Maths question

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	4375

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發表於 06-11-9 17:41 |只看該作者

What fraction of 8 hours is a day? Please help me to solve??

connieaunt

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發表於 06-11-9 17:51 |只看該作者

Re: Maths question

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worldpeace

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	4375

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發表於 06-11-9 18:35 |只看該作者

Re: Maths question

But the teacher said it is wrong .

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	3163

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發表於 06-11-9 19:12 |只看該作者

Re: Maths question

A day = 24 hours.
A day as a fraction of 8 hrs = 24 / 8 (=3)

Of course 1/3 is wrong.

Rham

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	101

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發表於 06-11-9 23:07 |只看該作者

Re: Maths question

The question itself is wrong. By definition, a fraction of something is smaller than the whole thing. One day is certainly longer than 8 hours.

The one who gave this question should learn proper English (or Chinese if the original question is in Chinese).

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	3163

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發表於 06-11-10 03:37 |只看該作者

Re: Maths question

Fractions can be larger than 1.
They can be a whole number (e.g. 24/8=3),
they can be a whole number plus a fraction (eg 26/8 = 3 2/8 = 3 1/4)

There is nothing wrong with the question itself.
But it is not written in straightforward English.
One can say it is tricky, and one needs to read the question well in order to answer it, but cannot say it is wrong.

The one setting the question may have copied it from a British exercise book.

Rham

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	101

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發表於 06-11-10 08:54 |只看該作者

Re: Maths question

Mathematically, a fraction can be a proper fraction (<1) or improper fraction (>1). In that defintion, a fraction is basically equivalent to a rational number. I accept that you can use this sense of fraction if the question is in a mathematical form.

But in everyday use, a fraction is part of something. When you say something is a fraction of anything thing, you can't say it is 3 times fraction. It really depends on context and language use.

In my opinion, such kind of question is very 無聊！

English book is NOT always right even for famous writer.

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	3163

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發表於 06-11-10 10:35 |只看該作者

Re: Maths question

Well, after all this is a Maths question (or I would call it an arithmatic question, which is slightly less inhibiting than Maths which should be of a "higher" level), written in "old" English.

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	3163

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發表於 06-11-10 10:38 |只看該作者

Re: Maths question

worldpeace,

I like your login name.

Rham

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	101

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發表於 06-11-10 19:53 |只看該作者

Re: Maths question

When I look at the question again, I have to say the question is just WRONG, both mathematically and in terms of language use.

A fraction is defined as an expression that indicates the quotient of two quantities, such as 1/3.

1/3 is a fraction, 8/24, 24/8, 3/1 are fractions, but 3 is NOT a fraction. 3 is a whole number.

A whole number can be the result of evaluating the the fraction, but it is not the fraction itself.

(My previous posting stating that a fraction is basically a rational number is therefore inaccurate.)

The question is bad Maths and bad English.

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	3163

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發表於 06-11-10 23:42 |只看該作者

Re: Maths question

worldpeace,

Did your kid learn anything about "improper fractions" ?
Can easily search from yahoo.
Pls take a look.

Ref No. 1 -
http://www.teachers.ash.org.au/jeather/maths/dictionary.html

Ref No. 2 -
http://www.mathleague.com/help/fractions/fractions.htm#whatisafraction

:idea:

judy

子爵府

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	11251

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發表於 06-11-11 09:49 |只看該作者

Re: Maths question

1/3 is a fraction, 8/24, 24/8, 3/1 are fractions, but 3 is NOT a fraction. 3 is a whole number.

我第一次聽到3/1<>3，好利害，生平僅見。

Rham

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	101

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發表於 06-11-11 14:42 |只看該作者

Re: Maths question

judy 寫道:
[quote]1/3 is a fraction, 8/24, 24/8, 3/1 are fractions, but 3 is NOT a fraction. 3 is a whole number.

我第一次聽到3/1<>3，好利害，生平僅見。

[/quote]

非也！類似情況其實在生活中經常見到，只不過大家可能沒有留意。

舉個例說，若然先前的問題改為

”What percentage ..... ?"

你會怎麼答？當然是 300%！可否答3？不可以。雖然
數值上 300% 和 3 是一樣的，但表達形式不同。既然問題是問 what percentage, 就只可以以 percentage 作答。日常生活使用上也要按上文下理使用正確的形式。

3/1 和 3 數值上一樣，形式不同。既然問題是問 "What fraction ....." 就應該以 fraction 作答。

3/1 是一個 fraction, 有 numerator, 有 denominator. 3 是一個整數，既沒有 numerator, 也沒有 denominator.

1/3, 2/6, 3/9, 4/12 等數值是一樣的，稱為 equivalent fractions.
1/1, 2/2, 3/3, 4/4 也是 equivalent fractions, 但 1 不是，因為 1 本身不是 fraction。
3/1, 6/2, 9/3, 12/4 也是 equivalent fractions, 但 3 不是。

要學好數學，必須掌握正確的概念。數值和形式是兩個不同的概念，不能混為一談。

manmum

別墅

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發表於 06-11-11 15:07 |只看該作者

Re: Maths question

Rham，

蚊蚊媽

emily06

洋房

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發表於 06-11-11 15:10 |只看該作者

Re: Maths question

I would not say the question is wrong. Mathematically, there is nothing wrong. And the English is also not wrong. But still I would say it is a poorly set question. It is just pointless.

I just do not see what the question is trying to test the child. His English? Or his Math? And does the teacher now find it satisfying since even adults are arguing what the answer should be?

Are "fractions" being taught in P2? Or P3? Some of those children may still be struggling in his English classes and still having problems with interpreting straight forward questions written in simple English.

But unfortunately, some teachers are very good at finding ways to give out as few "ticks" to students as possible. And this is really sad.

Rham

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	101

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發表於 06-11-12 08:50 |只看該作者

Re: Maths question

Yes, I have been saying that the question is pointless all along.  But I still have to insist that the question is wrong in a number of aspects.

If you want to know the colour of an apple, you won't ask "what size is the apple?"  If someone asks a question that won't get the expected answer, he/she is asking the wrong question.  If you expect an answer of 300%, you need to ask "what percentage".  If you expect an answer of 3:1, you need to ask "what ratio".  If you expect an answer of 3, you need to ask "how many times".  So the original question is wrong in terms of purpose.

Secondly, the question is also pedagogically wrong in (1) confusing the concept of value with notation (as explained before, fraction is a notation that must have numerator and denominator) and (2) confusing the language of Mathematics and English.

Let me elaborate more on this.  In daily language, a fraction almost always means a proper fraction (<1, and reduced to the lowest terms, e.g. one half, two third).  Yes, perhaps you may argue that it may also mean mixed fraction.  But improper fraction?  No way!  For example, when 5 apples are divided among 3 kids, each got 1 and 2/3 of an apple.  No one would say each kid got 5/3 apples.  The same word "fraction" has different definitions and usages in the language of Mathematics and English.

When a question is in the form of 文字題, we have to follow the rules, syntax and semantics of the English language.

As German mathematician R.L.E. Schwarzenberger says :

My own attitude, which I share with many of my colleagues, is simply that mathematics is a language. Like English, or Latin, or Chinese, there are certain concepts for which mathematics is particularly well suited: it would be as foolish to attempt to write a love poem in the language of mathematics as to prove the Fundamental Theorem of Algebra using the English language. - Schwarzenberger (2000)

老狐狸

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	244

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發表於 06-11-12 10:16 |只看該作者

Re: Maths question

The question is poor but not wrong (or only wrong in daily language).
answer = 3/1.