7.1 Strategies for a Challenging Problem

This section is designed to direct you through a challenging problem and illustrate strategies that can help make an exercise that contains fractions easier to tackle. You are not expected to complete this problem from scratch, but rather work through it as presented, in pieces, with guidance. Be sure to pay attention to the strategies used, as well as keep track of any difficulties you run into. Here’s the example of how fractions can be used in a practical problem.

Suppose you find an old photograph that you would like to hang in your house. The dimensions of the photograph are unique. You know custom framing and matting can be quite expensive, so you plan to do the work yourself. The photo will be framed by “matting” a piece of rigid cardstock material with a rectangular window cut out of it for the photo to show through. Then, you want to place the matted photo into a frame.

Note: The dimensions of this picture do not match those of the photograph you want to frame.

Matting is sold in standard sizes, so you will need to purchase a big enough piece and trim it down to the desired size. You will also need to cut an opening of the right size and shape to correctly expose the photograph. Next, you will mount the photo to the matting so that it is exposed through the “window.” The matting (with the enclosed photo) will then be placed in the frame. (For the second part of the problem, you can think of the matting as the “new” photo.) In other words, once you have the matting properly sized, you will need to purchase a frame that fits the matting rather than the photo. The photograph above shows a photograph that has been matted and framed, but with very different dimensions and proportions than the one you will be calculating in this exercise.

How much of the matting will need to be cut off and discarded? What are the overall dimensions of the framed picture?

7.0.3 What to Do When You Get Stuck—Revisited with Fractions!

7.1.1 Step 1: Do You Understand the Problem?