Last time, I explained the basic problems of sum and multiple to all the students, and clearly gave them in the questions. But some questions are not explicit, but obscure. Then let's see what we have hidden now. How can we solve it?

Example 1. When two numbers are divided by quotient 9, the remainder is 4. The sum of dividend, divisor and quotient is 89. What is the divisor?

Analysis: Let's analyze the following question. The quotient of dividing two numbers is 9, and the remainder is 4. namely

Dividend Divider = 9 ... Four

Can this sentence be put another way, for example, the dividend is more than 9 times the divisor? That's right, that's right, so do we see multiples here? Yes, it's also a matter of doubling. When we see multiples, our first thought should be drawing. Draw a picture, mark all the conditions in the question, and then we will draw a picture. Multiples are known, so their sum is 93? Of course not, because there is another quotient in it, so their sum is 93-9 = 84.

Now that the diagram is ready, can we easily find the value of a small triangle, that is, the divisor?

93 - 9=84

Divider: (84-4) ÷ 10 = 8

A: The divisor is 8.

Example 2. The circumference of a rectangle is 56 cm, and the length is twice the width and less than 2. How many centimeters is the length and width of this rectangle?

Analysis, a look at the problem, we read it twice, so we can use the line segment diagram again. Then look at the sum of length and width. The circumference given in the question is 56 cm. What is the formula for finding the circumference? Yes, circumference = (length+width) ×2, so the sum of length and width is 56÷2=28 (cm).

The picture is ready, and the conditions in the question are all marked. Now let's look at the picture. Isn't it kind? We can easily find the width.

? 56÷2=28 cm

Width: (28+2)÷3= 10 (cm)

Length: 10× 2-2 = 18 (cm)

Or 28- 10 = 18 (cm)

A: The length of the rectangle is 20 cm and the width is 10 cm.

Summary:

(1) As long as you encounter multiple relations, you should first think of drawing line segments, because multiples are easy to draw line segments.

Be sure to find the number that actually corresponds to the small triangle. Cut off the more and make up the less. Don't use division rashly. Be sure that division is an average score.