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
grrrr... thank you again..
I give up :p
Going to attempt to finish reading the posts.. and get to bed (0830 hre.. should have been in bed 10 hours ago :p)
Tonikaku (anyway)..
Bikk
2(9+3)= 2*(9+3)= 18+6, but the equation in question is /2*(9+3)= 4.5+1.5. There are 3 factors in the original equaiton: 48*(1/2)*(9+3), each of which commutes with any of the others. The / sign just indicates: multiply by the multiplicative inverse.
" How would you solve 48/2(a+b)?"
48*(1/2)*(a+b)= 48*0.5*(a+b)=0.5*48*(a+b) = (a+b)*48*0.5 = 0.5*(48a+48b) = 24(a+b)...
"do you see 48/(2a+2b)? It's kind of whacky using the "/" sign instead of writing it out the way math should be written. "
As above... The / sign just means multiply by the multiplicative inverse. Then it's 48(0.5a+0.5b).
Radio Shack says 288
I’m starting to understand the distributive argument you and others are presenting better, but I still have a problem not seeing 48/2 as the multiplier outside the parenthesis.
That would make the expression 24(9+3) = 24(12) = 288.
In order to evaluate the 2(9+3) before the 48/2, one would have to ignore the order of operations in the overall equation. I can’t find anything that tells me to ignore the left-to-right precedence outside the parenthesis.
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.
Whereas I can see x/24 as a possible answer.
Here is the applicable portion from the web site I posted earlier:
Distributive Property
The distributive property is actually a very simply concept to learn and apply. It will allow you to simplify something like 3(6x + 4), where you have a number being multiplied by a set of parenthesis. Let’s start with a simple problem:
6(4 + 2)
Based on the order of operations, you know that anything inside parenthesis should be done first. Adding 4 + 2 is simple enough, resulting in this:
6(6)
When you see a number next to parenthesis like this, it means multiplication, so what we really have here is this (remember that * means multiplication):
6 * 6 = 36
If you can’t figure this out, you are hopelessly confused.
If 6(6)=36 then 2(12) must equal 24.
Yeah, but it looks stupid when we don't have a neat horizontal line between the numerator and the denominator as the good lord intended. :-)
I think the major disconnect here is between those who see a “/” sign and just assume that everything after it is in the denominator of the division expression.
And those who see “/” as a mathematical operation between expressions on either side of it.
The former force implied parentheses into their evaluation.
The latter do not.
i think it's an implicit *
I work in a 4th grade classroom and we do this sort of problem all the time. The way we teach the kids:
48/2(9+3).....order of operations = PEMDAS or Please Excuse My Dear Aunt Sally...
1. parenthesis 9+3 = 12
2.multiplication and division are equal so you start at the left and work right......48/2 = 24
3. 24*12=288
That's how we teach our 4th graders.
What happens when you take 48/2 and “distribute” it to (9 + 3)?
You get 24 times 9 plus 24 times 3.
Which is 216 + 72
Which is 288.
Using the distributive property.
48/2(9+3)
Don’t distribute first! Distribution is a multiplication operation, which is done *after* the operations in parenthesis. When the ops in parens are evaluated first, there is no distribution left to do:
48/2(9+3) = 48/2(12) = 48/2*12 = 24 * 12 = 288
Parens first
Mult and div next
Add and subt last
If 2 operators have equal precedence, evaluate from left to right.
BINGO
48÷2*(9+3) = 48/2*(a+b)= (48*9)/2+(48*3)/2 = 48*(1/2)*(12) = 12*48*0.5
"It is not 48 divided by two times (9+3)
Yes it is. Otherwise it would be written: 48/(2(9+3)) = 48/(2*12) =48÷(2*12)
"There is a huge difference."
When you insert parenthesis that were never in the original equation; of course there is! You just changed the meaning of the equation by doing so.
Yes it is......order of operations requires that since multiplication and division are equal in terms of solving, you work the problem left to right.
Parenthesis is first (9+3=12)...then, working the problem left to right is 48/2 = 24. THEN 24x12 = 288.
It’s exciting to see that the Order of Operations is still being properly taught somewhere in our failed school system in America!
Can you teach your 4th graders the aritmetic properties of fractions? Way too many students do not understand that multiplication/division rules do NOT apply to addition/ subtraction (& visa versa) and totally fail algebra when they get to simplifying rational expressions & solving eational equations.
First you need to understand that 48 divided by 2 x (9+3) is not the same as 48 divided by 2(9+3).
2(12) is a number and that number is 24.
The problem is 48 divided by 2(12) and not 48 divided by 2 times 12.
The distributive property eliminates any confusion as to what should be calculated first:
An easy way is to think of 2(9+3) as (2(9+3)). By convention, it has been agreed that 2(9+3) is to be treated as (2(9+3)).
If the distributive property did not exist, 288 would be the correct answer, but it does exist, so the correct answer must be 2.
As for having a problem not seeing 48/2 as a valid multiplier, you just need to accept that the rules are the rules and having such rules make mathematical life simpler and less confusing. In your case, if you did not know the rule, I can see why you thought the answer was 288.
Now that you have additional information, I hope that you can now understand why the answer must be 2.
That's roughly what I was seeing - the division of two distinct expressions that required simplification before the dividing process needed to take place. Spunkets kind of broke it down a bit for me, got me to see it the other way.
That is a sad statement about the the teaching of math in our schools.
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