Simple Math Problem

Wrong. 1/3 does not equal 0.333.

Yes, but you are rounding it down to the nearest even number. When you work in millionths of an inch, it makes a difference.

But you made the prior mistake of rounding 1/3 down to 0.333, which is an error in the third decimal place; whereas Hendrik's is in some far later decimal place.

Again I agree, but 1÷3 will never reach 1. It can approach 1 till infinity, but never be = to 1.

Of course. Why express 1/3 as a decimal, bringing in rounding errors, when the following step gives an integer?

The question is ambiguous as it doesn't make clear the order of operations, and it's a bit odd to use ÷ and / in the same expression. In XL, where * and / are done first, followed by + and -, (and treating 3÷1/3 as 3/1/3), comes to 9 - 3/1/3 + 1 = 9. Older hand calculator treats it as (9 - 3)/1/3 + 1 = 3. Calling it 9 - 3/(1/3) + 1 = 1 as you say, and appears to be the expected answer.

Nobody works in millionths of an inch on anything mechanical.

That's 254 Angstroms.

It may be very few, but it's definitely not 'nobody'. For example, lenses are made by mechanical devices. Especially in today's tiny camera lenses, a millionth of an inch error could render it useless.

Only if you are from Mississippi do you think like that. Didn't they teach you how to divide apples?

Integers that start off as integers do not have a floating (decimal) part. Learn to walk before you take off running with scissors, Mississippi.

9-3÷1/3 +1 I get this as 9-3=6/ 1/3 = 18 +1 = 19

That was precisely the answer I first got because the 3÷1/3 expression was not enclosed by parenthesis, because of the omission of the "order of operations"

Parentheses are not necessary in that instance. The standard order of procedure is to do multiplications and divisions first, followed by additions and subtractions in the order as given.

By simply knowing precedence of operators, one does not need parentheses ever, except in cases where you are doing calculations in a computer spreadsheet, a complicated formula in a database calculated field, or in some other computer application.

I'll argue with you on that one! Any calculation requiring multiple sets of operations needs parentheses, and commonly nested parentheses, to clarify intent. Remove them, and at best it is like writing a long paragraph with no punctuation: even if the words are in exactly the correct order, without the punctuation, it is very difficult to read/understand, and may be impossible to decipher without ambiguity.

I agree completely (for a change). Especially when undertaking complicated formulae in spreadsheets or fields in database reports, it is highly critical to use parentheses to ensure the correct evaluation of the intended expression in the final cell or report field. Otherwise, one has the same old garbage in, garbage out.

Oh OK, I get it PEMDAS... This came after my time I guess...some exceptions...

You are applying the standard rules of arithmetic operations order that was taught you in the third grade, or was it the second grade.

More like nowhere.

Exactly right! New math, old rules.

Now do you know the reason behind this rule? Is it the commutation rules?

Remember the term PEMDAS

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

that is the order of operations.

As far as 1/3 is written I would write as 0.333 with an over score over the last (3) meaning it continues.

That was good until it choked on the last sentence. Converting 1/3 to 0.333 is the key mistake that has bedeviled Ron.

"Converting 1/3 to 0.333 is the key mistake that has bedeviled Ron." Correct.

https://en.wikipedia.org/wiki/Multiplicative_inverse

3 ÷ 1/3
Invert the fraction and multiply becomes 3 * 3/1 = 9

Actually, it didn't choke on the last sentence. He wrote 'with an over score over the last (3) meaning it continues'.

In one form of math notation an 'over score line' written over decimals means that those decimals repeat 'to infinity'.

Thus,

is exactly equivalent to 1/3.

But yes, Ronseto's mistake was equating 1/3 to 0.333, as on a calculator.

Thank you... That was high school math. Like rons question.

You could put the overscore over just the first 3, you know. And, of course, no one can divide by 0.3 (overscore), because it is impossible to enter infinitely many 3's.

Duh.

Just a btw...(for anyone who hasn't seen this, or has forgotten it)

If X = 0.333...... (repeating infinitely)

then 10X = 3.333.... (repeating infinitely)

10X - X = 3.333... - 0.333...

so 9X = 3

and thus X = 1/3.

A rose by any other name is still a rose.

I was under the understanding the over score goes over the last number to establish the pattern.

That was my understanding as well, except when the repeating value is a sequence, Then the first set of whichever characters are to repeat has the overline:

Same thing. Overscore above however many digits are repeated. 1 .. 2 .. 3 whatever.

I don't know how we missed exponents back when I learned this.

Phoenix911 is "more correct" but if you want one that is usually good enough and a little easier to remember:

Please My Dear Aunt Sally = Parenthesis, Multiplication, Division, Addition then Subtraction.

I can't think of an example where the order of evaluating exponents matters based upon proper rules. If you are using a calculator then something like 2-squared must (usually) be evaluated early since (most) calculators won't carry through the 2-squared since it is immediately evaluated to 4. If you are manipulating the equations on paper then 2-squared is still 2-squared even after you have done all your Please My Dear Aunt Sally stuff.

Let's add E, Bruce: Please Excuse My Dear Aunt Sally = Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction.

Not such a hot mnemonic; multiplication and division have no precedence over each other, nor do addition and subtraction. They are simply taken in the order given.

Some of us had a different one.

Pointless Exercises in Mostly Dumb A$$ Sh!t.

Word has it,... this is what you excel in. ....

And proud of it!

And then there is the resistor color code . . . .

Doorman nailed it in #15 (beat me to it).

Somebody beat him to it, too. (Every element having been mentioned beforehand.)

You're right. I was tired, and skimming through the posts, it was the first one I spotted that just used integers, inverted the fraction and changed the division to a multiplication.

Apologies to all concerned.

That's odd, when I worked it out, my answer was a 'Blue Chevrolet Cavalier'... Must of forgot to carry the '1' or something.

If you did carry the one, it would have been red instead.

Yep... I see my mistake... Yes, the answer is "Red Chevrolet Cavalier with a bad right front head light and left blinker that doesn't go off"

thanks, fellow Members. My cavalier is now running at 63.5% ... That's btw is 100% Cavalier exchange rate.

How do you rate an answer that is off-topic, but a good reply?

Yes I got something similar but it depends on how the original problem was written

3 ÷ ⅓ = 9 as the intention seems clear that the divisor is one third but

3 ÷ 1 / 3 = 1 as BSR has noted by doing the operations in order left to right but using the two different common symbols for division

So the limitations of the word processing operation may (WILL) have an impact

GA Totally agree. I always use parentheses for clarity instead of depending on operator precedence.

Too bad you don't work for GM, they don't seem to realize close tolerances matter! Maybe the problem required rounding off to the nearest whole number.

What I learnt in school was BOMDAS, = Brackets Of Multiplication Division Addition Subtraction.

9-3÷1/3 +1 = 9-(3÷1/3) +1 = 9-((3÷1/3) +1) = 9-(((3x3)/1) +1) = 9-10 = Answer -1.

Was that your joke of the day?

Yes Ha Ha, for an answer of 1 you have to subtract 9 from 9 then add 1, which is wrong, you have to add first then subtract. Or are you just joking.

(9-9)+1 or 9-(9+1)

As already discussed, the convention is to take additions and subtractions in the order given, so your second scheme is incorrect. Maybe two year of common core remedial math could fix that.

I seem to be at fault? To old for further education , but not to old to listen.

Order of Operations - BODMAS - Math is Fun

https://www.mathsisfun.com/operation-order-bodmas.html

1. Cached
2. Similar

Order of Operations - BODMAS. Operations. "Operations" mean things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an ...

9-3÷1/3 +1 = 9-(3÷1/3) +1 = 9-((3÷1/3) +1) = 9-(((3x3)/1) +1) = 9-10 = Answer -1.

Wrong!! Actually:

9-3÷1/3 +1 = 9-(3÷1/3) +1 = 9-((3÷1/3) -1) = 9-(((3x3)/1) -1) = 9-8 = 1

because a-b+c = a-(b-c) and not a-(b+c)

"because a-b+c = a-(b-c) and not a-(b+c)"

NO!

a-b+c =(a-b)+c

The technical term for this is that addition is associative, but combinations of addition and subtraction are not. That is why they are read from left to right, rather than being falsely grouped, as a responder or two have done.

Actually, both ( "a-(b-c)" and "(a-b)+c" ) are correct (and give the same result). If your "NO!" means that "(a-b)+c" should be used because it's the normal and easiest way, I totally agree. I just wanted to show him his mistake.

"Actually, both ( "a-(b-c)" and "(a-b)+c" ) are correct (and give the same result)."

Mathematically true, but to obtain "a-(b-c)" from the original "a-b+c", at least one intermediate step is required, including the knowledge that +c=-(-c), and it implies an incorrect ordering of operations.

See Tornado's post #59.

For anyone still having trouble with the 3÷1/3 part of this ( or having trouble explaining it to a young person), it may help to write it in words.

"What is three divided by one-third?" means the same as "how many one-thirds are there in three?" (just as "what is 64 divided by 8?" means the same as "how many 8s are there in 64?"). Now it's clear (by definition) that there are three one-thirds in a one, thence nine one-thirds in three ones.

The devil is in the details.

These 'internet' math challenges just cause time wasting confusion. The lack of parenthesis hinder the clarity of the question.

This is akin to the punctuation making all the difference between...

Don't stop. and Don't! Stop!

Re previous references by Phoenix911 #13 and jdretired #34

We were taught BODMAS (or sometimes BOMDAS) where O meant 'of' such as 1/4th of 5, or 2/3rds of 10.

But O also doubled up as Operator later we learned in our studies (Exponents and Indices were not known at the time) - but by then we had basic grounding in dealing with the order or sequence.

At a tangent to the OP, using a calculator to divide by 3 then multiplying by 3 produces some interesting results.

eg. 10 ÷ 3 x 3 = 10 on a good calculator, or 9.99999999 on a cheap one.

In the OP, 3÷1/3 has to be input as 3÷3(reciprocal)=9

There is no such thing as 1/4th or 2/3rds. The correct terms are 1/4 and 2/3.

There is no such thing as 1/4th or 2/3rds. The correct terms are 1/4 and 2/3.

Of course there is a 1/4th and 2/3rds. I have just used them. And so have you - so they must exist

Those terms are incorrect. That I quoted them doesn't mean that I used them for anything else. Learn how to write and say numbers correctly.

Hello Tornado: ".....Those terms are incorrect. That I quoted them doesn't mean that I used them for anything else. Learn how to write and say numbers correctly...".

The terms I use - 1/4th and 2/3rds - are not incorrect at all - I use them in speech all the time to great effect. I am sorry to hear you do not agree - but never mind.

1/4 and 2/3 are OK by me for use in writing formulas but 1/4th and 2/3rds (and many other fractions) are OK in speech.

Wrong again. Written fractions such as 1/4 and 2/3 are already correctly pronounced one-fourth and two-thirds. The ordinal letters are understood, but they are NOT written.

I am not wrong at all. 1/4 is pronounce as one quarter. To me one fourth is written as 1/4th - and is the way I write it - and will continue to do so because the distinction between the two is 100% clear in my mind and works perfectly in the way I relate to the world - although I admit that the fraction as written here is partly due to limitations of this primitive word processor - maybe ¼th is better - I don't mind you disagreeing though.

You are still completely wrong. Your cheap excuse for one-quarter versus one-fourth does not work anywhere else, such as for 1/3, 3/8, etc. What are you going do next, 1/2nd for one-half?

No, that is obviously one second. LOL.

You might pronounce it as one fourthth - I don't, I pronounce it as one fourth.

You blokes have pennies, shillings, and pounds. We have pennies, nickels, dimes, quarters, and dollars.

I will be easily able to show you the that 1/4 is not a quarter. All you have to do is start with 4 dimes.

LOL. I think we are once again suffering from the semantics of American versus English usage, context, and pronunciation.

1/4 is ein Viertel in Germany. That should totally settle the matter once and for all.

If you draw and quarter someone, do they not end up in 4 pieces, not necessarily equal?

Writing 1/4 as 1/4th is tantamount (as Solar mentioned) to saying "one-fourth-th". It sounds like Sylvester the tuxedo cat attempting to talk, with all three of his remaining teeth in play, God rest his catness.

You are perfectly correct. If you add more 3s, such as 0.3333333333333...

you'll get too close like a blade and your caliper would read it as 9.

Approximating by decimals was a completely wrong maneuver in the first place, and adding more of them scarcely improves matters.

X÷1/3 = Xx3 there is no need for rounding, converting to decimal, etc, by inspection the correct answer is 1

This problem uses two types of notation for division. ÷ and /. As such i could argue that it reads as 9- 3 divided by 1 and the whole/3 ( over 3 ) giving 9 minus 3 all over 3. answer being 2 + 1 = 3 Apologies for the longhand; this browser doesn't have the text, pics, etc. toolbar. Jim

If you knew what you were doing, you couldn't argue any such nonsense at all.

Unlike languages like English, French, Germany, etc... which changes and evolve.

Math is a universal language, the talk of 1/4ths and the like is incorrect and when pointed out may think that people that are pointing that out are anal purists... but they are only trying to maintain the integrity of math itself.

My college professor once said, "Math, you ether know it, or you don't. There is no in between". And what he meant by that is you have to follow the rules set forth. And not doing your own interpretations. Doing so, it wouldn't fail you with the problems the OP is having.

By the way, my college professor also made it clear, he doesn't grade using the 'Bell Curve' with the same reasoning he set forth about knowing Math..

I disagree. 1/4th is not incorrect. It is perfectly valid in speech. I have no problem with it. But I agree 1/4th does not lend itself to use in a formula or in a calculator, but using 1/4th in a verbal discussion of a maths process should not cause any problems - for anybody.

"1/4" is already pronounced "one-fourth"; the letters are superfluous and incorrect.

No! it is not incorrect. 1/4 is one quarter. You can pronounce it as one fourth if you like, but I add 'th' to remove any ambiguity to make it one fourth and IMO is essential if the correct pronunciation is required.

But does it really matter. In a strict maths context 'th' can't be input in formulas in calculators or computers.

The OP must be wondering what the fuss is about when all is required is clarification on how to divide by 1/3

which I would agree is one third and the same as 1/3rd - but I add 'rd' because I do like to be consistent.

Still incorrect. For what earthly reason do you have to "force" someone to say "one-fourth" versus "one quarter"? That's just another bogus excuse. Learn to write English correctly.

It is not incorrect, but you have a right to express an opinion that I am wrong. But that is all it is - an opinion.

I express a counter-opinion that I am not wrong. That's it. I will continue to use 1/4th and 1/3rd or 1/4 or 1/3 in the appropriate context.

I am much more interested in the engineering arguments to solve the OP's problem.

It seems to be the way dividing by 1/3rd 1/3 is handled. Manipulating fractions produces an accurate answer as long as the BODMAS sequence is followed.

Still incorrect; abominably bad form.

"Still incorrect; abominably bad form"

Only because you say so. I do not accept your opinion as the definitive view on this subject. I disagree with you. Please spare me the public lecture on what is right and wrong.

I use 1/4 when I mean one quarter and I use 1/4th when I mean one fourth. That's it. I am not asking you to use 1/4th or agree.

Click on Ω above and hover over 1/4 - and read the description - it is not one fourth - that's for sure.

Tell you what, get Savvi to change it to one fourth and I will stop using 'th' on CR4. How's that for a compromise.

It is not only because I say so; it is because the overwhelming weight of custom says so.

Not all opinions are equal to each other. If someone says that 2 + 2 = 4, you do not have the option of offering a "counter-opinion" that 2 + 2 = 5.

Bad analogy. On questions for which no answers are known, or even possible, all opinions are void.

In those instances, it is possible that all opinions are simultaneously void and valid. Adding -th to 1/4 is essentially the same as saying simultaneous at the same time. REDUNDANT.

for Christ's sake, the damned answer to this simple math problem is unity. We will have none of that here.

Let's move on to something of equal or more consequence, such as angels dancing on the tip of a sewing pin.