Questions to ponder

1. Questions to ponder • Why is math important in construction? • How do you think math is used in construction?

2. Intro to Construction Math

3. Whole Numbers Whole numbers are complete units without fractions or decimals.

4. Parts of a Whole Number 5 , 3 1 6 , 2 4 7 This number has seven digits. Digit – any of the numeric symbols from 0-9. tens units millions hundreds thousands ten thousands hundred thousands

5. 4,467,903 What number is in the thousands place? 7 What number is in the tens place? 0 What number is in the hundred thousands place? 4

6. Adding Whole Numbers When you add 2 or more numbers the total is called the sum. If you add 58+34: 58 + 34 Is the answer 8 12 ??? 8+1=9 …….thus the sum of 58+34 is 92 No, you have to carry the tens part of the sum from the units column to the tens column and add it there.

7. Subtracting Whole Numbers Subtracting one number from another is finding the difference. 13 – 6 = 7 Thus the difference between 13 and 6 is 7

8. Multiplying Simple Whole Numbers The most efficient way to add the same number together many times is multiplication. 3 + 3 + 3 + 3 + 3 + 3 = OR 3 X 6 = 18 18

9. Dividing Whole Numbers When dividing, the number you are dividing by is called the divisor. 14 2 divisor

10. Jobsite Applications If you have 364 boxes of drywall screws that must be divided equally between 7 job sites, how many boxes does each site get? 364 7 52 boxes Job sites Boxes/site

11. Jobsite Applications You have a piece of pipe that is 150 feet long. If you cut the pipe into 10 pieces of equal length, how long will each piece of pipe be? 150 10 15 feet per piece =

12. Using a Calculator The calculator is a very efficient tool for saving time. Basic functions: • Add • Subtract • Multiply • Divide • ON/C turns on and clears the calculator

13. Applications • You have a piece of wood 86 inches long. If you cut off one foot. How long will the piece of wood be? • Yesterday, a supply yard contained 93 tons of sand. Since then, 27 tons were removed. How many tons of sand is left in the supply yard? • A roof contains 11 trusses. A company is building 8 roofs. The company will need to order how many trusses? • A worker has been asked to deliver 15 scaffolds to each of 26 sites. How many scaffolds will the worker deliver? • If cast iron pipe weighs 8 pounds per foot, 65 feet weighs? • You need to lay a line of bricks that is 96 inches long. Each brick is 4 inches long. How many bricks will you need to build the wall?

14. Intro to Construction Math

15. Working with Measurements • Standard ruler/measuring tape – you MUST learn to recognize the distances shown on the standard ruler/measuring tape. - a yardstick is a standard ruler that is 3 feet long • Architect’s rule – scaled measurements: - ¼” = 1’ - 3/8” = 1’

16. Fractions Divides a unit into parts: 1 4 numerator denominator

17. Fractions on a Ruler A B C What is A pointing to? What is B pointing to? What is C pointing to? ½” 1 ½” 2 5/8”

18. Finding Equivalent Fractions ¼” = ___/16” 2/16” = ___/8” ¾” = ___/8” 10/16” = ___/8” 4/16” 1/8” 6/8” 5/8”

19. Finding Lowest Common Denominator • Reduce each fraction to its lowest terms • Find lowest common multiple of the denominators • If neither of the denominators is a multiple of the other, you can multiply the denominators together.

20. Find Lowest Common Denominator for the Following Fractions 2/6 and ¾ = _______ ¼ and 3/8 = _______ 1/8 and ½ = _______ 4/32 and 5/8 = _____ 12 8 8 8

21. Adding Fractions 5/8 ¼ + 3/8 = ______ 3/16 + ¼ = _____ 5/8 + ¼ = ______ 7/16 7/8

22. Subtracting FractionsReduce your answer to lowest terms 1/2 7/8 – 3/8 = ______ ½ - ¼ = ______ 7/8 – 3/9 = _______ 1/4 7/24

23. Multiplying Fractions • Multiply numerators together. • Multiply denominators together. • Reduce if possible. ¼ X ¼ = 1 X 1 4 X 4 Thus you get 1 over 16 or 1/16

24. Dividing Fractions Using: ½ / ¼ as an example, follow these steps: • Invert the fraction you are dividing by (1/4). ¼ becomes 4/1 • Change the division sign (/) to multiplication (X). ½ / ¼ ……now becomes ½ X 4/1 • Multiply the fractions. 1 X 4 = 4 2 X 1 = 2 • Reduce if possible. 4/2 reduces to 2

25. Decimals Machinist’s rules uses decimals instead of fractions. Thus a screw measuring 3 7/10 long is written as 3.70 inches

26. Decimals Put the following decimals in order from smallest to largest: .012, .210, .112, .201 .012 .112 .201 .210

27. Conversion Processes Decimals, fractions and percentages are just different ways of expressing the same thing. 4.25 = 4 ¼ 4.25% = .0425

28. Converting Percents to Decimals Convert 47% into decimal form. • Drop the percent sign 47 • Move the decimal point two places to the left 47. Thus 47% in decimal form is .47

29. Metric System Units of measure: • Grams = weight • Liters = volume • Celsius = temperature • Meters = length

30. Metric Prefixes The most common prefixes are: • Kilo • Milli • Centi *Blueprint measurements most often are given in centimeters and millimeters.

31. Job Site Application You need to mix 42 pounds of mortar. Each pound of mortar mix requires 0.03 liters of water. How many liters of water do you need? (round to nearest tenth). 42 pounds of mortar x .03 liters per pound 1.26 liters of water 1.3 liters of water

32. Construction Geometry Everything in construction is made up of different shapes: • Circles • Triangles • Squares • Rectangles

33. Angles Angles are important in construction. You use a tool called a protractor to measure the degrees of an angle

34. Shapes Rectangle – four sided shape with for 90-degree angles. (The sum of all four angles of a rectangle is 360 degrees)

35. Shapes Square – special type of rectangle with four equal sides and for 90-degree angles.

36. Shapes Triangle – closed shape that has 3 sides and 3 angles. (The angles of a triangle can vary but their sum is always 180 degrees).

37. Shapes Circle – closed curve around a center point (circles measure 360 degrees)

38. Area of Shapes Area is the measurement of the surface of an object. Square Inch = 1 inch X 1 inch = inch Square foot = 1 foot X 1 foot = foot Square yard = 1 yard X 1 yard = yard 2 2 2

39. Calculating Areas of Shapes • Rectangle – length X width ( L x W) • Square – length X width (L x W) • Circle – pi X radius (3.14 x r ) • Triangle – ½ X base X height (½ b x h) 2 2

40. Job Site Applications • You have to lay a floor for a 14 x 14 shed. The area of the floor is how many square feet? • You want to paint the walls of a 10 x 10 room. If the walls are 8 feet high, how many square feet will you be painting? • You want to lay marble in a 11’ x 15’ foyer. If the boxes of marble contain 11’ , how many boxes will you need? 2

41. Volume of Shapes Volume is the amount of space occupied in three dimensions. Cubic inch = 1 inch X 1 inch X 1 inch = inch Cubic feet = 1 foot X 1 foot X 1 foot = foot Cubic yard = 1 yard X 1 yard X 1 yard = yard 3 3 3

42. Calculating Volume of Shapes • Rectangle – length X width X height (LxWxH) • Square – length X width X height (LxWxH) • Cylinder – pi X radius X height (pi x r x H) 2 2

43. Job Site Applications • You are going to pour a concrete driveway that is 16’ by 22’. The thickness of the driveway will be 6”. What is the overall amount (volume) of concrete need in cubic feet? • Using the above example. If concrete is sold by the cubic yard, how many cubic yards would you need to order?