引用:
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作者Davidoff-Lite
同個網站有不太一樣的看法，供大家參考。
在這個網站上有人問了一個問題，ab/xy應該是a*b/x*y還是(a*b)/(x*y)。
http://mathforum.org/library/drmath/view/54341.html
直接挑文章的結論來看好了。
以下為無責任翻譯
所以回答你的問題，我想兩種答案都是可以被視為正確的，因為這題目本身就有問題。不過如果要回應學生的疑問，除非他們看的課本還是參考書籍有定義，不然我覺得以標準的運算方法來教導學生(即a*b/x*y)會比較好。但是在實務上，我如果遇到這樣的問題，我會去看這問題是怎麼來的，最後才來判斷。其實討論這個課題，不僅是去看有沒有規則可以去遵循，也是在告訴我們不要寫出模稜兩可的東西。那是會帶給別人困擾的。
彼得森 博士 於數學論壇。 |
這個DR.Peterson的結論不就跟之前DR.IAN一樣嗎!?都是建議將A*B/X*Y當成是(A*B/X)*Y,而不是 (A*B)/(X*Y)...
原文如下:
I prefer the standard way (your first answer) when talking to students,
unless their own text gives the "implicit multiplication first" rule...
請注意(your first answer)是指發問者的第一個算法,也就是(A*B/X)*Y而不是(A*B)/(X*Y), 原發問者問題如下:
The problem was presented like this:
a = 1.56
b = 1.2
x = 7.2
y = 0.2
ax/by = ?
Here are two ways that I solved it:
1) I first rewrote the problem as [1.56(7.2)/ 1.2](0.2). Second, a was
multiplied by x. The product was 11.232. Then, since no parentheses
were present, I followed the order of operations and divided 11.232 by
b, which was 1.2. The quotient was 9.36. Then I multiplied 9.36 by y,
which was 0.2. The final answer was 1.872.
2) The other way, the first thing I did was multiply a by x. The
product, which was 11.232, was set aside for the time being. Then b
was multiplied by y, which gave the product of 0.24. The problem was
now solved by dividing 11.232 (or ax) by 0.24 (or by) to reach a final
answer of 46.8.
Can you please tell us which answer is correct and why?