Babbler's Den: RE: [Math4u] Re: 4 situations

an equation has only one equal sign.

if there are two equal signs, it is (in fact) a shortening for a system of two equations.

opher

Opher Liba
Mathematics Educator, Researcher and Author
Mathematically (R), Center for Educational Enrichment
Jerusalem, Israel
www.Mathematically-JLM.com

To: Math4u@yahoogroups.com
From: brianejensen@prodigy.net
Date: Fri, 21 Dec 2007 05:19:50 +0000
Subject: [Math4u] Re: 4 situations

My thanks to Buck for clarifying this issue. My apologies to Vinaire
who was correct.

Books are perhaps even better reference, but websites are more
accessible. (What few books I have are hard to locate.)

One rule I will not personally follow is that a ratio can only be two
numbers. I solve many problems where I write a:b:c=d:e:f.

I also write equations which have more than 2 sides and more than one
equal sign. If a puzzle is given with 6 equations and these
equations can be combined into one equation with 7 sides and 6 equal
signs, then it is easier to solve in the rearranged form.

I understand from the definition that it is not proper to say "the
ratio of apples to oranges" but rather "the rate of apples to
oranges." Everyone uses the word "ratio" in this case however.

I cringe that this definition makes it look like the ratio sign is
the same as the division sign.

So let's say we pitch our aqueduct at 1 inch per 100 feet. This is a
rate. Can we use a colon? It is safer to use the word "per." So
the ratio would be 1:1200 or 0.000833. The workers would need to
hire a mathematician to figure it out.

Regards,
Brian

--- In Math4u@yahoogroups.com, Buck Dick <kcubar34@...> wrote:
>
> Brian and Vinaire,
>
> From "The Universal Encyclopedia of Mathematics," Simon and
Schuster, 1964:
>
> "The RATIO of two quantities a and b is their quotient a:b =
a/b. We read "a to b" or "a over b". If a:b = m, m is referred to
as the VALUE of the RATIO. Two quantities, in order to posess a
RATIO must be either PURE NUMBERS or MEASURES OF THE SAME TYPE. e.g.
20:5 = 20/5 = 4; 15 lb: 3 lb = 5. The VALUE of the RATIO
(PROPORTIONALITY FACTOR) is always a pure number."
>
> So, please (as Vinaire as indicated) don't confuse a RATIO with a
RATE (different measures) or a RATIONAL NUMBER.
>
> I have no idea whose websites those are, but I will bet they are
not edited by mathematicians if they allow a RATIO to have different
units, as in 2000 miles: 40 hours.
>
> Buck Dick
>
> Brian Edward Jensen <brianejensen@...> wrote:
> As usual I disagree with you.
>
> First website I found
>
> http://www.mathleague.com/help/ratio/ratio.htm
>
> gives ratios with different units, defines proportion, and says
rate
> involves time.
>
> Second website I found
>
> http://www.math.com/school/subject1/lessons/S1U2L1GL.html
>
> gives ratios with different units
>
> Third website I found
>
> http://www.purplemath.com/modules/ratio.htm
>
> gives ratios with different units
>
> The "Understanding" of others is often made up nonsense. What is
> taught in school is not reliable. Let's get some websites to back
up
> information.
>
> Regards,
>
> Brian
>
> --- In Math4u@yahoogroups.com, Vinaire <vinaire@> wrote:
> >
> > I think that by "Rationnel" you mean a rational number. A number
> and units are two different things. A rational number is a number
> that can be expressed as a ratio of two integers.
> >
> > When you compare two quantities of the same unit you have a
RATIO.
> When you compare two quantities of different units you have a RATE.
> That is my understanding. Others may clarify it further.
> >
> > PROPORTION simply means two equal ratios.
> >
> > I did not understand what you meant by "et." You seem to be
mixing
> some other language with English.
> >
> > I did not understand what you meant by "rapport."
> >
> > DIVISION simply means how many times you can take one quantity
out
> of another. It may be looked upon as repeated subtraction. When you
> divide a smaller quantity (number with a unit) by a larger number
you
> get fractions.
> >
> > I do not understand the situation where you would divide a number
> by a quantity. Can you give me a practical example of that?
> >
> > Vinaire
> >
> >
> >
> >
> >
> > ----- Original Message ----
> > From: testimprove <bonnerentree2003@>
> > To: Math4u@yahoogroups.com
> > Sent: Sunday, December 16, 2007 12:20:31 PM
> > Subject: [Math4u] Re: 4 situations
> >
> > Hi,
> > "I am not familiar with some of the symbols and terminology you
are
> using"
> > -Which symbols and terminology I use and you are not familiar
with?
> > your question :
> > "Were you taught that way in school?"suprised me.
> > I'd like before answering your question to let me know what you
> thing about this way.
> > Badriya
> >
> >
> >
> >
> >
> > --- In Math4u@yahoogroups. com, Vinaire <vinaire@> wrote:
> > >
> > > I asked that question because I am not familiar with some of
the
> symbols and terminology you are using. Were you taught that way in
> school?
> > >
> > > V.
> > >
> > > ----- Original Message ----
> > > From: testimprove bonnerentree2003@ ...
> > > To: Math4u@yahoogroups. com
> > > Sent: Sunday, December 16, 2007 6:54:25 AM
> > > Subject: [Math4u] Re: 4 situations
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > > Hi
> > >
> > > "What country are you from?"
> > >
> > > even I don't know what is the relation between this question
and
> the mathematic,I give an answer to your question:
> > >
> > > I am from France
> > >
> > > I wonder if my style in writing English is the purpose of your
> inquiry.
> > >
> > > I have studied Math in French ,and I really will be happy if
you
> point out the errors I 'll probably make while typing questions in
> this wonderful forum
> > >
> > > Badriya
> > >
> > > --- In Math4u@yahoogroups. com, Vinaire vinaire@ wrote:
> > > >
> > > > What country are you from?
> > > >
> > > > Vinaire
> > > >
> > > > ----- Original Message ----
> > > > From: testimprove bonnerentree2003@ ...
> > > > To: Math4u@yahoogroups. com
> > > > Sent: Saturday, December 15, 2007 5:17:43 PM
> > > > Subject: [Math4u] 4 situations
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > > Hello,
> > > >
> > > > I'd like to know if it is exact that any Rationnel has 4
> meanings.
> > > >
> > > > · example the rationnel 17/6
> > > >
> > > > · a) the numbers 17 and 6 are different units for
> > > >
> > > > example 17 liters of milk for making 6 kg of cheese
> > > >
> > > > so liters and kg are two diferent units.Here the
> > > >
> > > >
> > > >
> > > > fraction17/6 means a proportion
> > > >
> > > >
> > > >
> > > > · b) 17 et 6 are the same units , for example the
> > > >
> > > > heigth of a triangle is 17mm and the side is 6 mm,
> > > >
> > > > here the fraction 17/6 means a rapport
> > > >
> > > > · c) the number 17 is a unit and the number 6
> > > >
> > > >
> > > >
> > > > deosn't have a unit . For example to cut 17meters in
> > > >
> > > >
> > > >
> > > > 6 equal pieces.Here 17/6 means a divison
> > > >
> > > >
> > > >
> > > > · d) The number 17 doesn't have a unit and 1/6
> > > >
> > > > mm,we have 17x1/6 so here 17/6 is a fraction of the 1/6x17
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > > 
> > > >
> > > >
> > > >
> > > > 
> > > >
> > > >
> > > >
> > > > 
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
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_________
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> > >
> > > 
> > >
> > >
> > >
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> > >
> > >
> > >
> > > 
> > >
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Thursday, December 20, 2007

RE: [Math4u] Re: 4 situations

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