6th Grade Math Problem

[Chris Padilla]

A friend of mine sent this to me. It was a math question on his daughter's math test:

****
Insert parentheses and addition signs to make this equation true.
Remember that the parentheses can indicate multiplication.

5 4 2 3 = 32
****
There were a few spaces between each number but it isn't showing here.

[Stephen Tashiro]

There were a few spaces between each number but it isn't showing here.

Do the spaces prohibit using 5 + 4 + (23) ?

[Chris Padilla]

That was the solution, Stephen!

Now do you think that this is an "appropriate" "math" question? A buddy of mine posted this on his Facebook page and no one could solve it. When we found out the solution, a lot of people went crazy!

Personally, I found it interesting and "out of the box" thinking. I liked it.

[Eric DeSilva]

It is an interesting puzzle if posed as a word game, but it isn't mathematics. Putting two things together without an intervening operator in mathematical notation indicates multiplication, not what was done here. In other words, in mathematical notation, "ab" means "a x b," not "a x 10 + b."

[Chris Rosenberger]

That is very useful in everyday life.
I am always running into strings of numbers & wounder how I can make equal other numbers.
Schools are great these days.

[David Weaver]

Personally, I can't find anything wrong with it. It's a question, and as far as we know, the teachers may have gone through questions of that type as part of class.

Otherwise, the outside of the box type questions like that are more IQ questions than the standard school "i tell you something and then you take a test and tell me the same thing".

I'm reminded of a saying one of my professors used to say...."Learning is Painful". Sometimes there are questions only a few students get, and maybe only a few more of them understand why they didn't get them after that. I know a lot of people don't agree with me, but I don't think every question asked needs to be one that 80% of students get correct.

[Larry Browning]

A friend of mine sent this to me. It was a math question on his daughter's math test:

****
Insert parentheses and addition signs to make this equation true.
Remember that the parentheses can indicate multiplication.

5 4 2 3 = 32
****
There were a few spaces between each number but it isn't showing here.

Maybe I am not up on all math punctuation, but I have never heard of a parentheses indicating multiplication. Star(*) indicates multiplication. AFAIK multiplication is never implied. At least in my world (computer programming)
So far I haven't come up with the solution.

[Larry Browning]

Do the spaces prohibit using 5 + 4 + (23) ?

Wait a minute!!!! I call fowl. No where did it say you could remove spaces. In only allowed inserting parentheses and addition signs. Plus, if parentheses indicates multiplication of the numbers inside then 5 + 4 + (2 3) would equal 15 correct?

[Chris Padilla]

I agree that this isn't rigorous, rudimentary math but a careful reading of the problem statement doesn't say one can't take two of the single digits and "create" a two digit number from them. It further doesn't state that you can do this. As I biked into work this morning (a 50 minute commute), I pondered this "math" problem over and over and couldn't find a solution. When I saw the answer (that the teacher was looking for) posted, I was floored that I didn't think to do this. Like most of us, I suspect, it would not have occurred to us to make a two-digit number. Fundamentally, rigorously, it is not correct but it certainly isn't prohibited. Interesting stuff.

[Dan Hintz]

Maybe I am not up on all math punctuation, but I have never heard of a parentheses indicating multiplication. Star(*) indicates multiplication. AFAIK multiplication is never implied. At least in my world (computer programming)
So far I haven't come up with the solution.

Computer programmer here (but also an engineer)... multiplication was always implied/assumed throughout my engineering career. Blocks could be separated by (), [], or even {}. It was only when those symbols were used as operators that the multiplication symbol '*' was used to keep things straight.

[Chris Padilla]

Maybe I am not up on all math punctuation, but I have never heard of a parentheses indicating multiplication. Star(*) indicates multiplication. AFAIK multiplication is never implied. At least in my world (computer programming)
So far I haven't come up with the solution.

It is pretty fundamental, Larrry. Have you ever heard of PEMDAS? Parentheses Exponent Multiplication Division Addition Subtraction (Please Excuse My Dear Aunt Sally) These are orders of operation so if you see something like 5 * 4 + 6 / 3 = ??? Certainly, I could make it clearer: (5*4)+(6/3) = ??? or even ((5)(4))+ (6/3) = ???

[Chris Padilla]

Wait a minute!!!! I call fowl. No where did it say you could remove spaces. In only allowed inserting parentheses and addition signs. Plus, if parentheses indicates multiplication of the numbers inside then 5 + 4 + (2 3) would equal 15 correct?

Well, it didn't say you could remove them. It also didn't say you could NOT remove them. hahaha In this case, the parentheses were used to "group" the 2 and 3 together to "create" 23. Like I said above, fundamentally, this is not correct but it solves the problem.

[Chris Padilla]

That is very useful in everyday life.
I am always running into strings of numbers & wounder how I can make equal other numbers.
Schools are great these days.

Government math perhaps?

[Larry Browning]

I agree that this isn't rigorous, rudimentary math but a careful reading of the problem statement doesn't say one can't take two of the single digits and "create" a two digit number from them. It further doesn't state that you can do this. As I biked into work this morning (a 50 minute commute), I pondered this "math" problem over and over and couldn't find a solution. When I saw the answer (that the teacher was looking for) posted, I was floored that I didn't think to do this. Like most of us, I suspect, it would not have occurred to us to make a two-digit number. Fundamentally, rigorously, it is not correct but it certainly isn't prohibited. Interesting stuff.

It is clearly stated that that you must only insert parentheses and addition signs. It did not say you could remove a character. If I used the logic that since it didn't say I couldn't do something like removing a space between numbers, then I could do other things that it didn't say I couldn't do, like changing a number to a different number, or re-arranging the order. A space is a valid character just like a number is a valid character. I say the solution is bogus and violates the restrictions put on the problem. BO O O O GUS!

[Larry Browning]

Well, it didn't say you could remove them. It also didn't say you could NOT remove them. hahaha In this case, the parentheses were used to "group" the 2 and 3 together to "create" 23. Like I said above, fundamentally, this is not correct but it solves the problem.

If the logic is, it didn't say I couldn't remove a character and somehow that is ok to do, then it also didn't say I couldn't change the numbers all around and even remove some of them. So using this logic the correct answer could be 32 = 32. All I did was remove some of the numbers and spaces and then rearranged the 2 and the 3. The instructions didn't say I could not do that.
The poor space character just gets no respect these days We can just throw it away and ignore it any old time we want!

this is not correct but it solves the problem.

Yes, this is true!

Man! I sure hope that was a bonus question that didn't count as part of that poor girl's grade on the test.