Additional Math Pages & Resources

Tuesday, April 27, 2010

An inch here, and inch there - what does it matter?

Today's blog is based on a conversation with my pal Gary, as we sat and looked at the new window in my kitchen. It was replaced last year, but due to some fabrication issues it will have to be replaced again. I think this time I will ask for it to be enlarged a bit. This one is a couple inches too small in each direction. Some of the opening is "wasted."

You might wonder, What difference does a couple inches make in an existing window opening? It's still a window isn't it?

Here's a perfect time to use elementary school math to see the difference.

This photo shows the original window, from 1954 (sorry about the dirty dishes).


We will need the dimensions, so here they are on a drawing.

The old window was about 76 x 36 inches which works out to be 19 square feet of window area. I'm going to adjust for the center posts which are an inch wide (so each of them obstructs about 36 sq in of area). The total glass area is 18.5 square feet.

Here's a picture of the new window going in. You can see the gap around the top of the new window frame. It's difficult to remove the old steel window frames, so we left them in the walls. The decrease in size is measured from the old frame's inner edges, not from the opening in the wall.


Here's the drawing with the new dimensions. These indicate the size of the glass.

The new window has 13.77 square feet of window opening. The pillars in the middle are each 3 inches wide compared to 1 inch for the originals, so we subtract a bit more there.

An inch here and an inch there reduced the window to 74% of its original size (13.77 ÷ 18.50). I think we can do better. We now (after breaking out the old windows) know the sills are level and straight, so we don't need so much extra space around the new window frame.

If we could get half the space back, what would it do to the opening?

73 x 33.5 = 2445.5 - 124 = 2321.5 ÷144 = 16.12 square feet or 87% of the originals.

Is 87 halfway between 100% and 74%? Yes.