1. Climate Control Technology Math Climate Control Technology

2. Importance of math Why is math important in construction? * Provides accurate communication of measurements of materials, tools, and/or equipment

3. Numbers Whole Numbers: complete numbers w/o decimals or fractions 1 5 12 368 4,724 Non-Whole Numbers: 1.5 6 ½ 42.8 0.006

4. Digits Parts to Whole Numbers: Digits Units Tens Hundreds Thousands Ten Thousands Hundred Thousand Millions

5. Addition • Adding Whole Numbers 6 + 3 • 9

6. Addition continue • Carrying in Addition • 48 • + 64 • 112

7. Word Problems • Problem-Solving (Word Problems) • If a construction company had 14 workers on one job, 18 on another, and 32 on a third job, how many total employees do they have all together?

8. Applied Math • 14 • 18 • + 32 • 64 total workers

9. Applied Math Continues Subtracting Whole Numbers: • 38 • - 24 • 14

10. Subtraction • Borrowing during subtraction • 34 • - 28 • 6

11. Multiplying • Multiplying Simple Whole Numbers • 4 • x 8 • 32

12. Multiplying Continues • Multiplying Larger Whole Number • 75 • x 16 • 420 • 75_ • 1170

13. Division • Dividing Whole Numbers: • 10 div by 2 5 2 10 10 0

14. Division Continues • Dividing More Complex Numbers: 2 8. 7 12 345. 0 24 10 5 96 9 0 84

15. Importance of Measurements • Measurements • Divisions of an inch

16. Fractions Explained • Fractions – value expressed with a numerator and denominator • 1 • 2 Numerator Denominator

17. Fractions Explained • Equivalent fractions – different numerators and denominators but having the same value • 4 2 1 • 8 4 2

18. Fractions Explained • Reducing to lowest forms • Reduce to lowest terms possible by dividing both the numerator and numerator by the highest number possible

19. Dividing Fractions • 3 3 1 • 9 3 3

20. Dividing Fractions Explained • Lowest common denominator • Find lowest number that will EVENLY divide into both denominators

21. Less than Greater than • 3 5 • 4 8 Which is larger? or

22. Fractions • Adding Fractions • Find lowest common denominator • Use that denominator • Add the numerators • Reduce to lowest terms

23. Adding Fractions • 3 5 • 4 8 • 6 5 11 • 8 8 8

24. Subtracting Fractions • 3 5 • 4 8 • 6 5 1 • 8 8 8

25. Subtracting Continues • Subtracting a fraction from a whole number • 5 – ¼ =

26. Subtracting Continues 4 4/4 • 5 • - ¼ • 4 ¾ 3/4

27. Multiplying Fractions • 4 x 5 = 20 8 6 48

28. Dividing Fraction • Dividing Fractions • Invert (flip) 2nd fraction • multiply numerator • multiply denominator • simplify

29. Dividing Fraction Explains • 3 1 = 8 2 • 3 x 2 = 6 = 3 8 1 8 4

30. Metric rule • Reading metric rule • units of tenths • can be written as decimal or fraction

31. Metric rule Explains 0.2 0.7 1.0 1.6 2.1 2.7

32. Adding decimals • 4.561 • + 54.7 • 4.561 • + 54.7 = 59.261

33. Multiplying Decimals • Multiplying Decimals • Rule: answer must total number of decimal places in answer

34. Multiplying Decimals • 8.2 x 1.26 10332 (count 3 decimal places) = 10.332

35. Dividing decimals • Dividing decimals • if decimal in numerator, keep decimals in line • If decimal in denominator, move until right of units place. Must move same number of places for the numerator.

36. Rounding decimals • Rounding decimals • .5 or above, round up • .499999999999 or below, drop off

37. Calculators • Using calculators

38. Conversions • Conversion Processes • Decimal  Percentages • Percentages  Decimals

39. Conversion • decimals  percentage = # x 100 • percentage  decimals = # / 100

40. Conversion • Fractions  decimals • set up as division problem. • Review questions • p. 2.36

41. Conversion • Converting decimals  fractions • Setup with value over place value • Becomes fraction  reduce

42. Conversion • Converting inches  decimals • divide inches by 12 and place as decimal • Ex. 7” = _?_’ 7/12” = 0.583’

43. Angles acute right obtuse straight adjacent opposite Geometry

44. Shapes • Triangles – 180 , • equilateral • right • isosceles • scalene

45. Squares / Rectangles • 4 sides, right angles • diagonals • 360

46. Circles • 360 • circumference • diameter • radius

47. Pythagorean Theorem • a + b = c 2 2 2

48. Area • amount of space a shape takes up • measured in square in (sq in) or ft (sq ft)

49. Area • A (square) = l x w • A (rectangle) = l x w • A (circle) = Ii r • A (triangle) = ½bh 2

50. Area • find area 8’ 14’