Question

write naoki wants to center a canvas, which is 8 feet wide, on his bedroom wall, which is 17 feet wide. where on the wall should naoki mark the location of the nails, if the canvas requires nails every ⅕ of its length, excluding the edges? explain your solution process.

Explanation:

Step1: Find the available length for nailing on the wall

The wall is 17 feet wide and the canvas is 8 feet wide. The available length on the wall for nailing (excluding the part covered by the canvas) on each side is $\frac{17 - 8}{2}=\frac{9}{2}= 4.5$ feet.

Step2: Divide the available length by the nailing - interval

The canvas requires nails every $\frac{1}{5}$ of its length. First, we consider the available length on one side of the canvas on the wall. Let's assume we work on one - side of the canvas. The number of intervals of length $\frac{1}{5}$ feet in the available length of 4.5 feet is $4.5\div\frac{1}{5}=4.5\times5 = 22.5$. Since we are looking for the position of the nails, we consider the starting point of the nailing area.
The position of the first nail from the edge of the wall (closest to the canvas) for one - side:
The canvas is centered, so the distance from the edge of the wall to the start of the canvas is 4.5 feet. The first nail will be at a distance of $\frac{1}{5}$ feet from the start of the canvas - nailing area. So the distance from the edge of the wall is $4.5+\frac{1}{5}=4.5 + 0.2=4.7$ feet. And then we can place nails every $\frac{1}{5}$ feet within the available length on each side of the canvas.

Answer:

Naoki should mark the nails starting at 4.7 feet from one edge of the wall, and then every $\frac{1}{5}$ (or 0.2) feet towards the center of the canvas on both sides of the canvas's position on the wall.