Math Test

[jsharmon7]

It would be interesting to see which camp has people who took more than just basic algebra and trig in high school

I have a feeling it'd definitely be telling.

I failed college calculus, so I'm out!

 

[jtdet01]

I posted the Geek Test thread in response to the Math Test thread ...

If you did not respond to The Math Test or the Geek Test, please take a look...

Math Test: https://www.indianagunowners.com/forums/break_room/271638-math_test.html
Geek Test: https://www.indianagunowners.com/forums/break_room/271787-geek_test.html

 

[Bunnykid68]

It is still 9 unless someone can fully explain why you would multiply the 2 to (3) before you divide the 6 by 2.

I have confirmed my answer with both kids and one geometry teacher

 

[Double T]

It is still 9 unless someone can fully explain why you would multiply the 2 to (3) before you divide the 6 by 2.

I have confirmed my answer with both kids and one geometry teacher

Because from my POV the 6/2(2+1) should be simplified as such:

6
______
2(2+1)

the reason I fell that the problem should be done in such a way is because it is not notated as (6/2)(2+1), the use of parenthesis applies the 2 to the (2+1) and gives that factor precedence over the / sign.

I agree that the problem should be written better, and as such the answer is ambiguous.

Calculators aren't foolproof either they have given reproducible errors, though I seriously can't remember what my calc teacher showed as the errors.

 

[CathyInBlue]

Anyone who claims the answer is 1, explain why the answer to "6 - 2 + 2" should be 2 (incorrect. but arrived at by the same logic that says 6/2(1+2) = 1) and not 6 (correct).

 

[Bunnykid68]

Because from my POV the 6/2(2+1) should be simplified as such:

6
______
2(2+1)

the reason I fell that the problem should be done in such a way is because it is not notated as (6/2)(2+1), the use of parenthesis applies the 2 to the (2+1) and gives that factor precedence over the / sign.

I agree that the problem should be written better, and as such the answer is ambiguous.

Calculators aren't foolproof either they have given reproducible errors, though I seriously can't remember what my calc teacher showed as the errors.

But it is not even written like that, it is written like this 6 ÷ 2 (2 + 1)

The use of the parenthesis means do the math inside, has nothing to do with outside. Once you add 1+2 you have (3) nothing left to do in the ( )


It is helpful to treat division as multiplication by the reciprocal (multiplicative inverse) and subtraction as addition of the opposite (additive inverse).

Which would give you 6 x 1/2 (2 + 1) Do math in ( ) then work left to right

 

[ATM]

Anyone who claims the answer is 1, explain why the answer to "6 - 2 + 2" should be 2 (incorrect. but arrived at by the same logic that says 6/2(1+2) = 1) and not 6 (correct).

Well, if you ignore the rules, you can come up with most any answer you like.

[FONT=Verdana, Arial, Helvetica, sans-serif]Da Rulez

1. Calculations must be done from left to right.[/FONT] [FONT=Verdana, Arial, Helvetica, sans-serif]
2. Calculations in brackets (parenthesis) are done first. When you have more than one set of brackets, do the inner brackets first.[/FONT]
[FONT=Verdana, Arial, Helvetica, sans-serif]3. Exponents (or radicals) must be done next.[/FONT]
[FONT=Verdana, Arial, Helvetica, sans-serif]4. Multiply and divide in the order the operations occur.[/FONT]
[FONT=Verdana, Arial, Helvetica, sans-serif]5. Add and subtract in the order the operations occur.[/FONT]

I guess people just forget their pre-algebra fundamentals from grade school.

 

[SkullDaddy.45]

math test? last time i took a math test Billy Horton took my lunch money and beat me up! but i'll bite MMmm i'll say "BACON!!" aint that the answer to everything?

 

[Tactical Dave]

 

[williamsjr22]

I get one but then again, I suck at Math.

 

[kyotekilr]

Anyone who claims the answer is 1, explain why the answer to "6 - 2 + 2" should be 2 (incorrect. but arrived at by the same logic that says 6/2(1+2) = 1) and not 6 (correct).

There is a fundamental difference between 6/2(2+1) and 6 divided by 2(1+2). When the problem reads 6 divided by 2(1+2) you do not just multiply by the reciprocal of 2 you multiply by the reciprocal of the whole term 2(1+2).

Subtraction and Division are not commutative. Commutative means ab=ba or a+b=b+a. Does 2-3=3-2? Of course not. However, does 3+(-2)=(-2)+3? Yes. The same goes for division. 2 divided by 3 does not equal 3 divided by 2. 3(1/2)=(1/2)3. In you problem 6-2+2 it means 6+(-2)+2, when it is written with addition you can work from both right to left and left to right and get the same answer
6-2+2 = -2+6+2= -2+2+6.
You are getting lost in the notation vs. meaning. We use the subtraction and division sign as short hand and it is works fine when you understand it's meaning.

If the original problem was written as 6/2(2+1) with the quotient 6/2 I would agree that the answer is 9. But when the division sign is used as an operation it really means to multiply by the reciprocal of the whole term following the division sign. In this case it is 2(2+1).

Working from left to right and working from right to left will yield the same answer if you understand what the notation really means. If you do a problem and come up with two different answer by working right to left than you do working left to right you are doing it wrong.

 

[Benny]

Well, if you ignore the rules, you can come up with most any answer you like.



I guess people just forget their pre-algebra fundamentals from grade school.

You must have never taken a math course past HS trig (according to some people in here).



I'll be the first to admit that when I took trig in HS, the class SUCKED. I think it had something to do with my teacher getting cancer and having an idiot sub almost the entire year, but the order of operations never changed.

There is a small case for 6/2(2+1) =1 if it's written LIKE THAT. I can see it even though it should be:

6
2(2+1)

But it is written, 6 ÷ 2(2+1).

 

[rhino]

6 ÷ 2 (2 + 1) =

Aside from going left to right as pretty much all of the math books from which I've been teaching advocate, there is also this (I think benny was getting at it, maybe someone else in the middle of the posts, but I'm too tired to read them all).

If you don't go left to right, you're forcing the denominator of the fraction to be "2 (2 + 1)"

So it would be like this:

6
-----------
2 (2 + 1)


But that's not what it says. As it's written, with no further information, the expression implies:


6 (2 + 1)
------------------
2


or


6
---------- (2 + 1)
2


So I'm siding with the answer being "9."


I don't play a math teacher on TV, but I am one in real life. For what it's worth.

 

[rhino]

Yeah, I should have read more before I posted my message. CathyInBlue has dominated here, and she clearly owns this topic.

She is correct and her reasoning is sound. Don't let pride get in the way of acknowledging it (you know who you are).

ATM was in for the win as well.

All who say "9" get credit on the exam.

 

[kyotekilr]

Thinking a problem can only be worked from left to right and not right to left means you do not know the commutative property ab=ba.

 

[Bunnykid68]

A few are wanting to make 2(3) some kind of special math equation, it is simply 2 x 3 and nothing more.

In a simple problem like this one there is no reason to keep the parenthesis after the math is done 6 ÷ 2 (3) = 6 ÷ 2x3. So even if you keep the parenthesis it is still only 2 x 3. The 2 next to(3) is not an exponent and can be ignored as it does not give any special meaning to the (3) it is simply part of the equation which must be solved left to right

Both my HS math kids agree and one of their Geometry teachers agreed as well. It may be a poorly written math problem but simply following PEMDAS the only answer is 9

 

[CathyInBlue]

There is a fundamental difference between 6/2(2+1) and 6 divided by 2(1+2).

*BING!* *BING!* *BING!* *BING!* We have a winner! Now, for $65,000 and the trip to Aruba, notationally, how do you disambiguate "6/2(2+1)" and "6 divided by 2(2+1)"?

*Bzzzzzt!*

Oh, I'm so sorry. Time's up. "6 divided by 2(2+1)" is "6/(2(2+1))". That is what you are attempting to mutate "6/2(2+1)" into.

When the problem reads 6 divided by 2(1+2) you do not just multiply by the reciprocal of 2 you multiply by the reciprocal of the whole term 2(1+2).

Which you would do and be correct that the answer is 1, if the notation were "6/(2(2+1))", but it is not. The notation is "6/2(2+1)", hence, you are wrong, because the answer is 9.

Subtraction and Division are not commutative. Commutative means ab=ba or a+b=b+a. Does 2-3=3-2? Of course not. However, does 3+(-2)=(-2)+3? Yes. The same goes for division. 2 divided by 3 does not equal 3 divided by 2. 3(1/2)=(1/2)3. In you problem 6-2+2 it means 6+(-2)+2, when it is written with addition you can work from both right to left and left to right and get the same answer
6-2+2 = -2+6+2= -2+2+6.
You are getting lost in the notation vs. meaning. We use the subtraction and division sign as short hand and it is works fine when you understand it's meaning.

If the original problem was written as 6/2(2+1) with the quotient 6/2 I would agree that the answer is 9. But when the division sign is used as an operation it really means to multiply by the reciprocal of the whole term following the division sign. In this case it is 2(2+1).

Oooo! Ooo! OOO! I think I see a slivver of light creeping into your mathematics world!

Okay!

"6/2(2+1)" is the same as "6 ÷2 × (2+1)", would you agree? And by the same mechanism for ×÷ as you used for +- in turning "6-2+2" into "6+(-2)+2" that would become "6× 1/2 × (2+1)", yes? What you are trying to do is turn "6 ÷2 × (2+1)" into "6× 1/(2 × (2+1))", which is fundamentally and logicly identical to turning "6-2+2" into "6+(-2+2)". If you are not willing to assert that "6-2+2" is equivalent to "6+(-2+2)", why are you so adamant that "6/2(2+1)" is equivalent to "6/(2(2+1))"?

Working from left to right and working from right to left will yield the same answer if you understand what the notation really means. If you do a problem and come up with two different answer by working right to left than you do working left to right you are doing it wrong.

There are techniques whereby you can work from right to left, but you are not using them here. If I had something like 6/2*3*4*5, then I could work right to left, to a point.

6/2*3*4*5 = 6/2*3*20 = 6/2*60

But at that point, I have to stop working right to left, because I've encountered a factor whose operator is no longer multiplication. This right to left order only works for factors joined by multiplication and terms joined by addition. It completely breaks down for division and subtraction, which is the basic mathematics fact that you have either forgotten, never learned, or were taught incorrectly.

The final answer to my above right to left example would be 3 * 60 = 180. Your method would see it mutilated into 6/(2*3*4*5), which becomes 6/120 = 1/20. There's nothing in mathematics that says you are forbidden from doing the operations in the order you want, but you have to use the notation to mean that, if you do. The general rule is operations of equal precedence (+&- or ×&÷ or roots, exponents, and logarithms), must be done from left to right, the same order in which western languages are written and read. The only times you can go from right to left is when you're joining terms/factors that are only involved in addition/multiplication respectively.

Subtraction and division, as you point out, are non-commutative. Addition and multiplication are commutative.

 

[ATM]

The tribe has spoken.

 

[rhino]

6 ÷ 2 (2 + 1) =

The only way I see to correctly apply the commutative property is (and using more explicit notation):

6 * (1/2) * (2+1) = (1/2) * (2 + 1) * 6 = (2 + 1) * 6 * (1/2) = 6 * (2 + 1) * (1/2) = (1/2) * 6 * (2 + 1) = (2 + 1) * (1/2) * 6

In each case, the value of the expression is . . . 9. Left to right, forward or back, right to left.

Again, the problem some are having (or refusing to acknowledge) rests in failing to recognize that the division sign is operating only on the 2 and not on the (2 + 1).

As to whether or not it's a poorly written problem, I would ask what the goal of the problem was. If it were to test a student's ability to properly apply the established convention for order of operations, then it's fine. Especially in that context, there is no ambiguity, only a understanding of how to apply order of operations or a lack thereof.

 

[williamsjr22]

Now I know why I dropped out of Computer Science and went into a Business Information systems major. I suck at math until they put numbers into a monetary value.