Math is not my strong suit. Please tell me the equation I need to compute to find the value for x in this situation, please. I’m trying to figure out how to use ratios to determine the difference between two points, when measured at two different scales.

a is the diameter of a large sphere; say, 5 meters. b is a small fraction of that diameter; say, 1 centimeter. c is the diameter of a small sphere; say, 20 centimeters. x is the distance b would be if it were scaled down to compare to c.

The way I arrange it in my mind is not to think of an equation immediately, but to say 'b is to a, as x is to c, ’ or b:a = x:c. Replace the colons with a slash, which is a division bar, to come up with b/a = x/c. Then plug in the values as Nars Glinley did, and Bob’s your uncle.

I find that saying ‘this compares to this, in the same way that this compares to this’, even though I know that’s how it works and I’ve done it countless times, helps me to write the equation.

It’s not actually necessary to do all of your unit conversions first: You can do them at any time (or even not do them at all), so long as you’re careful about carrying the units through all of the calculations. It is usually easiest to do them first, though there are exceptions.

For instance, if you have a map with the scale 2 inch : 1 mile and you want to know how many miles 3 inches represents, you could convert the units and make that a scale of 1:31680, find out how many inches 3 inches represents, and then convert that back to miles… But it’s much easier in that case to leave the units as they are.