# Simple math question

## Main Question or Discussion Point

how much is two times bigger than 3?

i believe it is 6 because from my knowledge, two times bigger = 2 folds

but many people around me say it is 9.. And their reason, is 3 + 2(3)

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In general:

two times bigger than x

a. 2x

b. x + 2x

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so, which is it true?

## Answers and Replies

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Char. Limit
Gold Member
Why, A.

Your question amounts to "What is 200% as big as three?"

This is different than what they perceive the question to be, that is, "What is 200% bigger than three?" to which the answer is nine.

It just needs to be more clearly stated.

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sylas
Actually, I think this is a simple English question. Natural language can be ambiguous. Mathematical notation, on the other hand, comes with precise definitions.

Hearing the English phrase "twice as big as three", I think "2 x 3 = 6".
Hearing the English phrase "twice again as much as three", I think "3 + 2x3 = 9".

Hearing the English phrase "two times bigger than 3", I think the same as "twice as big as three", but since this in English, I'd be open to the speaker to clarify what they meant without thinking they have made a mathematical error. It might just have been poor phrasing.

Cheers -- sylas

hmm, thats what confusing me,

if "100% as big as 3" my answer would be 3. because i will thing 100% is "whole"
instead of "whole" + "whole"

yea english problem. hoho.

and i hope many people in PF will give their answers/ opinion

hmm, thats what confusing me,

if "100% as big as 3" my answer would be 3. because i will thing 100% is "whole"
instead of "whole" + "whole"
You are changing the question there, y is 2 times as big as x means y=2x while y is 2 times bigger than x means y=3x.

For example, if you say "I am 10% bigger than him", would by your definition mean that he is 10 times as big as me which sounds totally backwards.

owh yeaaaaaa, that make sense. "10% bigger than him" means "110% as big as him".
am i right?

owh yeaaaaaa, that make sense. "10% bigger than him" means "110% as big as him".
am i right?
Yeah, "10% bigger than" and "10% as big" are really different things. Some don't realize that there are two ways to say it and that they mean different things.

How much is two times bigger than the largest value of which that is of fewer which is of then 3.
I always hated those engrish word problems. What's so hard about just saying 2 times 3?

Heres the way the language is misleading - break it up.

What is one time bigger than 3?

6

So;

What is two times bigger than 3?

9

Q.E.D.

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Moonbear
Staff Emeritus
Gold Member
This may seem like a simple question, but it's very relevant to science and scientific papers, and often misused...or at least the terminology quickly gets confusing, leading to ambiguity.

The most confusing usage is when we see statements like, "There was a two-fold increase in response..."

It's that devilish word "increase" that causes trouble. Some use "two-fold increase" synonymously with "two-fold" and others mean "two-fold added to the original amount" when they add the word "increase."

My usual response when I see such terminology is that it is better to include a table or graph showing the actual numbers to eliminate ambiguity.

Office_Shredder
Staff Emeritus
Gold Member
Whenever someone uses "x-fold" whether or not they use the word increase I think of the meaning as being the same, it just increased by a factor of x.

Now that I'm thinking about it I can't figure out how to use the world "2-fold" without the word increase somewhere

When I hear two-fold, I think of a number times 2, added to the original number or x+2x.

Thank the 1600's for the use of standardized symbols!

A 2-fold increase means that it has increased twice the original. Which means y=2x where y is the new amount and x is the original, why would you add it to the original, why not just say 3-fold?

It seems redundant to have a phrase in our language where you multiply and add the same number. In fact looking it up in the dictionary shows the way I understand it to be. It uses the phrase 'doubled' for 2-fold which is a simple mathematical phrase you learn in grade 3. Doubled means 2x not 2x+x so therefore 2-fold means 2x as well.

The OP however has included the word 'bigger' so it changes what the phrase is asking for. It is asking for a number that is twice the size as 3 and the sum is how much larger it is than 3. If that makes sense, so the answer would be 9.

Asking something like '2 times AS big as 3' would give an answer of 6 though, since that is only asking for the value of 2(3). As in it is twice as big not two times bigger.

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It's that devilish word "increase" that causes trouble. Some use "two-fold increase" synonymously with "two-fold" and others mean "two-fold added to the original amount" when they add the word "increase."
PANIC. I'm now trying to think everywhere I have read a phrase such as that and might have misunderstood. And then used my misunderstanding for further working.

My usual response when I see such terminology is that it is better to include a table or graph showing the actual numbers to eliminate ambiguity.
This I shall do. And I'll also never use 'x-fold' anything again. Double, triple, two-and-a-half times will do nicely, thanks.

For the record, I expect I would always take 'two-fold increase' to mean 'double' without thinking about it. As with 'increased by two-fold'.

This question is not simple!

[PLAIN]http://img684.imageshack.us/img684/8752/foldi.jpg [Broken]

Okay, here is a black and grey card folded twice indicating what two fold actually means. The card is four times smaller.

(The B indicates the grey side of the card for illustrative purposes and is not seen in the 0 fold part, i.e. it's the other side of the card!).

If we make is half as small it is ½ it's original size.

If we fold it twice, two fold, it's (½)(½) = ¼ as small and this can be done "experimentally" by picking up a piece of paper and folding.

I think we can say that two fold would be multiplication (2ˣ) while two times bigger than X would be addition; x + 2x, because 1 time bigger is x + x = 2x, so two times bigger is x + 2x = 3x.

I sincerely hate the trickery of language in math word problems, the only reason I ever get them wrong is a misunderstanding of supposedly "concise" language

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You are changing the question there, y is 2 times as big as x means y=2x while y is 2 times bigger than x means y=3x.

For example, if you say "I am 10% bigger than him", would by your definition mean that he is 10 times as big as me which sounds totally backwards.
here's the question,

i realised that "200% bigger" equal "300% as big as"

example ( "9 is 200% bigger than 3" as "9 is 300% as big as 3"

but is "2 times bigger" or "200% times bigger" equal "300% bigger" ?

because it some kind sounds ironic, because if i assume 1=100%,
try "300% bigger" = "3 bigger"?

and i still hold by this

"two times bigger than x" = 2x

"200% bigger than x" = "300% as big as x" = 3x

and i think this lemma will never reach conclusion until someone explain some syntax or grammar error.

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alxm
That's not logical, because "1 time bigger than x" doesn't mean x, it means 2x.
It can't mean x, because it's bigger. It's akin to "a 100% increase".

"Two times greater than" means x + 2x and "Two times as large" or "twice the size" means 2x. This is by no means specific to English. It's the same in all Germanic languages:

Two times larger than/Twice as large
Zweimal größer als/Doppelt so groß (German)
Twee keer groter dan/Twee keer zo groot. (Dutch)
Två gånger större än/Dubbelt så stor (Swedish)

This is a very old and worn-in distinction, and the usage is quite consistent.

Can't people just use normal english or english in a normal way?

If I want to say its three times the size I dont say twice as bigger it's just stupid.

That's not logical, because "1 time bigger than x" doesn't mean x, it means 2x.
It can't mean x, because it's bigger. It's akin to "a 100% increase".
but sadly, some people assume "1 times bigger" equal "whole" including me, including some article or wikipedia i've read

Can't people just use normal english or english in a normal way?
yea, i wish.
i preferred to use "200% bigger", no confusion, ;P

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Char. Limit
Gold Member
All of this just goes to show that word problems are well named... They're a problem.

I've started a new group to get of these problems... We're the Coalition to Eliminate Word Problems, or CEW-P (pronounced kewpie).

Ah, if only. But can't we get people to write problems symbolically, rather than linguistically?