In a garden of fruit trees,1/2 are apple trees, 1/4 are peach trees, 1/6 are plum trees. you can calculate how many tree are in the garden by counting cherry trees. there are two hundred cherry trees, so how many trees are in the garden?

We need to find what fraction of the garden is cherry trees so we add the proportion of the other kinds of trees and subtract this from 1 like so:
1/2 + 1/4 + 1/6 = 11/12
1 - 11/12 = 1/12
This means that 1/12 of the all trees in the garden are cherry trees;
We know that there are 200 cherry trees;
If we let x = the total number of trees in the garden
Then, we can say:
1/12 * x = 200
x = 200 * 12
x = 2400

There are 2400 trees in the garden.