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**Contents**• Section 1—Introduction to Plumbing • Section 2—Plumbing Systems • Section 3—Plumbing System Design and Installation • Section 4—Plumbing Services • Section 5—Career Development and Plumbing History**Section 1**Introduction to Plumbing**Chapter 4**Mathematics for Plumbers**Objectives**• Read a rule accurately to nearest 1/16. • Add and subtract fractions and whole numbers. • Compute pipe offsets using the Pythagorean theorem and trigonometric functions. • Apply the formulas for finding area and volume. • Explain and apply SI metric measure in finding length, area, volume, and temperature. • Convert customary measure to metric measure.**Measurement**(Goodheart-Willcox Publisher)**Measurement**Reading Fractions of an Inch • Read from nearest 1/4 divisions to get precise reading. (Goodheart-Willcox Publisher)**Measurement**Adding Lengths (Goodheart-Willcox Publisher)**Measurement**Subtracting Lengths (Goodheart-Willcox Publisher)**Measurement**Subtracting Unequal Denominators (Goodheart-Willcox Publisher)**Measurement**Borrowing from the Whole Number (Goodheart-Willcox Publisher)**Changing Inches to Feet**(Goodheart-Willcox Publisher)**Changing Feet to Inches**Multiply the dimension given in feet by 12 to get the number of inches. (Goodheart-Willcox Publisher)**Review**Identify each measurement indicated. • 5 1/2 • A. • B. • C. • D. • E. • 4 9/16 • 3 13/16 • 3 1/16 • 1 11/16 (Goodheart-Willcox Publisher)**Review**Add the following dimensions: A. 6 5/8 + 1 3/4 = B. 3 3/16 + 4 3/4 = C. 2 8 3/8 + 4 6 15/16 = D. 5 4 13/16 + 9 5/8 = • 8 3/8 7 15/16 7 3 5/16 6 2 7/16**Review**Subtract the following dimensions: A. 9 3/4 – 3 3/8 = B. 1 2 1/4 – 8 1/8 = C. 12 6 3/4 – 7 4 7/8 = D. 6 9 11/16 – 3 10 13/16 = 6 3/8 6 1/8 5 1 7/8 2 10 7/8**Computing Pipe Offsets**(Goodheart-Willcox Publisher)**Computing Pipe Offsets**Pythagorean Theorem (Goodheart-Willcox Publisher)**Computing Pipe Offsets**Pythagorean Theorem (continued) • Pythagorean theorem applies to all right triangles. (Goodheart-Willcox Publisher)**Computing Pipe Offsets**Trigonometric Functions (Goodheart-Willcox Publisher)**Computing Pipe Offsets**Trigonometric Functions (continued) • Theoretical Length vs. Actual Length Actual length of pipe = Theoretical length –Laying lengthof fittings (Goodheart-Willcox Publisher)**Computing Pipe Offsets**Simple Methods (Goodheart-Willcox Publisher)**Computing Pipe Offsets**Plumber’s Rule (Goodheart-Willcox Publisher)**Review**• Find the travel of the pipe required to join two pipes at a 45 angle that are offset at each of the following distances: • A. 30 = • B. 18 = • C. 1 3 = • D. 2 9 = 42.42 or 4 7/16 25.45 or 25 7/16 22.21 or 22 1/4 46.66 or 46 11/16**Computing Area and Volume**Square or Rectangular Surface (Goodheart-Willcox Publisher)**Computing Area and Volume**Area of Circles (Goodheart-Willcox Publisher)**Computing Area and Volume**Volume of a Rectangular Tank (Goodheart-Willcox Publisher)**Computing Area and Volume**Volume of a Cylindrical Tank (Goodheart-Willcox Publisher)**Review**• Compute the area of the following: • A. 6 6 square = • B. 4 9 12 3 rectangle = • C. 8 6 diameter circle = • D. 4 9 radius circle = 42.25 sq. ft. 58.19 sq. ft. 2,289 sq. in. 10,202 sq. in.**Review**Compute the volume of these tanks: A.B. 615.44 cu. ft. 63 cu. ft.**Computing Slope of Pipe**(Goodheart-Willcox Publisher)**Metric Measurement**Length (Goodheart-Willcox Publisher)**Metric Measurement**Dry Volume**Metric Measurement**Liquid Measures**Metric Measurement**Temperature**Review**• Identify the metric units of measurement used when measuring: • A. Distance: • B. Liquid volume: • C. Dry volume: • D. Temperature: meter, centimeter, millimeter liter or cubic centimeter cubic meter Celsius or Kelvin**Review**• Convert each of the following customary measurements to the equivalent metric measurement. • A. Distance: 1 3 • B. Liquid measure: 22 cu. ft. • C. Dry volume: 135 cu. ft. • D. Temperature: 85 F 68.44 cm. 623.04 L 3.77 cu. meters 29.7 Celsius