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.
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)
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