be converted to equal fractions having common (the same) denominators. Each numerator must be increased the same number of times as its denominator to make it equal to the original fraction. To solve some problems involving the subtrac- tion of fractions, it is necessary to borrow from the whole number. This procedure is described in detail in Figure 4-7. The earliest record of the term plumber being used is traced to the Roman Empire. Plumbum is the Latin word for lead, and plumbarius means worker in lead. Since lead was used to make pipe and many fixtures, the term plumber was an appropriate name for the trade. 1 2 3 1 2 1 2 3 23⁄4″ + 1⁄16″ = 212⁄16″ + 1⁄16″ = 213⁄16″ 21⁄2″ − 1⁄16″ = 28⁄16″ − 1⁄16″ = 27⁄16″ 11⁄4″ + 1⁄16″ = 14⁄16″ + 1⁄16″ = 15⁄16″ Goodheart-Willcox Publisher Figure 4-3. Reading 1/16″ intervals is easier if you count from the nearest ¼″ dimension and add or subtract spaces. 1 1 1 2 2 2 3 4 5 6 23⁄8″ + 215⁄16″ = 55⁄16″ 23⁄8″ + 215⁄16″ = _______ Denominator Fractions can be added only when the denominators are equal. From Figure 4-1, it can be seen that 3⁄8″ = 6⁄16″. Therefore, the above problem can be rewitten as: Numerators 26⁄16″ + 215⁄16″ = _______ Adding fractions is accomplished by adding numerators. The denominators remain unchanged. 6⁄16″ + 15⁄16″ = 21⁄16″ Since the numerator is larger than the denominator, the fraction is greater than one (sixteen 1/16s = one). Therefore: 21⁄16″ = 16⁄16″ + 5⁄16″ = 15⁄16″ Returning to the original problem: 23⁄8″ + 215⁄16″ = Step 1 26⁄16″ + 215⁄16″ = Step 2 2″ + 2″ + 21⁄16″ = Step 3 2″ + 3″ + 5⁄16″ = 5 5⁄16″ Denominator Numerator In this case: Goodheart-Willcox Publisher Figure 4-4. You can add two or more dimensions by laying off the lengths on a scale. However, another way, shown above, is to add the dimensions together using mathematics. Chapter 4 Mathematics for Plumbers 73 Copyright Goodheart-Willcox Co., Inc.