How to solve the problem of planting trees

How to solve the problem of planting trees is as follows:

First, the three elements to solve the problem

When solving the problem of planting trees, we should pay attention to the trunk information and find three elements of planting trees: bus length, spacing (tree spacing) length and number of trees. If any two of the three elements are known, the third element can be found.

Two situations and formulas of planting trees

(a) the tree planting line is not closed

1. If the topic requires planting trees at both ends of the tree planting line, and the number of trees is greater than the number of segments, then the relationship among the total length, the number of trees and the spacing is as follows:

Number of trees = number of segments+1 = total length/spacing+1

Total length = spacing × (number of trees-1)

Spacing = total length ÷ (number of trees-1)

2. If the topic requires planting trees at one end of the route, then the number of trees is 1 less than the number of trees at both ends, that is, the number of trees is equal to the number of line segments, and the formula at this time is:

Total length = spacing × number of trees

Number of trees = number of segments = total length ÷ spacing

Spacing = total length and number of trees

3. If no trees are planted at both ends of the tree planting route, the number of trees is less than that at one end 1, so the formula is:

Number of trees = number of segments-1 = total length-1.

Spacing = total length ÷ (number of trees+1)

Total length = spacing × (number of trees+1)

(2) Close the tree planting route

Plant trees on circles, squares, rectangles, closed curves, etc. Because the ends of the head and tail overlap, the number of plants planted is equal to the number of divided nodes. The relationship among total length, number of plants and spacing between plants is: number of plants = number of nodes = perimeter ÷ spacing.

Third, the detailed explanation of examples.

There is a row of flowers at the school gate, with *** 10 pots. Jasmine ranks sixth from left to right, and Chinese rose ranks eighth from right to left. A bunch of red flowers are all placed between jasmine and Chinese rose. Calculate, how many pots are there in a string of red?

First of all, according to the stem, this is a tree planting problem with closed lines.

From left to right, jasmine is in the sixth place, so from right to left, jasmine is in: 10-(6- 1) = 5, and jasmine is in the fifth pot of flowers. It can also be seen that the third pot counts roses from left to right, and a bunch of red flowers are all placed between jasmine and rose, so a bunch of red flowers has: 10-5-3 = 2 (pot).

Planting trees is a relatively simple problem in primary school mathematics. The key is to understand the quantitative relationship between line points and line segments. As long as we find the known information in the stem, we can get the result according to the formula. I'll give you one more question. There is a path from bear's house to pig's house. Plant a tree every 45 meters and plant 53 trees at both ends. Now plant a tree every 60 meters. How many trees are left?