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
I originally figured that 288 was correct, and then got talked into the other. So, I hit the old algebra book. It really didn’t discuss this specific form; however, the precedence rules along with the associative and communitive rules just don’t provide a means to invent an imaginary parenthetical grouping. The answer really has to be 288.
The backslash is used to denote division not to make a fraction out of the problem. I have to use the backslash as my keyboard doesn’t have the division symbol.
I agree that those are the same; however, that is not the problem: The problem is: 48 divided by 2(9+3); not 48 divided by 2 times 12. 48 is the numerator and 2(9x3) is the denominator. 48 divided by 24 = 2.
Why is it that none of the "2" faction can cite any actual sources for their beliefs?
I gave the google page for order of operations. Pick one. Look at it.
“and an equation”
Sorry, I meant “an expression”.
THAT is what screws things up for us old-timers. Seriously, when you've used the "Vinculum" for so many years, you see the "/" as a horizontal line separating the numerator from the denominator. All the junk on the left divided by all the junk on the right. Heck, in the original expression, I think they used the division sign and I still saw it as a "/" which I read as a horizontal line. Old habits die hard.
I'll have to watch that one next time. Thankfully, I don't use the computer to do these things.
THAT is what screws things up for us old-timers. Seriously, when you've used the "Vinculum" for so many years, you see the "/" as a horizontal line separating the numerator from the denominator. All the junk on the left divided by all the junk on the right. Heck, in the original expression, I think they used the division sign and I still saw it as a "/" which I read as a horizontal line. Old habits die hard.
I'll have to watch that one next time. Thankfully, I don't use the computer to do these things.
Kindly divide my post by 2!
My post 337 explains why I see/saw things the way I did. It's danged hard to undo a decade of pre-computer math learning. Fact is, there is something of a trap in using "horizontal" notation for those of us that are very accustomed to having our fractions written in a vertical manner.
I won’t, but I will multiply it by one half!
Check Wikipedia:
"Division is often shown in algebra and science by placing the dividend over the divisor with a horizontal line, also called a vinculum or fraction bar, between them. For example, a divided by b is written
This can be read out loud as "a divided by b", "a by b" or "a over b". A way to express division all on one line is to write the dividend, or numerator then a slash, then the divisor, or denominator like this:
This is the usual way to specify division in most computer programming languages since it can easily be typed as a simple sequence of ASCII characters.
A typographical variation, which is halfway between these two forms, uses a solidus (fraction slash) but elevates the dividend, and lowers the divisor:
Any of these forms can be used to display a fraction. A fraction is a division expression where both dividend and divisor are integers (although typically called the numerator and denominator), and there is no implication that the division needs to be evaluated further. A second way to show division is to use the obelus (or division sign), common in arithmetic, in this manner:
"Fractions are hard - multiply it by 0.5 instead!
Page 3 is especially enlightening as to why the user should read the owners manual when using a calculator.
“If the problem was 48/2 x (9+3), 288 would be the correct solution, but that is not the problem.”
You obviously don’t know that 2(9+3) means 2 X (9+3).
the number immediately before something in parenthesis is a multiplier. It goes with what’s in the (..)s, not with what’s before it.
The answer is 288.
Those who have said the (.)’s have to be resolved first are correct. The only problem is the 2 goes with the (.)s...they can’t be separated on a whim....
the answer is 288.
__48__
2(9 + 3)
I saw it this way first also. It didn’t hit me quite right, however, so I went back to remind myself of the precedence rules. Those who get 2 are seeing 48/(2(9+3)), which is how it would be typed into the computer. Whoever suggested thinking of 48/2 as the coefficient of (9+3) had a good idea. The expression isn’t evaluated that way, but the grouping helps to see how the rules should be applied.
48/2(9+3) = (48/2)(9+3)
Distributing the (48/2) gives 216 * 72 = 288.
Or evaluating the original expression directly:
48/2(9+3) = 48/2(12) = 24(12) = 288
Yes, my post 308 had the same insight. I can understand people thinking everything to the right of “/” was the denominator. That’s a simple misunderstanding of notation.
But the people arguing that 2(3 + 4) and 2 * (3 + 4) are two different things, or that the distributive property means you ignore the rules of order are just grasping at straws.
SeaHawkFan wrote:
First you need to understand that 48 divided by 2 x (9+3) is not the same as 48 divided by 2(9+3).
and now you saying: I agree that those are the same; however, that is not the problem:
You seem to be changing what you say from post to post.
The problem is: 48 divided by 2(9+3); not 48 divided by 2 times 12. 48 is the numerator and 2(9x3) is the denominator. 48 divided by 24 = 2.
The original poster has a division sign in place of a backslash. The backslash is not meant for the problem to be written as a fraction with a numerator and a denominator. The backslash is another way of saying division just as * is used as x in multiplication.
Example 6, in particular, shows that there's two kinds of people in this world, TI-85 (old) and TI-86 (young). Whereas they show the results of TI-86 to be "as expected", I would have expected the results of TI-85 myself. Guess I'm getting old!
:-)
Wait. Now I’ve confused myself..
Also, note that the original expression did not use a "/", but a "÷"
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