Help me solve a couple of math problems?

[ChristyB in TN]

NPR's Science Friday has a fb page and a couple of the status updates were math problems which I promptly solved then posted on my wall. Now there is a big debate on my page, and theirs, about the correct answers. They won't post the stinking correct answers! Help?

6-1X0+2/2

 

I got 7

 

And 48/2(9+3)

 

I got 288

Edited September 1, 2012 by Mad Charity

[amo_mea_filiis.]

I get 7 and 288.

[Annie G]

For the first one, multiplication and division are done first. 1 times 0 is zero and 2 divided by 2 is one. That leaves the problem as 6-1, which is five.

 

For the second problem, parenthesis are done before multiplication and division, so you're left with 48/2(12). I'd write that as a fraction, do the bottom part first, making the problem read 48/24. So I get two.

Edited September 1, 2012 by Annie G

[amo_mea_filiis.]

Yes, 6-1 is 5, not 7! Lol.

 

Eta; i just looked at my paper and 7 seems to make sense. i did it as

 

6-1x0+2/2

6-0+1

7

 

This isn't right?

 

The second one

 

48/2(9+3)

48/2(12)

24(12)

288

Edited September 1, 2012 by amo_mea_filiis

[ChristyB in TN]

But 6-0+1=7

[Rivka]

For the first one, multiplication and division are done first. 1 times 0 is zero and 2 divided by 2 is one. That leaves the problem as 6-1, which is five.

 

 

No, it's 6 - 0 + 1 = 7.

 

For the second problem, parenthesis are done before multiplication and division, so you're left with 48/2(12). And since I'd write that as a fraction, I'd do the bottom part first, making the problem read 48/24. So I get two.

 

I couldn't tell if the 2(9 + 3) was supposed to be under the / or not. If so, I agree with you.

[ChristyB in TN]

Yes, 6-1 is 5, not 7! Lol.

 

Eta; i just looked at my paper and 7 seems to make sense. i did it as

 

6-1x0+2/2

6-0+1

7

 

This isn't right?

 

I think so! No one on my fb agrees, though.

[Annie G]

Yes, 6-0+1 is 7. I'll be right back- my brain must still be in bed, sleeping in.

 

As for the second one, we were taught when it's written as a fraction (which is how I see division problems, oddly enough), that you can 'do' the problem before you do the division. Which is why I did the 2 times 12 part first. But perhaps I was totally taught wrong- completely possible since doing it left to right would have me doing the division first then the multiplication, which gets your answer.

I'll happily concede. I hope the folks on your Facebook page play nice- it's no fun when people get mean on a social network!

Edited September 1, 2012 by Annie G

[cornelia9805]

NPR's Science Friday has a fb page and a couple of the status updates were math problems which I promptly solved then posted on my wall. Now there is a big debate on my page, and theirs, about the correct answers. They won't post the stinking correct answers! Help?

6-1X0+2/2

I got 7

 

And 48/2(9+3)

I got 288

 

You work left to right with multiplication and division at the same time and the same for addition and subtraction.

6-0+1=7

 

The parentheses comes before multiplication and division.

48/2(9+3)

48/2*12

24*12

288

[ThisIsTheDay]

Not looking at other responses yet.

 

6-1X0+2/2

multiply/divide first, 6-0+1

I get 7.

 

48/2(9+3)

parenthesis first, 48/2x12

multiply/divide 24x12

I get 288.

[Deniseibase]

Well, the images posted on FB don't show fraction bars, they show division signs, which seems to clarify some things. I think the internet convention of using the slash to indicate fraction bar for division may be causing some confusion here. With the first problem, it says -

 

6-1X0+2 (divided by) 2

Order of operations - multiply and divide first, from left to right, so 6-0+1

Add and subtract from left to right gives you seven.

 

With the second one, the FB image is very helpful. It shows -

48 (divided by) 2(9+3)

Order of operations says do the parentheses first, so 48 (divided by) 2(12)

Again, order of operations indicates to resolve the parentheses first, so 48 (divided by) 24

Then we multiply and get 2.

 

So I say 7 & 2.

[amo_mea_filiis.]

Well, the images posted on FB don't show fraction bars, they show division signs, which seems to clarify some things. I think the internet convention of using the slash to indicate fraction bar for division may be causing some confusion here. With the first problem, it says -

 

6-1X0+2 (divided by) 2

Order of operations - multiply and divide first, from left to right, so 6-0+1

Add and subtract from left to right gives you seven.

 

With the second one, the FB image is very helpful. It shows -

48 (divided by) 2(9+3)

Order of operations says do the parentheses first, so 48 (divided by) 2(12)

Again, order of operations indicates to resolve the parentheses first, so 48 (divided by) 24

Then we multiply and get 2.

 

So I say 7 & 2.

 

For the second one, doesnt order of operations say multiply or divide left to right? So i see it as 48/2(9+3), once the 9+3 is settled, the () just becomes a multiplication symbol. So now it's read from left to right as 48 divided by 2 times 12 which equals 288.

[Snickerdoodle]

nm

Edited September 1, 2012 by Snickerdoodle

[TXBeth]

The second one is ambiguous. There is a debate even among mathematicians, as some would say that the implied multiplication 2(12) takes priority over the explicit division 48/. The reasoning is that if you used a variable that is how it would be. 48/2x does not equal 24x. It equals 48 divided by double x.

[Lolly]

NPR's Science Friday has a fb page and a couple of the status updates were math problems which I promptly solved then posted on my wall. Now there is a big debate on my page, and theirs, about the correct answers. They won't post the stinking correct answers! Help?

6-1X0+2/2

 

I got 7

 

And 48/2(9+3)

 

I got 288

 

definitely 7 for the first.

 

The second it depends on how it is supposed to be written. The way the computer screen works you really can't tell. If it is a 48 division sign 2 times the quantity (9+3) you would work from right to left. 24 times 11=264. But, if it is 48 on top of fraction bar with 2(9+3) on the bottom of the bar you would work the bottom first and then divide. 48 divided by 24=2 It really just depends on how you perceive the fraction bar for this problem. I think if the entire quantity was supposed to be under the bar, brackets should have been used to denote that --48/{2(9+3)}--which makes the first answer correct since there were no brackets.

[Lolly]

The second one is ambiguous. There is a debate even among mathematicians, as some would say that the implied multiplication 2(12) takes priority over the explicit division 48/. The reasoning is that if you used a variable that is how it would be. 48/2x does not equal 24x. It equals 48 divided by double x.

 

Which is why the fraction bar should never be used diagonally. It should be ___! Then, you can tell what should be done in the correct order without any discussion. Personally, variables are different. They, to me, have a sticky quality that makes them attach to the number to their left. Regular numbers, in my warped little brain, do not have that sticky quality.

[Wheres Toto]

Yes, 6-1 is 5, not 7! Lol.

 

Eta; i just looked at my paper and 7 seems to make sense. i did it as

 

6-1x0+2/2

6-0+1

7

 

This isn't right?

 

The second one

 

48/2(9+3)

48/2(12)

24(12)

288

 

For the second one, doesnt order of operations say multiply or divide left to right? So i see it as 48/2(9+3), once the 9+3 is settled, the () just becomes a multiplication symbol. So now it's read from left to right as 48 divided by 2 times 12 which equals 288.

 

:iagree:

 

It's a little confusing but the parenthesis are resolved once you do the 9+3.

You would then work left to right.

 

If it was 48 over 2(9+3) it should have been written 48/(2(9+3)).

[EKS]

I found it striking how many people got the answers wrong on Facebook. I just saw them reposted, not on the NPR page.

 

My friend who reposted them, who is in a master's in teaching program and was a homeschooler in a previous life, said that the only people who got the problems right were the homeschoolers and that all the elementary ed types got them wrong. Which is frightening.

 

7 and 288 are correct.

Edited September 1, 2012 by EKS

[ChristyB in TN]

I found it striking how many people got the answers wrong on Facebook. I just saw them reposted, not on the NPR page.

 

My friend who reposted them, who is in a master's in teaching program and was a homeschooler in a previous life, said that the only people who got the problems right were the homeschoolers and that all the elementary ed types got them wrong. Which is frightening.

 

7 and 288 are correct.

It is crazy! I have been mesmerized by the responses and can't seem to stop looking at them. It is hilarious how snarky people are getting, too.

On my page, I am the only one with my answers, 7 and 288. Everyone keeps responding with PENDAS but I think they are missing the point that multiplication and division are sort of lumped together and should be solved as they come up, left to right. Not multiplication... THEN division. Now the problem is who is the authority everyone can agree on that solves the problem?

[TXBeth]

7 is definitely correct for the first one, but I still say either 288 or 2 is an acceptable answer for the second. Even with the division symbol it is ambiguous and hotly debated by mathematicians. Basically, it is a poorly written problem.

[ChristyB in TN]

Try it using algebra. I'm sooooo not an expert so please be kind.

I still get 7 and 288

[creekland]

7 and 288 would be correct in my math class and the way our state does state testing. ;)

 

As others have said, m & d go left to right once you're at that step. Ditto for + & -. If one had wanted it done differently one needed to use more parentheses - or brackets.

[regentrude]

The second problem is ambiguous and should never be written like this.

The fraction bar has to be horizontal; then it would be absolutely clear whether the (9+3) is in the denominator or next to the fraction as a separate factor.

There is no standard convention for the notation with the slant, and no way to answer the question when it is written as 48/2(9+3) because it is not clearly defined what this is supposed to mean. If the slant / has to be used for a fraction, the problem should be rewritten either as (48/2)(9+3) or as 48/(2((+3)) to avoid this ambiguity.

 

The problem is discussed here:

http://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html

Edited September 1, 2012 by regentrude

[blondeviolin]

I am shaking my head at the all kinds of wrong answers (and explanations) on the facebook page for the first problem. ESPECIALLY the one dude who believes "because their are no parenthesis the foil method is out."

 

THIS is one STRONG reason I've chose to homeschool. :001_huh:

[kiana]

The first one is unambiguously 7.

 

Although a strict reading of order of operations gives 288 for the second one (in other words, that's not WRONG), I believe the question to be ambiguous. The question is, does multiplication indicated by juxtaposition (i.e. 2x) take precedence over division indicated by fraction bars? For example, is 1/2x equal to 1/(2x) or (1/2)x? There is not a firm consensus here.

[ktgrok]

For the first one, multiplication and division are done first. 1 times 0 is zero and 2 divided by 2 is one. That leaves the problem as 6-1, which is five.

 

For the second problem, parenthesis are done before multiplication and division, so you're left with 48/2(12). I'd write that as a fraction, do the bottom part first, making the problem read 48/24. So I get two.

 

:iagree:

[Gailmegan]

The first one is unambiguously 7.

 

Although a strict reading of order of operations gives 288 for the second one (in other words, that's not WRONG), I believe the question to be ambiguous. The question is, does multiplication indicated by juxtaposition (i.e. 2x) take precedence over division indicated by fraction bars? For example, is 1/2x equal to 1/(2x) or (1/2)x? There is not a firm consensus here.

 

 

:iagree: