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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.

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    1. 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

    2. Section 1 Introduction to Plumbing

    3. Chapter 4 Mathematics for Plumbers

    4. 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.

    5. Measurement (Goodheart-Willcox Publisher)

    6. Measurement Reading Fractions of an Inch • Read from nearest 1/4 divisions to get precise reading. (Goodheart-Willcox Publisher)

    7. Measurement Adding Lengths (Goodheart-Willcox Publisher)

    8. Measurement Subtracting Lengths (Goodheart-Willcox Publisher)

    9. Measurement Subtracting Unequal Denominators (Goodheart-Willcox Publisher)

    10. Measurement Borrowing from the Whole Number (Goodheart-Willcox Publisher)

    11. Changing Inches to Feet (Goodheart-Willcox Publisher)

    12. Changing Feet to Inches Multiply the dimension given in feet by 12 to get the number of inches. (Goodheart-Willcox Publisher)

    13. 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)

    14. 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

    15. 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

    16. Computing Pipe Offsets (Goodheart-Willcox Publisher)

    17. Computing Pipe Offsets Pythagorean Theorem (Goodheart-Willcox Publisher)

    18. Computing Pipe Offsets Pythagorean Theorem (continued) • Pythagorean theorem applies to all right triangles. (Goodheart-Willcox Publisher)

    19. Computing Pipe Offsets Trigonometric Functions (Goodheart-Willcox Publisher)

    20. Computing Pipe Offsets Trigonometric Functions (continued) • Theoretical Length vs. Actual Length Actual length of pipe = Theoretical length –Laying lengthof fittings (Goodheart-Willcox Publisher)

    21. Computing Pipe Offsets Simple Methods (Goodheart-Willcox Publisher)

    22. Computing Pipe Offsets Plumber’s Rule (Goodheart-Willcox Publisher)

    23. 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

    24. Computing Area and Volume Square or Rectangular Surface (Goodheart-Willcox Publisher)

    25. Computing Area and Volume Area of Circles (Goodheart-Willcox Publisher)

    26. Computing Area and Volume Volume of a Rectangular Tank (Goodheart-Willcox Publisher)

    27. Computing Area and Volume Volume of a Cylindrical Tank (Goodheart-Willcox Publisher)

    28. 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.

    29. Review Compute the volume of these tanks: A.B. 615.44 cu. ft. 63 cu. ft.

    30. Computing Slope of Pipe (Goodheart-Willcox Publisher)

    31. Metric Measurement Length (Goodheart-Willcox Publisher)

    32. Metric Measurement Dry Volume

    33. Metric Measurement Liquid Measures

    34. Metric Measurement Temperature

    35. 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

    36. 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

    37. End of Chapter 4