We always express a Representative Fraction with 1 as the numerator — Page 281, Lesson 246

I want to walk you through how we handle Representative Fractions—RF—when the numerator isn't already 1, and then how we solve the three basic types of scale problems using one simple equation. Let's start with the RF itself. We always express a Representative Fraction with 1 as the numerator. So if you have something like 5 over 1,296,400, that's not in standard form. You divide both the numerator and the denominator by 5, and you get 1 over 259,280. That's your proper RF. Now, there's an easy calculator operation for this. The fastest way is to evaluate the denominator first, then divide by the numerator. For the example we just did, you'd enter: 7 times 1852 times 100, divided by 5. That gives you 259,280 as the denominator. Then you write it down as 1 over 259,280. If instead you enter the numerator first—5 divided by the whole denominator in brackets—you get the RF as a decimal, like 0.000003856. You could use the x⁻¹ key to flip that, but the first method is quicker. Now, let's move to the types of scale questions. There are two basic subdivisions: Simple Scale and Mercator Scale. Mercator Scale problems come in a later chapter. All simple scale problems are solved by substituting into one basic equation: RF equals CL divided by ED. CL is Chart Length, and ED is Earth Distance. That's the core relationship. Sometimes you're given the Chart Length and the Earth Distance and asked to find the RF—that's what we did in the previous example. Sometimes you're given the scale—the RF—and the Earth Distance, and asked to find the Chart Length. Sometimes you're given the RF and the Chart Length, and asked to find the Earth Distance. In every case, you substitute what you know into that equation, apply any conversion factors needed to get both CL and ED in the same units, rearrange if necessary to make the unknown the subject, and solve with your calculator. Let me show you Example 2. On a chart of scale 1 over 5,000,000, how many nautical miles on the Earth are represented by 1.7 centimetres? We start with RF equals CL over ED. So 1 over 5,000,000 equals 1.7 centimetres over ED. Rearranging, ED equals 1.7 times 5,000,000, divided by 1852 times 100. Why 1852 times 100? Because we need to convert centimetres to nautical miles. There are 1852 metres in a nautical mile, and 100 centimetres in a metre, so that conversion factor gets the Earth Distance into nautical miles. You work that through on your calculator and you get your answer. So the key takeaway: one equation, RF equals CL over ED, handles all simple scale problems. Just keep your units consistent, and you're set.