1. Constrution Mathematics Review9 16
Constrution Mathematics Review
24’ 5’
Unit 3

2. Unit 3 Construction Mathematics Review
Page 23
Learning Objectives
Add, subtract, multiply, and divide fractions
Convert between improper fractions & mixed fractions
Add, subtract, multiply & divide decimal fractions

3. Fractions 9 16 written with one number over the top of another
UNIT 3
page 23
written with one number over the top of another
numerator
denominator 9 16

4. Proper Fractions 7 16 3 4 numerator is less than denominator UNIT 3
page 23
numerator is less than denominator 7 16 3 4

5. Improper Fractions 5 4 19 16 numerator is greater than denominator
UNIT 3
page 23
numerator is greater than denominator 5 4 19 16

6. Using Fractions whole numbers can be changed to fractions UNIT 3
page 23
whole numbers can be changed to fractions

7. Using Fractions example:
UNIT 3
page 23
Using Fractions example: 6
change into fourths 6 1 x 4 = 24

8. Using Fractions
UNIT 3
page 24
mixed numbers can be changed to fractions by changing the whole number to a fraction with the same denominator as the fractional part & adding the two fractions

9. Using Fractions example:
UNIT 3
page 24
Using Fractions example:
convert 3 5/8 to an improper fraction 3 5 8 = 1 + x 24 29 ( )

10. Using Fractions
UNIT 3
page 24
improper fractions can be reduced to a whole or mixed number by dividing the numerator by the denominator

11. Using Fractions example: reduce to lowest proper fraction
UNIT 3
page 24 17 4 17 4
17 ÷ 4 = = 4 1

12. Using Fractions
UNIT 3
page 24
reducing fractions to lowest form by dividing the numerator and the denominator by the same number

13. Using Fractions example: reduce to the lowest fractional form
UNIT 3
page 24 6 8 6 8 = 2 ÷ 3 4

14. using fractions
UNIT 3
page 24
fractions can be changed to higher terms by multiplying the numerator & denominator by the same number

15. Using Fractions 5 8 5 8 = 2 x 10 16 example: changed to higher terms
UNIT 3
page 24 5 8
example: changed to higher terms 5 8 = 2 x 10 16

16. Adding Fractions denominators must all be the same
UNIT 3
page 24
denominators must all be the same
find the Least Common Denominator (LCD)
then add the numerators
convert to mixed number

17. ? Adding Fractions 5 16 3 8 11 32 + + = 32 What is the least
UNIT 3
page 24 5 16 3 8 11 32 ?
example: + + = 32
What is the least
common denominator?

18. What must you multiply to get a
Adding Fractions
UNIT 3
page 24 5 16 3 8 11 32 ?
example: + + = 32
What must you multiply to get a
common denominator? 5 16 x 2 = 10 32 3 8 x 4 = 12 32

19. Add & convert to a mixed number
Adding Fractions
UNIT 3
page 24 5 16 3 8 11 32 ?
example: + + = 32
Add & convert to a mixed number 11 32 10 12 + = 33 32 1 32 or

20. Adding Fractions
UNIT 3
take 15 minutes & do Activity
3-1 on page 24

21. Subtracting Fractions
UNIT 3
page 25
denominators must all be the same
find the LCD (Least Common Denominator)
subtract the numerators & retain the common denominator
convert to mixed number

22. Subtracting Fractions
UNIT 3
page 25
Subtracting Fractions
example: 3 4 5 16 ? - = 16
What is the least
common denominator?

23. Subtracting Fractions
UNIT 3
page 25 3 4 5 16 ?
example: - = 16
Change so the
denominator is 16 3 4 3 4 x = 12 16

24. Subtracting Fractions
UNIT 3
page 25
Subtracting Fractions
example: 3 4 5 16 ? - = 16
Subtract numerators & retain
the common denominator 5 16 12 - = 7 16

25. Subtracting Fractions
UNIT 3
take 15 minutes & do Activity on page 25

26. Multiplying Fractions
UNIT 3
page 25
change all mixed numbers to improper fractions
multiply all numerators
multiply all denominators
reduce to lowest terms

27. Multiplying Fractions
UNIT 3
page 25
example: 1 2 1 8 ? x 3 x 4 =
Change all mixed numbers
to improper fractions 1 2 x 25 8 4 =

28. Multiplying Fractions
UNIT 3
page 25 1 2 1 8 ?
example: x 3 x 4 =
Multiply all numerators and then
denominators to get the answer 1 2 x 25 8 4 =
100 16

29. Multiplying Fractions
UNIT 3
page 25 1 2 1 8 ?
example: x 3 x 4 =
Reduce the fraction
to lowest terms
100 16 = 4 6 1 4 6 =

30. Multiplying Fractions
UNIT 3
take 15 minutes & do Activity on page 25

31. Dividing Decimals
UNIT 3
page 28
identical to dividing whole numbers, except that the point must be properly placed
count number places to right of the divisor
add this number to the right in the dividend & place decimal point above in the quotient

32. ? Dividing Fractions -32 96 8 8 -3 296 6 -2 472 . 4.12 . 36.50 32 .
UNIT 3
page 28 ?
example: ÷ 4.12 =
-32 96 8 8
-3 296 6
-2 472 .
4.12 . .
3 543
2 472

33. Dividing Fractions
UNIT 3
take 15 minutes & do Activity on page 29

34. Area Measurement area length x width use same units
page
area
area of a floor, walls
square feet, yards, meters
length x width
use same units
two sides must be the same

35. Square & Rectangular example: area of a room 10’ x 12’ = 120 sf
UNIT 3
page 29
Square & Rectangular
example: area of a room
10’ x 12’ = 120 sf
76” x 12’ 5” = ?
76” x 149” = sq inches
or ÷ 144 = sf

36. Triangular Area 5’ 24’ 5 (height) x 24 (base) = 120 sf example: UNIT 3
page 30
example:
24’ 5’
5 (height) x 24 (base) = 120 sf

37. Triangular Area 5’ 24’ 5 (height) x 24 (base) = 120 sf
UNIT 3
page 30
multiply the base times the height then divide the sum by 2
example:
24’ 5’
5 (height) x 24 (base) = 120 sf
120 sf ÷ 2 = 60 sf

38. Circular Area circumference - distance around the circle UNIT 3
page
circumference - distance around the circle

39. Circular Area diameter
UNIT 3
page
diameter - length of line running between two points and passing through the center circle
diameter

40. Circular Area radius radius - one-half the length of the diameter
UNIT 3
page
radius - one-half the length of the diameter
radius

41. Circular Area
UNIT 3
page
pi () is used when determining the area or volume of a circular object.
pi is the ratio of the circumference to the diameter and is equal to

42. Circular Area
UNIT 3
page
x r2 (radius) 
area of a circle =

43. Circular Area r example area of a patio Area =  x r2 Area =  x 15’2
UNIT 3
page
example area of a patio
x r2
Area = 
Area =  x 15’2
Area = x (15’ x 15’)
Area = x 225 sf
Area = sf
30’ r

44. Volume Measurement volume is a cubic measure
UNIT 3
page 31
Volume Measurement
volume is a cubic measure
volume is found by multiplying area by depth

45. convert inches to decimal feet
Volume Measurement
UNIT 3
page 31
example: volume of concrete for
a 4” thick patio that is sf
convert inches to decimal feet
4”/12” = ( )
sf x 4” ( ) = ft3
put in cubic yards
÷ 27 = 8.71 yrds3

46. Test Your Knowledge
UNIT 3
take 15 minutes and do problems on page 31

47. Problems in Construction
UNIT 3
Take 30 minutes & complete Activity 3-8 on page 33
END OF UNIT 3