Why you can't trust your calculator, or What is 48/2(9+3)?

Good lord, when I was in school, we did not use any other symbol than plus, add, divide, multiply, fractions were used, not percentages, long division was pain, never mastered it, however, I was good in history, writing (pen and paper), geography, and basic science, like water is two atoms of hydrogen and one of oxygen, actually that's all I do remember of that lesson!

y = 48 / 2(9+3)

To throw fuel on the fire... lets refactor.
Start by moving the "2" (sorry for the leading zeroes- used for formatting only):
y = 48 / 2(9+3)
2 = 02 / 00002

... end up with ...
y / 2 = 24 / (9+3)

So, put that 2 back on the other side so that:
(y / 2) * 2 = (24 / (9 + 3)) * 2
y = 24 / 12 = 2 = 2 * 2 = 4
????

Maybe go the other way and move the (9+3):
y / (9+3) = (48 / (9+3)) / (2(9+3) / (9+3))
So, y / 12 = (48 /12) / (24 / 12)
Then, y / 12 = (4) / (2)
y/12 = 2; y = 24?

I need some licorice.

Waiting for someone to point out my errors.

so is 2/1+1 equal 1 or 3 ?

that is why Obelus ÷ is better then Vinculum / where writing on ine line rather then on a page.

windowns XP calculator have / to mean ÷ so 48/2(9+3) is 288

Might be worth pointing out that with the equation:
48 / 2(9+3)

"2(9+3)" is ONE term and cannot be distributed using reciprocals unless it is used as a whole. It MUST be solved before any other math is complete.
Just as 2x is one term, and 2 * x are two terms in the equation. Were it written as "2 * (9+3)" that would make two terms.

The latter, "2 * (9 + 3)" is explicit, as in this is exactly how you want it evaluated expression, but "2(9+3)" is implicit as it is one term and it is implied that it will be solved for before any other calculation can depend on it. The fact the "2" is directly adjacent to the parenthesis should be sufficient for anyone to know that it is a direct part of that calculation. It is like 2x, not 2 * x where distributive and commutative properties work without fail.

This is where some things fall apart: not realizing or recognizing what term or factor in an equation is an independent or co-dependent entity.

so 1/2x=0.5x ? or 1/2x=1/(2x) ?

reply to post by bastion


Wrong. There is a reason the older calculator answered incorrectly (2) and every calculator sense then answers as 228. There really is no other way to interpret it without adding/changing or misinterpreting the problem.

reply to post by abecedarian


No. Wrong. There is an implied multiplication sign between the 2 and the "(." Following order of operations you are left with 48/2·12. Then following order of operations again you solve left to right.

You guys are wrong and I dont understand how you can over complicate it. The older calculator was incorrect. The consensus of the article even says 288. I can type it into mu smart phone and when I put a parenthesis it automatically puts an multiplication symbol between the number/letter and the parenthesis.

abecedarian
y = 48 / 2(9+3)

To throw fuel on the fire... lets refactor.
Start by moving the "2" (sorry for the leading zeroes- used for formatting only):
y = 48 / 2(9+3)
2 = 02 / 00002

... end up with ...
y / 2 = 24 / (9+3)

So, put that 2 back on the other side so that:
(y / 2) * 2 = (24 / (9 + 3)) * 2
y = 24 / 12 = 2 = 2 * 2 = 4
????

Maybe go the other way and move the (9+3):
y / (9+3) = (48 / (9+3)) / (2(9+3) / (9+3))
So, y / 12 = (48 /12) / (24 / 12)
Then, y / 12 = (4) / (2)
y/12 = 2; y = 24?

I need some licorice.

Waiting for someone to point out my errors.

edit on 3/2/2014 by abecedarian because: (no reason given)

This is hilarious. Ive never seen someone workso hard to over complicate a third grade math problem and get the wrong answer.

48/2·(9+3)
48/2·12
24·12
288

Simple and correct. As agreed upon by everyone who knows what they are doing.

Implied or explicit the answer is 288. Working it out in my head I got the same answer. Then checking with my smartphone and my calculator which is a ti graphing calculator.

Makes sense to me. However, it all depends on how the equation is written. So after doing the parentheses the division has to be done first. With the way it was wrote; how can you build a 24x12 box without first dividing your 48x box?

If you think the answer is 288, please read my post here. Its algebra based solution with simple substitution for the proof of work.
It is very clear the answer is 2.

The reason your calculator show 288 because of - "immediate execution", the calculator DOES NOT KNOW about the parentheses/bracket/() before hand. A human simply will see the () and solve it first, calculator simply solve the keyed input immediately on the spot and did not see the () until you key it in, thus giving wrong answer.

Please stop replying to this thread so tl;dr people can see the solution.

if you have y/b(a+b) and y=1 b=2 its 1/2(a+b).


if you have y/b(y/b)
and y=1 b =2
y/b(y/b)=1/2(1/2) =0.25

why would addition in the parenthesis make a difference ?

dude1
if you have y/b(a+b) and y=1 b=2 its 1/2(a+b).


if you have y/b(y/b)
and y=1 b =2
y/b(y/b)=1/2(1/2) =0.25

why would addition in the parenthesis make a difference ?

substitute y = 3, b = 4 and see if its still the same.
y/b(y/b) is equal to
y
--------
b(y/b)

but

(y/b)(y/b) is (x)(y) or simply xy
---------------------------------------------------
Proof of work

How about we simplify y/b(y/b) to y/z ?

y = y // total number of cow
z = b(y/b)

//z is number of grass bales can eat
// b is number of stomach
//(y/b) is grass bales size each stomach can fill

y/z = ? // how many cows can eat how many bales of grass ?

substitute y =3, b = 4
z = b(y/b) // how many bales can eat ?
z = 4(3/4) // 4 stomach can eat 3/4 bales of grass EACH
z = 3 // so 4 stomach can eat 3 bales
//we got y = 3 cows, so....
y/z = 3/3 = 1 // 3 cows, eating 3 bales = 1 bales each

Proof of work
y/b(y/b) = 3/4(3/4) = 0.75*0.75 = 0.5625 // really ? more cows = less grass bales ?

This proof y/b(y/b) is not equal to (y/b)(y/b)
so your y = 1, b = 2 only work in that simple condition, change a bit and it break.

Lets try with main equation
48/2(9+3) translate to 48 cows, with 2 stomach each, which can fill 9 and 3 bales of wheat
means, each cows can eat 2(9+3) = 2(12) = 24 bales of grass
means 2 cows share 1 bales of grass.

So, anyone who find their cows eating 288 bales of grass EACH is pretty offshoot.
This is quite fun to do algebra, it light up some of my gray cells

If you think the answer is 288, please read my post here. Its algebra based solution with simple substitution for the proof of work.
It is very clear the answer is 2.

The reason your calculator show 288 because of - "immediate execution", the calculator DOES NOT KNOW about the parentheses/bracket/() before hand. A human simply will see the () and solve it first, calculator simply solve the keyed input immediately on the spot and did not see the () until you key it in, thus giving wrong answer.

Please stop replying to this thread so tl;dr people can see the solution.

reply to post by NullVoid


Yes calculators DO know about parenthesis before hand. The answer is 288 when you do parenthesis first.
We arent talking about cheap calculators. Hell my calculator wouldnt have parenthesis inputs if it didnt know their purpose.

NullVoid

sheepslayer247
I'm not a math wiz or anything, but I was taught the parentheses are dealt with first: (9+3) = 12

Then you would calculate 48/2: 24

So you are left with 24(12) or 24x12. That equals 288.

I'm smarter than a calculator!

I got 2.

I dont know about BODMAS or whatever, but it is a must to simplify the equation first, so...

48/2(9+3)
after (9+3) = 12, you are left with 48/ 2(12), simplify!, so 48/24, simplify! so.... 2
trying algebra approach,
a/b(x+y)
a/(bx+by)

substituting a=48,b = 2, x = 9 and y = 3...
a/b(x+y) = a/(bx+by)
a/(bx+by) = 48/2(9+3)
a/(bx+by) = 48/(2(9)+2(3))
a/(bx+by) = 48/(18+6)
a/(bx+by) = 48/(24)
a/(bx+by) = 2

notice, you still have to solve the bx+by part first ? if you solve 48/2 part first, that would break the algebra
to properly arrive at 288, a new bracket/paren should be introduce
(48/2)(9+3)
moving to algebra
(a/b)(x+y)
((a/b)x) + ((a/b)y)
substitute
((a/b)x) + ((a/b)y) = ((48/2)x) + ((48/2)y)
((a/b)x) + ((a/b)y) = (24x) + (24y)
((a/b)x) + ((a/b)y) = (24(9)) + (24(3))
((a/b)x) + ((a/b)y) = (216) + (72)
((a/b)x) + ((a/b)y) = 288

so, in short,
48/2(9+3) = 2
(48/2)(9+3) = 288
or am I missing something ?

edit on 1-3-2014 by NullVoid because: (no reason given)

You answered the problem incorrectly. After you do the parenthesis you then solve left to right. You guys that think you multiply 2 by 12 first are wrong. The answer is 288.

See the cow problem above.
Hope this helps.

reply to post by NullVoid


I dont have to. The OPs own source indicates 288 is the answer. OP misinterpreted it.

A number next to a parenthesis always implies multiplication so it doesnt need to be explicit.

reply to post by GogoVicMorrow


Yes, but when translated to algebra its treated explicitly. It have to. Since its explicit and algo based, you can put any number and still get the correct answer.

GogoVicMorrowThe answer is 288 when you do parenthesis first.

Are we talking about this
a/b(x+y)
which is
a
--------
b(x+y)
Result = 2

or this

(a/b)(x+y)
Result 288

?
Convert it to algebra and try substitute with different number, there are differences. Show your work so we all can see how you can arrive at 288 without adding parenthesis/bracket.

The implicit function xy, where x=2, y=(9+3), can be written as 2(9+3). The result of this must be resolved before any further math can be completed. Pure, simple, true.

But for fun, again....
48 / 2(9+3) and you can't solve the equation until 2(9+3) is solved first, since as mentioned 2(9+3) is one term in the equation and cannot be explicitly distributed across the equation with having been solved for first (i.e. = 24).

2(9+3) is ONE term and must be solved for before continuing evaluation of the equation.

Multiplication by juxtaposition. Nothing much else needs said, as that is the consensus of the mathematical community.
That is also what I was taught from 1982 through 1988 by my pre-algebra, algebra, geometry and trig teachers.
I'm sorry your teachers weren't up to snuff.

Imagine these thoughts applied to E=MC^2. If M = 48 and C^2 = 1/2(9+3) what would your answer be?

reply to post by NullVoid


But its not algebra, there are no abstractions. It's a straightforward math equation.