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30÷2(2+3)÷5=?

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发表于 29-4-2011 12:07 AM | 显示全部楼层
如果说 2 是参数的话,那么楼主那个题目里的 2 也是参数了。如果把题目变成这样的演算

30÷2(2+3) ...
flash 发表于 28-4-2011 11:50 PM


参数 = number in front of a VARIABLE.
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发表于 29-4-2011 12:31 AM | 显示全部楼层
这些都是计算机interpreting的差别。真正数学写法应该就要避免如此的混淆。
我猜,计算机学生可能就会 ...
斷羽鳥 发表于 29-4-2011 12:03 AM



That's because, even though multiplication and division are at the same level (so the left-to-right rule should apply), parentheses outrank division, so the first 2 goes with the [2], rather than with the "16 divided by". That is, multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication.  

那么难道数学也不是这么算吗?
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发表于 29-4-2011 12:31 AM | 显示全部楼层
不晓得谁有权利去定这些规则,但等官方来决定好了。。

在youtube 还可以找到一些很搞笑的理论。
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发表于 29-4-2011 12:39 AM | 显示全部楼层
That's because, even though multiplication and division are at the same level (so the left-to- ...
flash 发表于 29-4-2011 12:31 AM


parentheses outrank division 。。。这个我倒是真的没有听过。 只是知道INSIDE paren 要先算! 其实在比较低级进算计语言,是没有 x(y) 酱的写法的,只有 x*y, 以免引起不必要的混淆。 比较高级的语言就加入这项, 引起混淆。 其实wolfgam之前就意识到酱的问题了,所以就用[] 和 () 来区分计算等级。
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发表于 29-4-2011 12:50 AM | 显示全部楼层
parentheses outrank division 。。。这个我倒是真的没有听过。 只是知道INSIDE paren 要先算! 其实在 ...
斷羽鳥 发表于 29-4-2011 12:39 AM



对,而且如果有多重 parentheses 的话,还要先做 inner 然后才到 outer。
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发表于 29-4-2011 12:51 AM | 显示全部楼层
不晓得谁有权利去定这些规则,但等官方来决定好了。。

在youtube 还可以找到一些很搞笑的理论。
tensaix2j 发表于 29-4-2011 12:31 AM


这些都是鸡蛋/石头的辩驳 。。。没什么意义。就是促使有关机构去standardize这些咯 。。。
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发表于 29-4-2011 09:06 AM | 显示全部楼层
参数 = number in front of a VARIABLE.
斷羽鳥 发表于 29-4-2011 12:07 AM



参数:parameter
系数:coefficient
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发表于 29-4-2011 09:09 AM | 显示全部楼层
在这情况下,没有乘号 (*)就不能随便加上乘号。例如

10y ÷ 2y = ?

解了这题你就明白了。
flash 发表于 28-4-2011 09:12 PM



按照常理处理
这里xy=(x*y)

所以根据你的方式
30÷2(2+3)÷5
=30÷(2*(2+3))÷5
=30÷(2*5)÷5
=30÷10÷5
=3÷5
=0.6
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发表于 29-4-2011 12:44 PM | 显示全部楼层
参数:parameter
系数:coefficient
puangenlun 发表于 29-4-2011 09:06 AM


这个对 。。。是我摆了乌龙。
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发表于 29-4-2011 02:18 PM | 显示全部楼层
按照常理处理
这里xy=(x*y)

所以根据你的方式
30÷2(2+3)÷5
=30÷(2*(2+3))÷5
=30÷(2*5)÷ ...
puangenlun 发表于 29-4-2011 09:09 AM



对,理由就如我在 42 楼所说的。
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发表于 30-4-2011 02:31 PM | 显示全部楼层
本帖最后由 ~HeBe~_@ 于 30-4-2011 03:56 PM 编辑

答案是0.6。

记得上次我曾经写过类似的解释。忘了我那个帖放去那里了。

  30÷2(2+3)÷5       [先解所有括号内的运算]
=30÷2(5)÷5           [先解除所有括号,才可以解无括号的运算]
=30÷10÷5              [从左到右解答。注意:乘和除运算是归同一级;加和减运算是归同一级的。]
=3÷5
=0.6
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发表于 30-4-2011 04:11 PM | 显示全部楼层
本帖最后由 ~HeBe~_@ 于 30-4-2011 04:51 PM 编辑

这是我在2005年写的, 整理后在2009年再使用在我的工作领域。[英文不好,别见怪。]

I was written below statements in 2005 and reused for my working project in 2009.



CHAPTER 2: LITERATURE REVIEW



Section 2-1 Combined Operation

Combined operations: in a same computation, its involve 2 types or above different calculates’ symbolic, i.e. plus、minus、times、divide or bracket,







Section 2-2 In Ascending Order for Combined Operation



1. In computation combined operations, we should calculate second level operation, followed by calculate first level operation.

(Addition and subtraction are known as first level operation, whereas multiplication and division are known as second level operation. In other words, the precedence of multiplication and division are higher than the precedence of addition and subtraction)

2. If there are brackets, we should perform computation operation in a small bracket, followed by perform computation operation in a standard bracket before perform computation operation in a big bracket.

3. If the signs of operation are in same level operation, we hence should perform calculation from left to right.







Section 2-3 In Ascending Order for Same Level Operation



Involving in a same level operation should follow in ascending order operation that calculates from left to right.

When teaching:

1. First of all, teacher gives explanation for combined operations involving addition and subtraction, and then gives explanation for combined operations involving multiplication and division. Then after making conclusion: Operations involving addition and subtraction or multiplication and division must follow ordering computation from left to right.

2. Students are required to familiar the simple oral in which 2 steps of operation i.e. multiply or divide first, then plus or minus when solving the combined operations. Meanwhile, students are required to use method of writing to calculate it. When they use standard form to do computation, the students are advised to separate the standard form in two sections i.e. the first standard form for combined operation involving addition and subtraction, moreover, the second standard form is for combined operation involving multiplication and division.

3. Teacher should give more explanation for those students who usually make mistake in calculation.







Section 2-4 In Ascending Order for Different Level Operation



If an operation consists of first level operation and second level operation at the same time, therefore perform the second level operation followed by the first level operation i.e. times、divide first, then plus、minus.

If an operation consists of first level operation, second level operation and brackets at the same time, therefore perform the computation within the brackets, then the second level operation followed by first level operation i.e. perform the computation within the brackets first, then times、divide first, followed by plus、minus.

When teaching:

1. Teacher is required to explain the combination of 2 types level operations in ascending order, in order to avoid students misunderstand that is ‘times first then divide, plus first then minus’ instead of ‘times、divide first, then plus、minus’.

2. Guide students apply specific mathematically language to read out 2 steps or 3 steps of operation.

3. Guide students to use the proper operation in which in ascending order to perform accuracy of calculations.

4. Teacher should rectify students who usually make common mistaken, such as 45 + 0 x 2 write wrongly as 45 x 2, 100 ÷ 25 + 25 x 0 write wrongly as 100 ÷ 50 x 0 and so on.







Section 2-5 Brackets

The symbol bracket is used to change the in ascending order operation. Usually we use: small bracket “( )” , also known as parenthesis; standard bracket “[ ]”, also known as square bracket; big bracket “{ }”, also known as curly bracket. Primary students usually apply small bracket and stand bracket.

When involving brackets in computation, must following from internal bracket to external bracket, that is perform computation operation in a small bracket followed by computation operation in a standard bracket before perform computation operation in a big bracket. If operation inside the bracket, we still following the rule of “times、divide first, then plus、minus”, whereas same level operation must calculate from left to right.







Section 2-6 Summary


Same Level Operations

• For combined operations involving +and - .

Work the computation from left to right.


• For combined operations involving × and ÷.

Work the computation from left to right.




Different Level Operations

• For combined operations involving +, - , × and ÷.

Perform the computation from left to right that

i) × or ÷ first, followed by (second level operation)

ii) +or - . (first level operation)


• For combined operations involving+, - , × ,÷ and brackets.

Perform the computation from left to right within the

i) ( ) first,

ii) then × or ÷ , (second level operation)

iii) followed by +or -. (first level operation)


• Inside the bracket,( ), if there consists of different level operation.

Then, perform the computation from left to right that

a) × or ÷ first, followed by (second level operation)

b) +or -. (first level operation)
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发表于 30-4-2011 07:16 PM | 显示全部楼层
本帖最后由 楼猪 于 30-4-2011 07:20 PM 编辑
答案是0.6。

记得上次我曾经写过类似的解释。忘了我那个帖放去那里了。

  30÷2(2+3)÷5       [先解 ...
~HeBe~_@ 发表于 30-4-2011 02:31 PM


先做掉挂号,然后再依序从左到右做乘除,妳说的标准是正确的。可是妳的做法有miss了。。。

30÷2(2+3)÷5      
=30÷2(5)÷5   (先做掉括号)
=15(5)÷5        (然后从左开始除乘)
=75÷5
=15

即使把它写的明晰一点也是一样:

30÷2x(2+3)÷5=15   
                            或者  
30/2(2+3)/5=15

重要的是自己要清楚在做的某某问题,然后才了解它要用的正确算式。。。
因为一些人比较不会依照标准写法或者懒得写清楚,所以会写得很直接和含糊不清。。。

不管在什么情况下,我们都要避免把算式搞乱,像这样:30/2(2+3)÷5,
所以要把括号写得明确一点: (30/2)(2+3)÷5
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发表于 30-4-2011 08:50 PM | 显示全部楼层
即使把它写的明晰一点也是一样:

30÷2x(2+3)÷5=15   
                            或者  
30/2(2+3)/5=15

楼猪 发表于 30-4-2011 07:16 PM


这两个写法的答案不一样。。。。。


前者是 15,但后者是 30/2(2+3)/5=30/10/5 = 0.6
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发表于 30-4-2011 08:54 PM | 显示全部楼层
先做掉挂号,然后再依序从左到右做乘除,妳说的标准是正确的。可是妳的做法有miss了。。。

30÷2(2+3)÷5      
=30÷2(5)÷5   (先做掉括号)
=15(5)÷5        (然后从左开始除乘)
=75÷5
=15

楼猪 发表于 30-4-2011 07:16 PM


红色的部分不对,应该是 30÷10÷5 = 3 ÷ 5 = 0.6
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发表于 30-4-2011 09:39 PM | 显示全部楼层
先做掉挂号,然后再依序从左到右做乘除,妳说的标准是正确的。可是妳的做法有miss了。。。

30÷2(2+3)÷5      
=30÷2(5)÷5   (先做掉括号)
=15(5)÷5        (然后从左开始除乘)
=75÷5
=15

即使把它写的明晰一点也是一样:

30÷2x(2+3)÷5=15   
                            或者  
30/2(2+3)/5=15

重要的是自己要清楚在做的某某问题,然后才了解它要用的正确算式。。。
因为一些人比较不会依照标准写法或者懒得写清楚,所以会写得很直接和含糊不清。。。

不管在什么情况下,我们都要避免把算式搞乱,像这样:30/2(2+3)÷5,
所以要把括号写得明确一点: (30/2)(2+3)÷5
楼猪 发表于 30-4-2011 07:16 PM


你认为
30 ÷ 2 x (2+3)÷5 = 30 ÷ 2(2+3) ÷ 5  
是LHS=RHS吗?   

其实很多人认为括号就是乘。
对,括号是有‘乘’的含义,
但是,并非如此简单。

其实,
30 ÷ 2 x (2+3)÷5 30 ÷ 2(2+3) ÷ 5。

解答:
i)
    30 ÷ 2  x    (2+3)÷5   
= 30 ÷ 2  x  1(2+3)÷5        [其实‘()’前是有coefficient 1,只是隐藏起来]
= 30 ÷ 2 x    1(5)    ÷5        [‘乘号’ 和 ‘(  )’ 的priority相比之下,
= 30 ÷ 2  x    5        ÷5         ‘(  )’ 的precedence高于加减乘除。先解除‘(  )’]
=       15  x    5         ÷5
=            75               ÷5
=  15

ii)
    30 ÷ 2(2+3) ÷ 5。
= 30 ÷     2(5)  ÷ 5          [‘乘号’ 和 ‘(  )’ 的priority相比之下,
= 30 ÷     10     ÷ 5           ‘(  )’ 的precedence高于加减乘除。先解除‘(  )’ ]
=              3       ÷ 5
=  0.6

前者和后者的题目不同,所以很多人把后者的题目当作前者的题目看待!
再来把以上两者的其中运算拿来比较:

30÷2 x 5÷5    和      30÷2(5)÷5   

前者的括号已经解除了; 然而后者的括号依然存在,所以必须先解除它
其实不是重点,重点是很多人把30÷2(5)当作 30÷2 x 5来看待!

30÷2(5) 30÷2 x 5

请问前者,precedence÷高还是precedence ()高?答:解除(),才来从左做到右。
请问后者,x 和 ÷的priority一样。答:从左做到右。
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发表于 30-4-2011 10:20 PM | 显示全部楼层
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发表于 30-4-2011 11:24 PM | 显示全部楼层
本帖最后由 unnamedx 于 30-4-2011 11:27 PM 编辑



30/2(2+3)÷5 = ((30 / 2) * (2 + 3)) ÷ 5 = 15

http://www.google.com.my/search?hl=en&source=hp&q=30%2F2(2%2B3)%C3%B75&btnG=Google+Search&aq=f&aqi=&aql=&oq=&gs_rfai=
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发表于 30-4-2011 11:43 PM | 显示全部楼层
30/2(2+3)÷5 = ((30 / 2) * (2 + 3)) ÷ 5 = 15
unnamedx 发表于 30-4-2011 11:24 PM



30/2(2+3)÷5 不等于 ((30 / 2) * (2 + 3)) ÷ 5,google 给的答案是根据 ((30 / 2) * (2 + 3)) ÷ 5 来算。
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发表于 1-5-2011 12:07 PM | 显示全部楼层
其实,
30 ÷ 2 x (2+3)÷5 ≠ 30 ÷ 2(2+3) ÷ 5。
~HeBe~_@ 发表于 30-4-2011 09:39 PM


抱歉,我不赞同这个解释。

30 ÷ 2(2+3)
以上这个算式写法本来是很有歧义的,它可以写成 30/(2(2+3)) 或者 (30/2)(2+3) 然后给出不一样的答案。

a x b 可以写成 ab, 或者 a • b,这只是缩短乘法的juxtaposition而已。

如果括号旁边任何数字都要先做的话,那么正确标准的写法就应该是这样:30 ÷ (2(2+3))

http://cforum2.cari.com.my/redir ... 56&pid=35211672
~HeBe~_@ 发表于 30-4-2011 09:39 PM [/url]


我对这则新闻没有印象,可是,如果只根据“那位工程师”来解释的话,我觉得没有说服力。




这要看你的顺序,如照你自己的常理的话就是: (30/(2(2+3)))/5 = 0.6
在这不明显情况下,就用标准的算法(左至右):30/2(2+3)/5 = 30/2(5)/5 = 15(5)/5 = 75/5 = 15
不管怎样看也一样: 30 ÷ 2 x (2+3) ÷ 5 = 15 x (5) ÷ 5 = 75 ÷ 5 = 15

如果题目的表示这样:30 ÷ (2 x (2+3))  ÷ 5, 那么才可以这样做:= 30 ÷ 10 ÷ 5 = 0.6
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