48÷2(9+3) = ?

[d00df00d]

Originally Posted By: Vikas
48 gallons
2 gallon/hour
(9 + 3) hours/day

Equation:-
48÷2(9+3) = ? days

I wouldn't write it that way at all.

I probably would write it as the product of three fractions, arranged so that the "days" unit ends up in a numerator and all the other units cancel:
48 gal * (1 hr / 2 gal) * (1 day / (9+3) hr)

That, of course, simplifies to:
(48/2) * (1/12)

And the answer is 2.

 

[mechanicx]

Originally Posted By: d00df00d
Originally Posted By: Vikas
48 gallons
2 gallon/hour
(9 + 3) hours/day

Equation:-
48÷2(9+3) = ? days

I wouldn't write it that way at all.

I probably would write it as the product of three fractions, arranged so that the "days" unit ends up in a numerator and all the other units cancel:
48 gal * (1 hr / 2 gal) * (1 day / (9+3) hr)

That, of course, simplifies to:
(48/2) * (1/12)

And the answer is 2.


Exactly. You can't write a word problem that has a correct answer, and then write a formula incorrectly/vaguely to prove a point. Sneaky

.

 

[KrisZ]

Originally Posted By: mechanicx
Originally Posted By: d00df00d
Originally Posted By: Vikas
48 gallons
2 gallon/hour
(9 + 3) hours/day

Equation:-
48÷2(9+3) = ? days

I wouldn't write it that way at all.

I probably would write it as the product of three fractions, arranged so that the "days" unit ends up in a numerator and all the other units cancel:
48 gal * (1 hr / 2 gal) * (1 day / (9+3) hr)

That, of course, simplifies to:
(48/2) * (1/12)

And the answer is 2.


Exactly. You can't write a word problem that has a correct answer, and then write a formula incorrectly/vaguely to prove a point. Sneaky

.



Sure you can, just like writing down an equation the way it's punched into the calculator, but would not be expressed that way in a written form 40 years ago or in any school not allowing calculators in math class.

 

[Reelizmpro]

Originally Posted By: QuadDriver
Originally Posted By: Reelizmpro
I was curious...how do you 288 guys reciprocate 5(2+3)/8(1+2)?


If I read what you wrote the correct answer is:


1 / (5(2+3)/8(1=2))


Correct but to simplify further it's 8(1+2)/5(2+3). Would we all agree it's just flip flopped? I hope so. I also noticed you included all the terms instead of just 5/8 or 8/5. =]

So how would we convert 48 / 2(9+3) to a multiplication problem?

 

[d00df00d]

Originally Posted By: KrisZ
Originally Posted By: mechanicx
Exactly. You can't write a word problem that has a correct answer, and then write a formula incorrectly/vaguely to prove a point. Sneaky

.



Sure you can, just like writing down an equation the way it's punched into the calculator, but would not be expressed that way in a written form 40 years ago or in any school not allowing calculators in math class.

That doesn't change the fact that it's better to make the notation as clear as possible, and that if you fail to do so, you can't put all the blame on someone else for reading it incorrectly.

When it comes to calculators, I'm actually MORE cautious about notation because I can't see what they're doing behind the scenes to get their answers.

 

[3311]

PEMDAS!
P Parentheses first
E Exponents (ie Powers and Square Roots, etc.)
MD Multiplication and Division (left-to-right)
AS Addition and Subtraction (left-to-right)

Divide and Multiply rank equally (and go left to right).

Add and Subtract rank equally (and go left to right)

48÷2(9+3)
48/2(12)
48/2x12
24x12
288

Check this page for kids, I had forgotten about left to right,m=d and +=-.
:http://www.mathsisfun.com/operation-order-pemdas.html

 

[QuadDriver]

Originally Posted By: Reelizmpro
I also noticed you included all the terms instead of just 5/8 or 8/5. =]



Cuz as I said in another post your 'equation' is syntactically "the function named '5', that returns a value and accepts a single numeric value as input, whose returned value is divided by the returned value from the funcation named '8' who returns a value after being passed a single numeric value.

Context free grammar.

 

[Reelizmpro]

y divided by x is the same as y multiplied by 1 / x.

So how do you rewrite our equation?

 

[mechanicx]

Originally Posted By: Reelizmpro
Originally Posted By: QuadDriver
Originally Posted By: Reelizmpro
I was curious...how do you 288 guys reciprocate 5(2+3)/8(1+2)?


If I read what you wrote the correct answer is:


1 / (5(2+3)/8(1=2))


Correct but to simplify further it's 8(1+2)/5(2+3). Would we all agree it's just flip flopped? I hope so. I also noticed you included all the terms instead of just 5/8 or 8/5. =]



For 5(2+3)/8(1+2)the "288 guys" get:

Inside parentheses first:
5(5)/8(3)

Multiplying and dividing left to right:
25/8(3)=75/8

For the reciprocal of 5(2+3)/8(1+2):
1/(5(2+3)/8(1+2))

Inside parentheses left to right first:
1/(5(5)/8(3))

Inside parentheses multiply and divide left to right:
1/(25/8(3))=1/(75/8)=1*(8/75)

Multiply and divide left to right:
8/75

8/75 is the reciprocal of 75/8

Quote:
So how would we convert 48 / 2(9+3) to a multiplication problem?


48*1/2*(12)

 

[Reelizmpro]

Originally Posted By: mechanicx
Originally Posted By: Reelizmpro
Originally Posted By: QuadDriver
Originally Posted By: Reelizmpro
I was curious...how do you 288 guys reciprocate 5(2+3)/8(1+2)?


If I read what you wrote the correct answer is:


1 / (5(2+3)/8(1=2))


Correct but to simplify further it's 8(1+2)/5(2+3). Would we all agree it's just flip flopped? I hope so. I also noticed you included all the terms instead of just 5/8 or 8/5. =]



For 5(2+3)/8(1+2)the "288 guys" get:

Inside parentheses first:
5(5)/8(3)

Multiplying and dividing left to right:
25/8(3)=75/8

For the reciprocal of 5(2+3)/8(1+2):
1/(5(2+3)/8(1+2))

Inside parentheses left to right first:
1/(5(5)/8(3))

Inside parentheses multiply and divide left to right:
1/(25/8(3))=1/(75/8)=1*(8/75)

Multiply and divide left to right:
8/75

8/75 is the reciprocal of 75/8

Quote:
So how would we convert 48 / 2(9+3) to a multiplication problem?


48*1/2*(12)



Let's not operate on anything yet. You acknowledge the reciprocal here:
For the reciprocal of 5(2+3)/8(1+2):
1/(5(2+3)/8(1+2)) ...OR 8(1+2)/5(2+3)

y divided by x is the same as y multiplied by 1 / x.

So in our original problem 48 / 2(9+3) what is Y and what is X?

according to you, Y = 48 and X = 2 but what about the (9+3)? Why the separation? In the previous example which we agree to be correct...you took the entire numerator and denominator NOT (8/5) (1+2)(2+3). X = 2(9+3) The reciprocal of 2(9+3) is [1/(2(9+3))]

 

[crinkles]

my sis being an actuary with many years of math and financial math behind her, says the right answer is 288...

 

[mechanicx]

Originally Posted By: Reelizmpro
Wow. Leave it alone...don't operate on it. You acknowledge the reciprocal here:
For the reciprocal of 5(2+3)/8(1+2):
1/(5(2+3)/8(1+2)) ...OR 8(1+2)/5(2+3) right?




No, the reciprocal of 5(2+3)/8(1+2):
1/(5(2+3)/8(1+2)) ... OR (5(2+3)/8(1+2))/1 . In other words 1/(5(2+3)/8(1+2)) equals 1*(5(2+3)/8(1+2))/1.

You are treating the "/" division symbol as a fraction bar that you can then find the reciprocal by flipping around. If that's the case you need to rewrite the question as, "What is the reciprocal of (5(2+3))/(8(1+2)) ?"
And I'm saying the problem as written requires me to either solve the equation by order of operation resulting in 75/8 or to reciprocate the whole problem with brackets resulting in 1/(1/(5(2+3)/8(1+2)). Deos that make sense?

 

[mechanicx]

Originally Posted By: Reelizmpro
Let's not operate on anything yet. You acknowledge the reciprocal here:
For the reciprocal of 5(2+3)/8(1+2):
1/(5(2+3)/8(1+2)) ...OR 8(1+2)/5(2+3)

y divided by x is the same as y multiplied by 1 / x.

So in our original problem 48 / 2(9+3) what is Y and what is X?

according to you, Y = 48 and X = 2 but what about the (9+3)? Why the separation? In the previous example which we agree to be correct...you took the entire numerator and denominator NOT (8/5) (1+2)(2+3). X = 2(9+3) The reciprocal of 2(9+3) is [1/(2(9+3))]


You edited your question in a way that makes it easier to answer where the differences is.

I'm not seeing "/" as a fraction bar, but as a normal division symbol. If you mean everything after "/" is considered the denominator then you have to put it in parentheses or at least draw a discernable fraction bar which is admittedly hard to do here. You are defining the problem as y/x and I'm saying it's more like y*x with Y=48/2 and X=(9+3).

If you asked me the reciprocal of 48 / 2(9+3) I would interpret it as 1/y*x which is 1/288. Maybe I'm wrong for not looking at the "/" as a fraction bar, but until we agree on that we'll never agree.

 

[Reelizmpro]

Originally Posted By: mechanicx
Originally Posted By: Reelizmpro
Wow. Leave it alone...don't operate on it. You acknowledge the reciprocal here:
For the reciprocal of 5(2+3)/8(1+2):
1/(5(2+3)/8(1+2)) ...OR 8(1+2)/5(2+3) right?




No, the reciprocal of 5(2+3)/8(1+2):
1/(5(2+3)/8(1+2)) ... OR (5(2+3)/8(1+2))/1 . In other words 1/(5(2+3)/8(1+2)) equals 1*(5(2+3)/8(1+2))/1.



Uhhhh WHAT? 1*(5(2+3)/8(1+2))/1 is just our original equation. What is the reciprocal?

1/(5(2+3)/8(1+2)) *[8(1+2)/8(1+2)] = 8(1+2)/5(2+3)

it IS a fraction. Very simply, y divided by x is y multiplied by (1/x).

 

[mechanicx]

Let me try to explain it one other way. You are saying "/" in 5(2+3)/8(1+2)is a fraction bar with 5(2+3) the numerator and 8(1+2) the denominator, and so the to find the reciprocal it can be flipped around. Simplified 25/24 and the reciprocal is 24/25.

I'm saying since there it is not written as (5(2+3))/(8(1+2))then it is not clear that "/" is a fraction bar and the problem is a fraction. Simplified 75/8 and the reciprocal is 8/75. I'm being consistent. Does it make sense now?

 

[mechanicx]

Originally Posted By: Reelizmpro
it IS a fraction. Very simply, y divided by x is y multiplied by (1/x).






No it ISN'T a fraction the way it is written. Go back and reread what I said. You are just not getting my point. You can't define y and x after the fact. You have to state it beforehand.

 

[Reelizmpro]

Originally Posted By: mechanicx
Let me try to explain it one other way. You are saying "/" in 5(2+3)/8(1+2)is a fraction bar with 5(2+3) the numerator and 8(1+2) the denominator, and so the to find the reciprocal it can be flipped around. Simplified 25/24 and the reciprocal is 24/25.

I'm saying since there it is not written as (5(2+3))/(8(1+2))then it is not clear that "/" is a fraction bar and the problem is a fraction. Simplified 75/8 and the reciprocal is 8/75. I'm being consistent. Does it make sense now?


I'm sorry, I thought that was understood when I asked for the reciprocal. Here you go...(5(2+3))/(8(1+2)).

The point I was trying to make is that y divided by x is y multiplied by (1/x). 48 / 2(9+3) = 48 * 1/(2(9+3)) with x = 2(9+3)...not just 2. Was just trying to show the problem from a different angle.

 

[Reelizmpro]

Bare with me...

Now without solving, the reciprocal of (5(2+3))/(8(1+2)) is (8(1+2))/(5(2+3)). Which is proven here...

http://www.algebra.com/algebra/homework/Inverses/FIND-reciprocal-of-a-FRACTION.solver

So the reciprocal of 2(9+3) is 1/(2(9+3))

In the end, when you multiply both fractions together you get 1. This is the essence of the reciprocal property.

So 48 * 1/(2(9+3)) = 2

I'm trying to prove it's incorrect to just take the 8 from 8(2+3), just as it's incorrect to just take the 2 from 2(9+3).

 

[Quattro Pete]

Originally Posted By: Reelizmpro

So 48 * 1/(2(9+3)) = 2


You do realize that this outer parenthesis wasn't there in the original problem, and that's why the answer was 288, right?

Just checking...

 

[Volvo_ST1]

Originally Posted By: Reelizmpro
Bare with me...


I prefer doing math while wearing clothes.