48÷2(9+3) = ?

[grundle]

Texas Instruments TI-85 says:

48÷2(9+3) = 2

But Texas Instruments TI-86 says:

48÷2(9+3) = 288

[Fresh Wind]

Get rid of the toys and get a Hewlett-Packard reverse Polish calculator.

[re_nortex]

The distributive property of multiplication tells me that 2(9+3) = 2(9)+2(3) = 18+6 = 24. It is a single expression. It could be 2(a+b) or 2(x+y). The entire expression must be dealt with before the expression is used in the remainder of the equation.

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:

bc 1.06
Copyright 1991-1994, 1997, 1998, 2000 Free Software Foundation, Inc.
This is free software with ABSOLUTELY NO WARRANTY.
For details type `warranty'. 
48 / 2 * (9 + 3) 
288

Much of the math in computing is derived from the C language where the Operator Precedence rules have been adopted by ANSI for several decades.

[SoothingDave]

The distributive property is irrelevant. Unless you imagine there are parentheses around the 2(9+3) that AREN’T there.

Division and multiplication have equal precedence. Left to right tells the order.

288

[Retired Greyhound]

LOL, I think you just solved the deficit crisis

[meyer]

Nothing places multiplication above division, but 2(9+3) is not the same as 2*(9+3). Alone, the answer is the same, but used in an equation, they are not the same thing.

Individually, the result is 24 either way, but when used in an equation, adding the “*” sign between the 2 and the parenthesis lowers the priority to the equivalent of the division process, which produces a different (and algebraically incorrect) answer.

[SoothingDave]

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?

Thanks

[Ladysmith]

That’s how I was taught. Agrees with the PEMDAS rule.

Answer = 2

[SeaHawkFan]

When you have a bunch of operations of the same rank, you just operate from left to right. Not true. In fact, the problem is 48 divided by 2x12 = 2. If it was 48 divided 2 x (9+3), 288 would be correct; butthat is not the problem. IOW, the problem is 48 over 2x(9+3) = 2.

[Forty-Niner]

“Except that the 2 is preceded by “48/”.

If the 2(9+3) was the whole equation, then there would be no discussion over precedence.”

Using your logic would have gotten my knuckles rapped pretty well by Sister Mary Joseph’s ruler! :)

Guess all those years taking algebra/calculas/trig/geometry were wasted......LOLOLOLOLOL

[Bikkuri]

Sweet :) needed you about 2 hours ago ;)
Wish I had the speaking/typing skills you do :D

Bikk

[SoothingDave]

but 2(9+3) is not the same as 2*(9+3).

Nonsense. The multiplication operator is implied in the first, but the math is exactly the same.

Please cite a source saying that an implied multiplication does not follow the rules of operator precedence.

[jwalsh07]

Both calculators gave the correct answer according to their programming. TI-85 gives precedence to implied multiplication over explicit multiplication/division. Problem is data entry on TI-85. Correct answer is 288.

When using a TI-85 use parentheses when in doubt or use the * to make multiplication explicit.

Carry on.....

[spunkets]

"The distributive property of multiplication tells me that 2(9+3) = 2(9)+2(3) = 18+6 = 24. "

Wonderful, however this problem is: /2(9+3) = *1/2(9+3) = 4.5 +1.5 = 6. The division sign causes the factor to be "1/2", the multiplicative inverse of the value operated on, not "2"-as if there was only a simple multiplication sign. Note that the concept of multiplicative inverse allows for the commutative property to hold. Then 0.5*12*48 = 48*12*0.5 = 12*0.5*48 = 48*0.5*12 = 288.

[hattend]

That’s how I was taught to solve.

Parenthesis first, then the rest of the equation.

[Bikkuri]

well... math has everything to do with this problem (formulas).

I am not “dissing” you in any way at all... I just see the outcome different than you see it. And, obviously one of us is incorrect... (or in this day and age... are we_?)....

[jwalsh07]

Of course, I could be wrong. :-]

[RBranha]

“Nothing places multiplication above division, but 2(9+3) is not the same as 2*(9+3). Alone, the answer is the same, but used in an equation, they are not the same thing.”

They absolutely *are* the same.

By distributing first, you are multiplying before evaluating the operation(s) in the parens. This is incorrect.

In the original problem [ 48/2*(9+3) ] the parens are evaluated first, and leave a mult and div operation, which are evaluated from left to right.

48/2(9+3) =
48/2*12 =
24*12 =
288

[Forty-Niner]

“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?”

Sister Mary Joseph’s 12 inch rule rapped across the hand. 5th grade algebra class 1950’s.

Do they still teach algebra in the 5th grade?

[SoothingDave]

So, you can’t cite any rule, then? You have the whole wide internet at your disposal.

[RBranha]

PurpleMath says:
“When you have a bunch of operations of the same rank, you just operate from left to right.”

And SeaHawkFan says:
“Not true.”

If you claim PurpleMath is incorrect, you’ll have to cite your source. However, you should be aware that Excel, Google, C#, JavaScript, my RPN HP50g, PHP, and bc all say that the answer is 288.