Through the previous study, we know that the problem of sum and difference is: knowing the sum and difference of two numbers, find the value of these two numbers; I also know that the problem of sum and multiple is to find the sum and multiple of two numbers. So now we're going to learn about differences. Do you already know its definition? Yes, the problem of difference times is to find the value of two numbers by knowing their differences and multiples. Let's use examples to deepen our understanding of it.

Case study 1

Football is three times as much as volleyball, and football is more than volleyball 18. How many football and volleyball are there?

Analysis: We see multiples in the problem, so the first thing that comes to mind is to draw line segments. After drawing the line segments, mark the equal parts with small triangles. So much 18 only corresponds to which part? Yes, it is the value of two small triangles. So we can get the number of volleyball.

Volleyball: 18÷2=9 (only)

Football: 3×9=27 (only)

A: There are 27 footballs and 9 volleyballs.

This is the most basic difference problem, but the difference problem often digs holes in the process, so that you can't see the real difference. At this time, we need to think about it.

Example analysis 2: The oil weight of barrel A and barrel B is the same. Add 26 kg of oil to barrel A and 14 kg of oil to barrel B. At this time, the weight of barrel B oil is three times that of barrel A oil. How many kilograms are there in two barrels of oil?

Analysis, this is a problem involving the process. At this time, we can't see the difference at once. But don't panic, it's a process, so act it out. First draw two equal-length line segments side by side (this one should be distinguished from the multi-line segment diagram just now), one replaces A and the other replaces B, and the armored barrel takes 26 kilograms, so we erase a part of the armored segment; 14g was added to bucket b, so we added a paragraph to bucket b ... Well, look at the picture below, is it easy to see the difference between the two buckets? That is 26+ 14=40 (kg). Then draw the difference line segment diagram that appears, as shown in Figure 2. At this time, can we find out the weight of the armor now, and then we can find out the weight of the armor. Of course, this is not the end, because what we want in the question is how many kilograms. Because the original weights are equal, we only need to find one.

(Now) A: (26+ 14)÷2=20 (kg)

(Original) A: 20+26 = 46 (4g)

Another thing to be reminded is:

Process problems like this are easy to dig holes in the solution. Therefore, before you start to solve the problem, you must see clearly what the problem requires, and don't take it for granted, because it will save you a few steps. Don't write this question naturally because all the questions you have done before are asking this question, so you must improvise.

Summary:

1, in case of multiple relation, draw a line segment diagram, mark the line segments with equal length with a small triangle, and then mark all the conditions in the problem into the diagram. Then find out the small triangle, and everything else can be represented by small triangles.

2, usually need to find the data implied in the question, don't take it for granted, you can draw a picture on paper or demonstrate the process again with a small hand.