Math Question Help Needed
 

My son has a problem in his math book that has not shown itself in previous lessons and I was hoping someone here could help.

If a * b = a - 3b and a # b = 2a+3b, evaluate the expression (4 *3) # 5.

In a problem like this, what does # mean? He has several of these types of problems in the next few lessons and I want to make sure we understand it fully. I have looked in my teacher's book and it has a poor explanation.

TIA

" it has a poor explanation"

there ya go.

It's not you (or kid) it's the teacher not defining the language. (symbols)

It's not for a programming class, right?

I homeschool so I am the teacher.

If it helps, this is a trig/pre-calculus book.

Ha!

Okay, let's learn about typo's ! :D

If not, let's see the explanation.

so.. # is the symbol for an unknown math operator? As in, solve for #(unknown math operator) ?

yeah ...

Why doesn't the problem ask it that way? (I know, math geeks are weird)

The solution:

We are given that a * b= a - 3b. To evaluate 4*3, we must recognize that a corresponds to 4 and b corresponds to 3.

If a*b=a-3b, 4*3=4-3(3)=-5
Since 4*3=-5, (4*3) #5 = -5#5

To evaluate -5#5, we see that a#b=2a+3b, and recognize that, in this case, a corresponds to -5 and b corresponds to 5.

If a#b = 2a+3b, -5#5 = 2(-5)+3(5)=5
So, (4*3)#5=5

I believe the answer is 2(4-3(3))+3(5)=5

Seems more like a logic puzzle than a math question, though. I can tell you I have an engineering degree and never came across this question.

Dang, you beat me to it. :)

+1 to Flieger (never seen anything like that)

fwiw, I've always maintained that the problem with math is that it is usually taught by math majors. --they get in to useless math games. I would hate math if it were not for engineering teachers demonstrating the power of math in application. (a tool)

To put it another way, math is but a language for representing quantifiable relationships. Essentially, equations are sentences, with math syntax, which model relations. Math geeks, however, get into the structure of the syntax and completely lose sight of application. Thus, they create ridiculously useless syntax puzzles like above.

Thanks for all the help. Please excuse any dumb questions, it is still a little above me.

In the explanation I put up, the first line reads:

If a*b=a-3b, 4*3=4-3(3)=-5

Where does the -5 come from?

Nevermind. Working through it again and it just clicked. Sometimes my brain does not move as fast as I want it.

Thanks for all your help.

My daugher is only 11 and her math already makes me think on occasion. I am so doomed.

I know. Next year he will take Calculus at the local university and he will only be 16.

Ultimately with this problem, I overcomplicated things in my head. It really is a simple substitution problem but I was thinking it must be something more because of the level of math book. That will teach me to think too much. ;)

Please Excuse My Dear Aunt Sally. ;)
.
.
.
.
.
.
.
Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.

This type of question has been commonly showing up on HS Introductory algebra tests for decades

the # and * are abstract operations which are defined in the statement of the problem, other symbols, &,%,? etc. are commonly used as well, * is not multiplication this is mistake one.

The object of the question is to determine if the student can follow the abstract rules as presented w/o having any prior experience w/ them and then evaluate the resulting expression using the common math operations.

a * b = a - 3b is the definition of the * binary operator in terms of the usual subtraction binary operator and implicit binary multiplication using the variable values of a & b

similarly a # b = 2a+3b is the definition of the # binary operator in terms of the usual addition and implicit multiplication binary operators using the variable values of a & b.

the substitution principle, use of parenthesis and the use of the unary - operator are also involved in the solution.

starting w/ a=4, b =5 because it is inside parenthesis
a * b = a - 3b
becomes
4 * 3
4 - 3(3) per the def of * and substituting
4 - 9 regular arithmetic
-5

and then using the def of #
a # b = 2a+3b
(4 * 3) # 5 note that the current value of a was derived in the previous step as -5
(-5) # 5 implicit multiplication by 1 implies 1(-5) = -5
-5 # 5 the current value of a is -5 and the current value of b is 5
2(-5) +3(5) per the def of #
-10 + 15
5

42

I guess I don't love maths.

42

Bill,

Thank you. That is the great explanation. Were you a teacher, perhaps? There is no doubt that after 20 years there is some things I don't remember. For the most, Kyle self-teaches and I come in to help if he has issues. We are definitely getting to the point in which that becomes a little harder. Luckily, he will have a professor teaching him next year.

This is always the correct answer.

I never heard of that one till much later in life, we were taught BEDMAS or PEDMAS and told it was our choice which one we like. I think because they were both saying the same thing that it stuck.

thank you all so much for re-introducing the migraine that I used to get in statistics class 40 years ago.
Bill K

bk - hate to be the grammar Nazi, but it's sadistics. ;)

Wow.

Convoluted and confused for the sake of confused convolution. -silly math major geeks.

Perhaps their _ key was broken.

Really, bad ch*ice there. I get that divergent thinking people won't be much phased by that (esp when stated at start) but for those whom crave consistency . . yikes, what a disservice it is. What next? the symbol 3 == elephant and the symbol 1 == e But "==" no longer means "set equal to" instead it means "does not equal. Now if 3*1 =/=.... :rolleyes:

If by mistake you mean mistake in the presentation of the problem, I agree.
If commonly accepted symbols for operations are arbitrarily redefined, the all of the commonly accepted symbols for operations are open to redefinition. Under these circumstances, why assume ( x+xx ) means three numbers and an addition operation are inside brackets? Why assume there is a set of brackets at all? The left bracket could have one meaning the +could have another meaning, and the end bracket could have yet another meaning. I understand this as an exercise in logic and deduction, but mixing redefined common symbols for operators with arbitrary meanings for operators is just chaos.

Don't agree with you (usually) on a political level, but I'm 100% with you on this one, WD!

In an academic environment * is not a symbol for multiplication, it has come into common usage in non academic environments first w/ typewriters and later computer keyboards

wiki has a fair summary of what is correct, some will be familiar to you others will not

when these problems are presented the symbols are generally chosen to avoid vernacular confusion, often using Greek or other non ambiguous symbols

no this isn't convoluted or confused, just something most of you aren't familiar w/

when a macro is written for use on a computer you are doing exactly the same thing, ie defining a function that dies something to one or more arguments, similarly all the functions contained in an Excel ss are functions the define a procedure to be applied to various types of data

There are all sorts of transformations and manipulations in higher math that rely on the ability to follow the rules w/ processes and symbology that are not always familiar to the new user.

There are four lights.

and 1* Oreo cookies.

Are you sure?

Or did you just not -get- the convolution reference?

http://forums.pelicanparts.com/uploa...1438026212.jpg

;) get it now.. confused convolution used in a thread about avoiding vernacular confusion about *

https://en.wikipedia.org/wiki/List_of_mathematical_symbols#Other_non-letter_symbols

I maintain, this was a poor choice of operational variable.

As I said the asterisk is a convenience first used by typists and then further promulgated by lazy computer users

In my textbooks, a dot was multiplication, * (star) was the convolution of two functions. Came across it with Laplace transforms.

Whats all the discussion/confusion about basic simaltaneous equations?

Spelling simultaneous ?

Here we go; basic simultaneous equations

http://forums.pelicanparts.com/uploa...1438107941.jpg

any questions?


(Thx, Sam.)

"no this isn't convoluted or confused, just something most of you aren't familiar w/"

True enough. I cannot understand why b=5. Does = mean "equals" or something else? Why does being inside parenthesis make it 5?


"starting w/ a=4, b =5 because it is inside parenthesis
a * b = a - 3b
becomes
4 * 3
4 - 3(3) per the def of * and substituting
4 - 9 regular arithmetic
-5"

From Porschegal’s explanation, “We are given that a * b= a - 3b. To evaluate 4*3, we must recognize that a corresponds to 4 and b corresponds to 3.”

Here, for some reason, we are to recognize that b "corresponds" to 3. Why?

So b has some relationship to 5 (equals 5?) and "corresponds" to 3. WTH does that mean??

I totally agree. I was so confused in high school by the attention to syntax that I thought I was bad at math. Cured by taking physics with calculus where suddenly math was a tool to figure stuff out. I think the folks that geek out about math syntax are teachers because they're otherwise unemployable!

Guys, syntax is critically important. That is why your teachers wanted you to pay attention to it. Without uniform syntax properly written, it would be impossible to convey even the simplest mathematics, much less complicated mathematics.

Just because some "math majors" use that uniform syntax to create "useless math games" does not mean the one should not pay attention to syntax structure.

For example:

6÷2(1+2)=?

Without proper evaluation of the uniform syntax, you might think the answer was "1" when it is "9".

http://forums.pelicanparts.com/uploa...1438180802.jpg

Not this sheet again :D

seriously, that is a good example of sloppy syntax. I mean, ÷ --who the hell uses that symbol when / is right there?

6/2(1+2)=? is expected. But, 6÷2(1+2)=? ... from the OP we should consider that ÷ is an unknown operator. :cool:

No really, sloppy people are with abacus, still a tally it is when something done gets [/Yoda]