot to start from the LEFT.. “48÷2”
make a BIG difference, obviously..
Don’t tell me. I was asking those who think the answer is 2 to provide a rule showing their thinking is correct.
Here’s what bothers me about the answers you guys have given:
It requires that the assumption be made that 48/2 is not the coefficient in front of the parenthetical expression.
Being represented in a left-to-right form, I have assumed a left-to-right parsing schema.
Using x for the value 48 would give x/2(9+3) as the equation.
Perhaps because I have been jaded by my computer science background, I read that as x/2 times the parenthetical sum.
In any event, It’s been a fun debate.
The original notation is poor... No serious math student would write a math expression that way, unless they were lazy or typing it out on an iPad keyboard (like me).... as written, both answers could be right...
“In the original problem [ 48/2*(9+3) ]
That is not the problem; it is 48/2(9+3)”
It *is* the same problem.
48/2(9+3) = 48/2*(9+3)
Here is the problem as copied and pasted from the title of the thread:
48÷2(9+3) = ?
It is not 48 divided by two times (9+3)
There is a huge difference.
If you are going to scew #s up like that.. It’s not even worth wasting my time...
I’m sorry. I thought I was helping you.
Oh well. Maybe someone who thinks the answer is 2 will read what I wrote.
“So, 48/2(9 + 3) = 48/2(12) = (48/2)(12) = 24(12) = 288”
UHHHH.............
So 48/2(9+3) = 48/2(12) = 48/2 * 48/12 = 96
!t’s just as valid a solution as your’s!
The correct answer to the universe is 2.........
“48÷2(9+3) = ?
It is not 48 divided by two times (9+3)”
The correct order of operations is the same no matter how you pronounce the problem in English.
48/2(9+3) = 48/2(12) = 48/2*12 = 24*12 = 288
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