I have a 36 inch piece of wood (Length) I will placing 6 coat hanger hooks along the length of the wood. The first hook will be placed 1 inch down the length from one end and the last hook will be placed 1 inch from the other end of this 36 inch piece of wood. Question how to find the equal distance between the other 4 hooks to be placed on this wood. All six hooks need to be spaced evenly.
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You want to consider the remaining 34 inches (since you want the 1st and last to be 1inch from the edge) and divide them into 5 equal distances. This means you will need to place the 2nd hook (34/5) inches from the first and then continue in that fashion.
It is not clear whether the question is about arithmetic, or about a practical method to be used in construction. I think it is about arithmetic, in which case Peejay's answer is exactly right. But I will answer it as a woodworker too, as this also contains mathematical ideas. Don't measure anything. Use "dividers" (the tool by that name) if you have them, otherwise take a scrap of paper and mark two points at the edge which you guess might be near the right spacing. Them move the paper along the wood, lightly marking the tentative positions, and of course you will come out too far to the left or right for hook number 6. Then put new marks on your paper using your best guess again a little more or less than before, and repeat. The result: pretty soon you will hit it near enough. Mathematically what you have done is to create a convergent sequence of marks on your paper, which might be either a monotone sequence if you are very cautious, or requires the squeeze theorem if you are a little more aggressive in your adjustments.