Refutation: "Expanding to several times means multiplying by several times, and reducing to 1/ a few (fractions) means dividing by several times, and several times is not zero."
In the reply to the article "The absurdity of reply from the formula of [original] growth (times)" (2005-04-25 15:45), Guilin said: In the past two years, we have been arguing with the People's Education Society, and we should abandon their absurd "multiplying several times is multiplying several times". Shrinking several times means dividing by several times, and replacing it with "expanding to several times means multiplying." When it is converted into 1/ a fraction, it is divided by a few, not zero. "
I don't think that's appropriate. I think, although the abandonment is "multiplied by several times." Reducing several times means dividing by several times, not "expanding to several times or multiplying" Turning it into 1/ a few (fractions) means dividing by a few, and a few are not 0 ".
The title is "rebuttal", multiply it by several times. When it is converted into 1/ a fraction, it is divided by a few, not zero. ",in fact, the rebuttal is not" expanded to several times or used several times. Reducing to 1/ several (a fraction) means dividing by several, not 0 ",but replacing", in other words, "expanding to several times means multiplication, and reducing to 1/ several (a fraction) means dividing by several, not 0", which cannot replace "expanding to several times means multiplication". Reduce by several times and divide by several times.
Why?
"Expanding several times is to use several times. Several times smaller divided by several times. " It's good.
"To expand to several times is to use several times. Turning it into 1/ fraction means dividing it by a few. What other mistakes are there that are not 0 "?
Neither.
I often go to the K 12 community forum: Education and Teaching Forum to read the post-because I think it is a good place-"The absurd law of People's Education Society should have stopped a long time ago! ! ! ! ! This post has been posted for so long that I should read it. But because I know little about primary school mathematics, I don't have a deep understanding (to put it bluntly, I am a layman and know nothing about primary school mathematics). There is a saying that "an expert looks at the doorway and a layman looks at the excitement." Just browsing the posts without thinking is not impressive. In February 2006, around 10, I saw "Is it wrong to reduce 18 by three times to -36 (minus 36)? "I feel very strange and incredible! 18 Three times equals -36? ! ! Isn't that ridiculous? I am a 60-year-old man, and I always think that the three subtractions of 18 are equal to 6( 18÷3=6). How can it be -36? "18" was not found. Is it wrong to subtract 3 times from -36 (subtract 36)? " -I haven't found it yet. Isn't it wrong to use "Guilin is getting old" or "18 minus three times equals -36 (minus 36)?" I searched in the forum for people's education and the problem column, but I couldn't find it. -I don't know how to demonstrate in the article. I've been thinking about it for four or five days, in the dark and during the day, and I understand that subtracting 18 three times really equals -36! This idea is very meaningful and interesting. For some reason, I posted it after I finished processing it, and the content of the debate was basically not disclosed. But careful people can easily see the intention: there are both affirmation and negation of Guilin's antiquated view; There are both the denial of textbooks and the understanding of people's education society. ) From this, I feel the weight of this topic.
From a mathematical point of view, it is completely correct to "multiply to several times, divide to 1/ a few (fractions), and multiply to four times, 8×4=32, 32 is four times that of 8, and expand to four times that of 8 is four times that of 8; Reducing 8 to 1/4 is divided by 4, 8÷4=2, and 2 is 0/4 of 65438+8.
No matter from what point of view, "expanding several times means multiplying several times." There is no doubt that dividing by several times is wrong.
However, it is not "multiplied by several times", but converted into 1/ several (fractions), and then divided by several times, it is not zero. It is absolutely inappropriate to reduce it several times and divide it several times.
First of all, they are not the same thing.
"Expanding several times is to use several times. Reducing several times means dividing by several times ",which means" expanding, reducing ","expanding to several times means multiplying, and reducing to 1/ several (a fraction) means dividing by several times, which is not zero ",which means" expanding to, reducing to, reducing to and reducing to can be the same thing? The old age in Guilin has shown more than once that the two are not the same thing. The original road was 8 meters wide, but it was later expanded by 2 meters, reaching 10 meter. (After talking about expansion, let's talk about expansion. Naturally, students will have no difficulty in understanding it. Even people who can't read can tell this. Why do you get confused when you get to a literate person? What the textbook needs to solve is how to calculate "expanding several times" and "shrinking several times". "Enlarge to several times is how to multiply, reduce to 1/ several times (fraction) is how to divide by several times, and how to calculate" enlarge to several times "and" reduce to several times ". This is irrelevant, the answer is different.
How to enlarge it several times? How to reduce it several times? There is no solution. In this case, how to replace it?
Secondly, how many times, 1 times, 1 times, and 1 times? What is 8? 8× 1=8, can this be called inflation? Isn't this equivalent to expanding 8 1 times and multiplying it by 1, not counting expansion? It is stipulated that it is not allowed to expand to 1 times. Is it necessary to stipulate that it is not allowed to expand to 1 times? Then it should be noted that if it is expanded to 1 times, it is expanded to 0 times, not expanded. -Look, it's back to expansion. Why not go straight, but make a detour?
In addition, it was asked that "multiplied by several times" cannot replace "multiplied by several times". Then, can't "decreasing to 1/ fraction" replace "dividing by several times"?
It is necessary to talk about another meaning of the sentence "Multiply several times, and turn it into 1/ a few (fractions) is divided by several, and several are not zero". Although there is no answer to how to calculate expansion and contraction, the meaning of a×n and a/n is reiterated: a×n is n times that of a, and a/n divides a into n parts on average. These meanings were learned when I first learned multiplication and division. The textbook says, "multiply by several times is multiply by several times." A few times smaller is divided by several times. I don't want to repeat how to calculate N times of A, but how to calculate how to expand A by N times. I don't want to repeat how to divide A into n equally, but how to calculate how to subtract N times from A.. I'm not talking about how to "expand to" or how to "shrink to". Knowing how to calculate expansion and contraction, how to calculate expansion and how to calculate contraction, it will come naturally.
What's more, the students haven't learned the scores yet. How to understand 1/ fraction?
Also, the absurdity of the reply is seen from the formula of the growth (multiple) rate-five refutations to the statement in the reply of the legal representative of the People's Education Society. We want to emphasize in particular that any number that is expanded several times must be equal to (n+ 1) times of the original number, and any number that is reduced several times must be equal to (n-65438+) times of the original number. )。 This can be calculated by the formula (1). (* Here is the calculation, which I summarized. )
In that case, why not say "expand" or "shrink" but "expand to" and "shrink to"? Isn't "arrival" a snake's foot?
Multiply by "several times larger". Shrinking several times means dividing by several times, and expanding to several times means multiplying. It is not appropriate to reduce it to 1/ fraction, even if it is divided by a few, it is not 0 ". Enlarging it several times means using it several times. A few times smaller is divided by several times. "I don't understand how to zoom in and out several times." To multiply it several times is to multiply it. Scaling down to 1/ several (a fraction) is divided by several, and several is not equal to 0 ".It is not clear how to calculate how to zoom in and out several times. From this perspective, the two are the same thing. However, the difference between the two is also obvious. "Expand several times, is multiplied by several times. The statement that "reducing several times is dividing by several times" is wrong, and that "expanding several times is multiplying several times" is the correct statement that reducing to 1/ several (a fraction) is dividing several times, and several times is not equal to 0 ". Reducing by several times is dividing by several times "is a false statement about how to calculate how to expand and reduce by several times." To multiply it several times is to multiply it. Narrowing down to 1/ a few (fractions) means dividing by a few, and a few is not equal to 0 ",which is the correct statement about how to expand to several times and narrow down to several times.
As mentioned above, we can't use "multiply by several times when expanding, and divide by several times when reducing to 1/ (fraction)" instead of "multiply by several times when expanding". A few times smaller is divided by several times. "
What to replace it with?
Use a+na = a× (1+n) to enlarge it several times, and use a-na = a× (1-n) to reduce it several times.
What about the written statement?
Imitate "to expand several times is to multiply several times." Shrinking several times is divided by several times, which means "expanding several times, shrinking several times and reducing several times."
Now let's call it "expanding several times and reducing several times and reducing several times" as a copy.
One imitation: "expand several times and add a few, shrink several times and subtract a few."
In order to prevent "expanding several times and reducing several times and reducing several times" from being read as "expanding several times and reducing several times and reducing several times", Guilin has had it since ancient times.
Two imitations: "magnification (1+ number) and reduction (1- number)."
Good, there will be no ambiguity. There is no ambiguity, but whether it is written in this way or read out, it is still "multiply a few times a few times, multiply a few times a few times a few times a few times", otherwise you have to read "one plus a few in brackets", which is awkward.
By the way, teachers, how do you pronounce 8×( 1+2)? Can "eight times one plus two" be the same as "eight times one plus two"?
Otherwise, copy it again-
Three imitations: "multiply a few times one plus a few, multiply a few times one minus a few". For example, how to expand 1 times? Multiply by 1+ 1, 1+ 1=2, multiply by 2; How to enlarge it by 2 times? Multiply by 1+2, 1+2=3, multiply by 3; How to reduce 1 times? Multiply by 1- 1, 1- 1 = 0, multiply by 0; How to reduce it by 2 times? Multiply by 1-2, 1-2 =- 1, multiply by-1.
Imitate it again-
Four imitations: "multiply the sum of one plus a few, multiply one minus a few." For example, how to expand 1 times? Multiply by the sum of 1+ 1, and the sum of 1+ 1 =2, multiply by 2; How to enlarge it by 2 times? Multiply by 1+2, 1+2=3, multiply by 3; How to reduce 1 times? Multiply by 1- 1, 1- 1 = 0, multiply by 0; How to reduce it by 2 times? Multiply by 1-2, 1-2 =- 1, multiply by-1.