48÷2(9+3) = ????

[Bill Verburg]

Originally Posted by winders

No one wanting to be clear would write "1/2x". What did they mean?

1/(2x)?

(1/2)x?

Math Forum: Ask Dr. Math FAQ: Typing Math

Scott

No one w/ a clear understanding of 7th grade math would be confused, the rules are unambiguous and usually reviewed the first week or two of the school year all the way through 9th grade
1/(2x) is not equivalent to (1/2)x

division is not associative, you cannot add parentheses as you can w/ multiplication

1*2*x = (1*2)*x = 1*(2*x) =1(2*x) = 1(2x) = 1*(2x) because multiplication is associative

[Bill Verburg]

Originally Posted by winders

Huh?

1 / 2 * 3 is the same as 1 / 2 x 3....both equal 1.5.

By convention, division and multiplication have equal precedence. By convention, you start at the left.

Scott

excellent, give the boy a gold star

now think hard here, what operation was done first, ether method is ok to follow through on

[winders]

Originally Posted by winders

Huh?

1 / 2 * 3 is the same as 1 / 2 x 3....both equal 1.5.

By convention, division and multiplication have equal precedence. By convention, you start at the left.

Scott

Originally Posted by Bill Verburg

No one w/ a clear understanding of 7th grade math would be confused, the rules are unambiguous and usually reviewed the first week or two of the school year all the way through 9th grade
1/(2x) is not equivalent to (1/2)x

division is not associative, you cannot add parentheses as you can w/ multiplication

1*2*x = (1*2)*x = 1*(2*x) =1(2*x) = 1(2x) = 1*(2x) because multiplication is associative

Bill,

Instead of being stubborn, read the link I provided. Or do you have a problem with the Drexler University mathematics department too?

Read this too:

http://www.cwu.edu/~glasbys/M153SUM.PDF

1/2x lacks clarity is open to interpretation. Period. No self-respecting mathematician would write it out that way.

Scott

[DARISC]

Originally Posted by winders

Huh?

1 / 2 * 3 is the same as 1 / 2 x 3....both equal 1.5.

Of course they do - and this, '', always equals joking/laughter/LOL, etc.

Originally Posted by winders

By convention, division and multiplication have equal precedence. By convention, you start at the left.

Of course you do...after you complete what's to be done in parentheses - Oh yeah! Here's a fine example with all steps shown:

As a "word problem", as they were called when I was in the 8th grade:

Question - What number do you end up with when you multiply 48 by twice the sum of 9+3? Express this question in the form of an algebraic equation and show each step of your work.

Answer - the equation is 48÷2(9+3) = n (or 48/2(9+3) = n).

The steps to solving for n are:

48÷2(9+3) = 48÷2(12) = 48÷2x12 = 24x12 = n = 288

OK, now you surely understand, right?

[Aragorn]

the answer is 42...

[winders]

There is a convention that says you do implicit multiplication before division. Based on that convention, you get:

48÷2(9+3) = n

48÷2(12) = n

48÷24 = n

n = 2

Also, you word problem doesn't match your results.

"Question - What number do you end up with when you divide 48 by twice the sum of 9+3? Express this question in the form of an algebraic equation and show each step of your work."

That would be written out as follows:

48 / (2 x (9 + 3)) = n

Scott

[DARISC]

Originally Posted by winders

...1/2x lacks clarity is open to interpretation. Period. No self-respecting mathematician would write it out that way.

Bill Verburg isn't being stubborn; he's trying to teach you a bit of math, a discipline which is totally devoid of emotions such as stubbornness.

1/2x doesn't lack clarity; it clearly means, one half of the number x, or it means one half (.5) times some unspecified number.

It means 1/2 * x/1 = 2x = 1 = x = 1/2

That "No self-respecting mathematician would write it out that way" has nothing to do with clarity or interpretation. It has only to do with convention being followed to avoid mistakes. Not following convention doe not equate to incorrect math.

[Bill Verburg]

Originally Posted by winders

Bill,

Instead of being stubborn, read the link I provided. Or do you have a problem with the Drexler University mathematics department too?

Read this too:

http://www.cwu.edu/~glasbys/M153SUM.PDF

1/2x lacks clarity is open to interpretation. Period. No self-respecting mathematician would write it out that way.

Scott

It is neater and clearer to use parentheses but it is not ambiguous w/o them.

you did so well on 1 / 2 * 3 too does 1/2(3) have a different result? or (1/2)3 or (1/2)*3

what is the difference or where does lack of clarity enter for 1/2x

the 2 expressions are structurally identical, having 3 operators and only 2 of the same operations

[winders]

Originally Posted by Bill Verburg

what is the difference or where does lack of clarity enter for 1/2x

Did the person writing the equation mean "1/2 of x" or "1 divided by 2x"?

Look at the links I provided.....

Scott

[Bill Verburg]

Originally Posted by winders

Did the person writing the equation mean "1/2 of x" or "1 divided by 2x"?

Look at the links I provided.....

Scott

I have read your links and agree w/ everything stated in them, nevertheless we have pinpointed your lack of understanding

you seem to feel incorrectly that 1/2*3 has different rules from 1/2x
they are identical in form and function
as you so clearly stated 'By convention, division and multiplication have equal precedence. By convention, you start at the left.'

so in both expressions first 1 is divided by 2 to give the result .5 then that result is multiplied by the next operand which is 3 in the first example and x in the second.

or if you prefer to work w/ rational expressions instead of decimal



and





Math has rules that must be consistently followed or you get erroneous reslts.

[DARISC]

Originally Posted by winders

There is a convention that says you do implicit multiplication before division. Based on that convention, you get:

48÷2(9+3) = n

48÷2(12) = n

48÷24 = n

n = 2

You begin correctly with:

48÷2(9+3) = n

48÷2(12) = n

48÷24 = n then at this step you err.

48÷2(12) = n is the same as

48÷2*12 = n

BY CONVENTION, you then proceed from left to right, the first operation is division:

24*12= n

and THEN multiplication:

n= 288,

not

n = 2[/QUOTE]

Originally Posted by winders

...Also, you word problem doesn't match your results.

Oops.I made a typo, corrected below:

"Question - What number do you end up with when you divide 48 by 2, then multiply that number by the sum of 9+3? Express this question in the form of an algebraic equation and show each step of your work."

Answer - the equation is 48÷2(9+3) = n (or 48/2(9+3) = n).

The steps to solving for n are:

48÷2(9+3) = 48÷2(12) = 48÷2x12 = 24x12 = n = 288

As per the rules of math, you begin at the left, performing the first operation, 48/2=24.

Then you perform the second operation, which is to multiply 24 by the sum of the numbers inside the parentheses, which is 12.

24*12=288

Nothing unclear, nothing ambiguous, nothing to argue about.

Hope this finally clears up this basic algebra confusion for you.

[DARISC]

Originally Posted by winders

Did the person writing the equation mean "1/2 of x" or "1 divided by 2x"?

Look at the links I provided.....

Scott

Ignore my last post. I'm sure that what Bill Verburg posted while I was typing out my screed has gotten you squared away much better than I ever could.

[winders]

What is the answer to this:

1/2pi = ?

[winders]

Originally Posted by winders

There is a convention that says you do implicit multiplication before division. Based on that convention, you get:

48÷2(9+3) = n

48÷2(12) = n

48÷24 = n

n = 2

Also, you word problem doesn't match your results.

"Question - What number do you end up with when you divide 48 by twice the sum of 9+3? Express this question in the form of an algebraic equation and show each step of your work."

That would be written out as follows:

48 / (2 x (9 + 3)) = n

Scott

Originally Posted by DARISC

You begin correctly with:

48÷2(9+3) = n

48÷2(12) = n

48÷24 = n then at this step you err.

48÷2(12) = n is the same as

48÷2*12 = n

BY CONVENTION, you then proceed from left to right, the first operation is division:

24*12= n

and THEN multiplication:

n= 288,

not

n = 2

Did you read the part of my post that says "There is a convention that says you do implicit multiplication before division. Based on that convention, you get:"???

Scott

[gr8fl4porsche]

Originally Posted by sammyg2

3 traveling salesmen were headed to a convention and since money was tight, they agreed to share a room.
The hotel clerk told them it was $30 so they each kicked in $10

Later the hotel manager was looking at the books and realized the clerk had charged $30 for a $25 room.
He took five $1 bills from the register and headed up to the room to give a refund.
On the way he started wondering how he was going to split $5 three ways.
He was no math genius so he decided to refund each one of the salesman $1 and put the remaining $2 in his pocket, which he did.

So each saleman paid $10 and got one back, or $9 each.

3 times $9 is $27, plus the $2 in the manager's pocket is $29, where the heck did the other dollar go?

This old riddle is fun to discuss after a few drinks. Once you start to add $27 and $2 to get $29 it sort of sucks you in.

The answer is that you subtract the $2, not add.

The room is now $25. $27 ( $30 - $3) paid by the salesmen minus $2 for the clerk = $25

Hotel $25 + $3 salesmen + $2 clerk = $30

[DARISC]

Originally Posted by winders

What is the answer to this:

1/2pi = ?

1st operation, beginning at left: divide 1 by 2 to get .5

Next operation, multiply .5 times 3.14159 to get 1.50795:

1/2pi=.5x3.14159/2=1.50795

Did you ask just to excercise someone?

[winders]

Look at what Google comes back with: 0.15915494309

[DARISC]

Originally Posted by winders

Did you read the part of my post that says "There is a convention that says you do implicit multiplication before division. Based on that convention, you get:"???

Scott

Yes i did. The equation is solved correctly as I laid it out. The correct answer is 288. If Bill Verburg can't explain why, I certainly can't.

[Bill Verburg]

Originally Posted by winders

Did you read the part of my post that says "There is a convention that says you do implicit multiplication before division. Based on that convention, you get:"???

Scott

another thing you don't understand

'There is a convention that says you do implicit multiplication before division'

is a rule only in your world, it is not a convention recognized anywhere else except in the minds of others that don't understand math.

the overarching rule is left to right
exponents
then multiplication(doesn't matter whether implicit or explicit) or division
then addition or subtraction

unless modified by some other consideration, there are many, but parenthesis is the common one here

by your thinking
1/2(3) is somehow different from 1/2*3
both expressions have 1 division and 1 multiplication and they must be performed left to right, even you got that right,

1/2(x) is exactly the same as 1/2x or 1/2*x

they all have 1 division and 1 multiplication that are performed left to right

when I taught Calculus I insisted that my students convert any expression into rational form so as to clearly understand what was involved, this conversion isn't necessary it merely helps to clarify

in rational form the above expressions are


and



it further helps to remember that every operand, lets call it x has 1 for a coefficient, 1 for a divisor and 1 for a denominator unless specified differently

[winders]

If you mean 1/2 of pi, write it out as "pi/2". If you mean 1 divided by 2 x pi, write it out as 1/(2pi).

1/2pi is ambiguous. As is 1/2x and 48÷2(9+3)....

Scott