You are reducing a map of dimensions 2ft by 3ft to fit to a piece of paper 8in by 10in. What are the dimensions of the largest possible map that can fit on the page?

6 2/3 in by 10 in

To determine the dimensions of the largest possible map that can fit on the page, we need to compare the dimensions of the map and the dimensions of the paper and find the proportionate scale factor.

First, let's convert all measurements to the same unit, either inches or feet. Let's choose inches for consistency.

Given:
Map dimensions: 2ft by 3ft
Paper dimensions: 8in by 10in

Since 1ft is equal to 12 inches, the map dimensions in inches would be:
Map dimensions: 2ft × 12in/ft by 3ft × 12in/ft
= 24in by 36in

Now we have the map dimensions in inches as 24in by 36in and the paper dimensions as 8in by 10in.

Next, we can find the scale factor by comparing the dimensions of the map to the dimensions of the paper:
Scale factor = Map dimensions / Paper dimensions

For the length: Scale factor = 24in / 8in = 3
For the width: Scale factor = 36in / 10in = 3.6

The scale factor indicates how many times larger or smaller the map needs to be to fit onto the paper. Since the scale factors are different for the length and the width, we need to use the smaller scale factor to ensure both dimensions of the map fit on the paper.

Therefore, the largest possible map that can fit on the page would have dimensions:
Length: 8in × 3 = 24in
Width: 10in × 3 = 30in

So, the dimensions of the largest possible map that can fit on the page are 24in by 30in.