Constrution Mathematics Review

1
Constrution Mathematics Review
Unit 3
2
Unit 3Construction 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
UNIT 3 page 23

• written with one number over the top of another
• numerator
• denominator

4
Proper Fractions
UNIT 3 page 23

• numerator is less than denominator

5
Improper Fractions
UNIT 3 page 23

• numerator is greater than denominator

6
Using Fractions
UNIT 3 page 23

• whole numbers can be changed to fractions

7
Using Fractionsexample
UNIT 3 page 23
6
change into fourths
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 Fractionsexample
UNIT 3 page 24

• convert 3 5/8 to an improper fraction

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 Fractionsexample reduce to
lowest proper fraction
UNIT 3 page 24
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 Fractionsexample reduce to the
lowest fractional form
UNIT 3 page 24
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
UNIT 3 page 24
5 8

• example changed to higher terms

16
Adding Fractions
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
UNIT 3 page 24
5 16
3 8
11 32
?

• example

32
What is the least common denominator?
18
Adding Fractions
UNIT 3 page 24
5 16
3 8
11 32
?

• example

32
What must you multiply to get a common
denominator?
19
Adding Fractions
UNIT 3 page 24
5 16
3 8
11 32
?

• example

32
Add convert to a mixed number
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

• example

5 16
3 4
?
-

16
What is the least common denominator?
23
Subtracting Fractions
UNIT 3 page 25
5 16
3 4
?

• example

-

16
24
Subtracting Fractions
UNIT 3 page 25

• example

5 16
3 4
?
-

16
Subtract numerators retain the common
denominator
25
Subtracting Fractions
UNIT 3
take 15 minutes do Activity 3-2 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 8
1 2
?
x
3
4

x
Change all mixed numbers to improper fractions
28
Multiplying Fractions
UNIT 3 page 25
1 8
1 2
?

• example

x
3
4

x
Multiply all numerators and then denominators to
get the answer
29
Multiplying Fractions
UNIT 3 page 25
1 8
1 2
?

• example

x
3
4

x
Reduce the fraction to lowest terms

30
Multiplying Fractions
UNIT 3

• take 15 minutes do Activity 3-3 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
UNIT 3 page 28
?

• example 36.5032 4.12

.
4.12
.
36.50 32
.
3 543
2 472
0
33
Dividing Fractions
UNIT 3
take 15 minutes do Activity 3-7 on page 29
34
Area Measurement
UNIT 3 page 29 - 30

• 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
UNIT 3 page 29

• example area of a room
• 10 x 12 120 sf

76 x 12 5 ? 76 x 149 11324 sq
inches or 11324 144 78.64 sf
36
Triangular Area
UNIT 3 page 30

• example

5 (height) x 24 (base) 120 sf
37
Triangular Area
UNIT 3 page 30

• multiply the base times the height then divide
  the sum by 2
• example

5 (height) x 24 (base) 120 sf 120 sf 2 60 sf
38
Circular Area
UNIT 3 page 30 - 31

• circumference - distance around the circle

39
Circular Area
UNIT 3 page 30 - 31
diameter - length of line running between two
points and passing through the center circle
40
Circular Area
UNIT 3 page 30 - 31
radius - one-half the length of the diameter
41
Circular Area
UNIT 3 page 30 - 31

• 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 3.1416

42
Circular Area
UNIT 3 page 30 - 31

• area of a circle

43
Circular Area
UNIT 3 page 30 - 31

• example area of a patio

Area ? x 152
Area 3.1415 x (15 x 15) Area 3.1415 x 225
sf Area 706.86 sf
44
Volume Measurement
UNIT 3 page 31

• volume is a cubic measure
• volume is found by multiplying area by depth

45
Volume Measurement
UNIT 3 page 31

• example volume of concrete for
• a 4 thick patio that is 706.86 sf

convert inches to decimal feet 4/12 ( 0.334 )
706.86 sf x 4 ( 0.334 ) 235.38 ft3
put in cubic yards
235.38 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