1. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website.  Goodheart- Willcox Co., Inc. Permission granted to reproduce for educational use only.

2. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. 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

3. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Section 1 Introduction to Plumbing

4. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Chapter 4 Mathematics for Plumbers

5. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. 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.

6. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Measurement (Goodheart-Willcox Publisher)

7. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Measurement Reading Fractions of an Inch Read from nearest 1/4  divisions to get precise reading. (Goodheart-Willcox Publisher)

8. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Measurement Adding Lengths (Goodheart-Willcox Publisher)

9. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Measurement Subtracting Lengths (Goodheart-Willcox Publisher)

10. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Measurement Subtracting Unequal Denominators (Goodheart-Willcox Publisher)

11. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Measurement Borrowing from the Whole Number (Goodheart-Willcox Publisher)

12. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Changing Inches to Feet (Goodheart-Willcox Publisher)

13. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Changing Feet to Inches Multiply the dimension given in feet by 12 to get the number of inches. (Goodheart-Willcox Publisher)

14. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Review Identify each measurement indicated. A. B. C. D. E. 1 11/16  3 1/16  3 13/16  4 9/16  5 1/2  (Goodheart-Willcox Publisher)

15. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. 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 

16. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. 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 

17. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Computing Pipe Offsets (Goodheart-Willcox Publisher)

18. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Computing Pipe Offsets Pythagorean Theorem (Goodheart-Willcox Publisher)

19. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Computing Pipe Offsets Pythagorean Theorem (continued) Pythagorean theorem applies to all right triangles. (Goodheart-Willcox Publisher)

20. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Computing Pipe Offsets Trigonometric Functions (Goodheart-Willcox Publisher)

21. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Computing Pipe Offsets Trigonometric Functions (continued) Theoretical Length vs. Actual Length Actual length of pipe = Theoretical length – Laying length of fittingsLaying length (Goodheart-Willcox Publisher)

22. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Computing Pipe Offsets Simple Methods (Goodheart-Willcox Publisher)

23. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Computing Pipe Offsets Plumber’s Rule (Goodheart-Willcox Publisher)

24. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. 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 

25. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Computing Area and Volume Square or Rectangular Surface (Goodheart-Willcox Publisher)

26. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Computing Area and Volume Area of Circles (Goodheart-Willcox Publisher)

27. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Computing Area and Volume Volume of a Rectangular Tank (Goodheart-Willcox Publisher)

28. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Computing Area and Volume Volume of a Cylindrical Tank (Goodheart-Willcox Publisher)

29. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. 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.

30. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Review Compute the volume of these tanks: A. B. 63 cu. ft. 615.44 cu. ft.

31. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Computing Slope of Pipe (Goodheart-Willcox Publisher)

32. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Metric Measurement Length (Goodheart-Willcox Publisher)

33. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Metric Measurement Dry Volume

34. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Metric Measurement Liquid Measures

35. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Metric Measurement Temperature

36. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. 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

37. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. 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

38. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. End of Chapter 4

39. Copyright Goodheart-Willcox Co., Inc. May not be posted to a publicly accessible website. Laying length: The amount of a run of pipe, measured along the centerline, that is taken up by the fitting. Plumber’s rule: A measuring device that has a standard scale on one side and a scale for measuring the length of 45  offsets on the other side. Pythagorean theorem: Formula that states the hypotenuse of a right-angle triangle is equal to the sum of the squares of the other two sides. Trigonometric functions: Mathematic functions, such as sine and tangent, that give the ratio between parts of a triangle. ←