Modern Plumbing 9e Page 103 (117 of 576)

Copyright Goodheart-Willcox Co., Inc. Chapter 6 Mathematics for Plumbers 103 more accurate than attempting to count the number of spaces. To prevent costly errors, recheck each measurement before cutting materials. The reduced waste in both time and materials makes this procedure worthwhile. 6.1.2 Adding and Subtracting Lengths Frequently, you will need to add two lengths that are given in fractions of an inch. Figure 6-4 illustrates how to perform direct addition by putting two scales together. It also shows how to add measurements given in fractions. 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 6-3. Reading 1/16˝ intervals is easier if you count from the nearest 1/4˝ dimension and add or subtract spaces. 1 2 3 4 5 6 23⁄8″ + 215⁄16″ = 55⁄16″ 23⁄8″ + 215⁄16″ = _______ Denominators Fractions can be added only when the denominators are equal. From Figure 6-1, 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: 1 2 3 Goodheart-Willcox Publisher Figure 6-4. You can add two or more dimensions by laying off the lengths on a scale. However, another way, shown here, is to add the dimensions together using mathematics.

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Copyright Goodheart-Willcox Co., Inc. Chapter 6 Mathematics for Plumbers 103 more accurate than attempting to count the number of spaces. To prevent costly errors, recheck each measurement before cutting materials. The reduced waste in both time and materials makes this procedure worthwhile. 6.1.2 Adding and Subtracting Lengths Frequently, you will need to add two lengths that are given in fractions of an inch. Figure 6-4 illustrates how to perform direct addition by putting two scales together. It also shows how to add measurements given in fractions. 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 6-3. Reading 1/16˝ intervals is easier if you count from the nearest 1/4˝ dimension and add or subtract spaces. 1 2 3 4 5 6 23⁄8″ + 215⁄16″ = 55⁄16″ 23⁄8″ + 215⁄16″ = _______ Denominators Fractions can be added only when the denominators are equal. From Figure 6-1, 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: 1 2 3 Goodheart-Willcox Publisher Figure 6-4. You can add two or more dimensions by laying off the lengths on a scale. However, another way, shown here, is to add the dimensions together using mathematics.

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Copyright Goodheart-Willcox Co., Inc. 102 Section 1 Introduction to Plumbing 6.1 Measurement The basic measuring tools used by the plumber are the folding rule and the steel tape. Whichever is used, the scale printed on the tool is the same. Figure 6-1 illus- trates how the basic scale is divided into parts of an inch. 6.1.1 Reading Fractions of an Inch Reading a rule accurately and quickly requires care- ful attention to the markings on the scale and some practice. The lines marking the scale vary in length. The longest lines are the inch divisions. The short- est lines on many rules are sixteenths of an inch. Figure 6-2 shows several examples. The easiest way to read a scale accurately to the nearest 1/16″ is to use the 1/4″ divisions as a start- ing point. Then add or subtract the smaller parts of an inch from the larger divisions to get the correct reading, Figure 6-3. This method is much faster and 1 2 2 1 1 2 1 2 2 1 1 2 1 4 3 4 1 4 3 4 1 2 2 1 1 2 1 4 3 8 1 8 3 4 7 8 5 8 1 4 3 8 1 8 3 4 7 8 5 8 1 2 2 1 1 2 1 4 3 8 1 8 1 16 3 16 5 16 7 16 9 16 11 16 13 16 15 16 1 16 3 16 5 16 7 16 9 16 11 16 13 16 15 16 3 4 7 8 5 8 1 4 3 8 1 8 3 4 7 8 5 8 1 2 Inch dimensions ½″ dimensions divide each inch into two equal spaces ¼″ dimensions divide each inch into four equal spaces 1⁄8″ dimensions divide each inch into eight equal spaces 1⁄16″ dimensions divide each inch into sixteen equal spaces Goodheart-Willcox Publisher Figure 6-1. Reading a standard rule accurately and quickly is a skill that every plumber must master. Study the fraction above to fix the division of an inch firmly in your mind. 1 2 3 4 5 6 1 2 3 1 2 3 4 5 1 2 3 4 51⁄8″ 41⁄2″ 33⁄16″ 23⁄4″ Goodheart-Willcox Publisher Figure 6-2. Learn to recognize each scale marking by length and position.

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Copyright Goodheart-Willcox Co., Inc. 104 Section 1 Introduction to Plumbing Subtracting dimensions given in fractions of an inch is another skill you will need. The procedure, shown in Figure 6-5, is nearly identical to that for addition. Note that the fractions must have common denomina- tors before they can be subtracted. When the denominators of the fractions are not the same number, follow the procedure shown in Figure 6-6. The fractions must be converted to equal fractions hav- ing common (the same) denominators. Each numera- tor 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 subtraction of fractions, it is necessary to borrow from the whole num- ber. This procedure is described in detail in Figure 6-7. 6.2 Converting Feet to Inches and Inches to Feet It is often necessary to change dimensions given in inches to equal dimensions in feet and inches. Since there are 12 inches in a foot, this is done by dividing dimensions given in inches by 12, Figure 6-8. Feet can be changed to inches by multiplying the number of feet by 12 (the number of inches in a foot). 6.3 Computing Pipe Offsets The illustration in Figure 6-9 presents a typical pipe offset problem. Two parallel pipes must be joined by a 1 2 3 4 1 2 3 4 5 6 53⁄4″ – 41⁄4″ = ______ 41⁄4″ 53⁄4″ Subtracting the numerators of the fractions produces the following results: 53⁄4″ – 41⁄4″ = ______″4⁄2 Subtracting the whole numbers gives: 53⁄4″ – 41⁄4″ = 12⁄4″ Now, 2⁄4″ can be written in a simpler, reduced form: 53⁄4″ – 41⁄4″ = 11⁄2″ Goodheart-Willcox Publisher Figure 6-5. Dimensions can be subtracted using the same methods shown in Figure 6-4. 1 2 3 4 1 2 3 4 5 6 61⁄2″ – 43⁄16″ = ______ 61⁄2″ 43⁄16″ When the denominators of the fractions are unequal, the fractions must be changed to equal fractions having common (equal) denominators. From Figure 6-1, it can be seen that 1⁄2″ = 8⁄16″. Therefore, the above problem can be written as: 68⁄16″ – 43⁄16″ = ______ Subtracting the fractions produces the following results: 68⁄16″ – 43⁄16″ = ______″16⁄5 Subtracting the whole numbers completes the problem: 68⁄16″ – 43⁄16″ = 25⁄16″ Goodheart-Willcox Publisher Figure 6-6. Method of subtracting dimensions given in fractions of an inch and having unequal denominators.

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Page 176Section 2 Plumbing Systems click to expand contents

Page 272Section 3 Plumbing System Design and Installation click to expand contents

Page 454Section 4 Plumbing Services click to expand contents

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