Reasoning and understanding mathematics
The topic is like this: A gives B half of his own pictures, and B gives A quarter of his own pictures. At this time, each of them has 12 pictures. How many photos do they have?
When I first saw this problem, my first feeling was to list the equations, but how to list them properly was difficult at the moment. Today, we will talk about solving mathematical problems by reverse deduction.
In the first part, we draw the meaning of the question according to the meaning of the question.
The question in the stem is, how many pictures did A and B originally have? Then let's start rowing down step by step according to the meaning of the question.
According to the meaning of the question, for the first time, A gave one-fifth of himself to B, so A lost one-fifth of himself, and B got one-fifth of A at this time. Let's go down.
The second time, it was B who gave A a quarter of what he had, so at this time, B itself lost a quarter and A gained a quarter. At this time, A and B each have 12. So according to the meaning of the question, we can see that the sum of A and B is 12+ 12=24.
At this time, according to the reasoning of the meaning of the question, we can see that this problem can be solved by reverse deduction. The so-called backward method is to change the "condition-oriented method" we usually use into the "target-backward method" When doing things, we are often used to the "condition-oriented method", that is, starting from the existing conditions, doing the best possible, that is, the conditions determine the results. Reverse inference is that we use the conditions of the problem to speculate from back to front.
Looking at this problem, from the last step "B minus a quarter equals 12", we can draw the conclusion that "B does not give the value before a quarter". that is
The first step in solving the problem: the number of pieces in B is16;
Step 2: According to the sum of A and B is 24, it can be concluded that the number of pieces in A is 8 at this time.
Then start the third step:
According to the existing number of A, the original number of A is obtained, that is, the original number of A is 10, and the original number of B is obtained according to the total number.
That is, 24- 10 = 14 tablets.
The final result is that A has 10 tablets and B has 14 tablets.
Through the above examples, we should pay attention to: ① proceed from the results and reason step by step.
② In the process of forward reasoning, every operation is the reverse of the original operation.
(3) Pay attention to the sequence of operations and use parentheses correctly.