Download Unit 3

9
16
5’
24’
Unit 3
Page 23
Construction
Mathematics Review
Learning Objectives
Add, subtract, multiply, and divide fractions
 Convert between improper fractions &
mixed fractions
 Add, subtract, multiply & divide decimal
fractions

UNIT 3
page 23
Fractions

written with one number over the top of
another
– numerator
– denominator
9
16
Proper Fractions

numerator is less than denominator
7
16
3
4
UNIT 3
page 23
Improper Fractions

numerator is greater than denominator
5
4
19
16
UNIT 3
page 23
Using Fractions

UNIT 3
page 23
whole numbers can be changed to fractions
Using Fractions
example:
6
6
1
change into fourths
x
4
4
=
24
4
UNIT 3
page 23
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
Using Fractions
UNIT 3
page 24
example:
convert 3 5/8 to an improper fraction
5
3
8
5
24
5
29
3
=
x
+
=
+
=
8
1
8
8
8
8
8
(
)
Using Fractions

UNIT 3
page 24
improper fractions can be reduced to a
whole or mixed number by dividing the
numerator by the denominator
Using Fractions
UNIT 3
page 24
17
example: reduce
to lowest proper
fraction 4
17 = 17 ÷ 4 = 4 1
4
4
Using Fractions

UNIT 3
page 24
reducing fractions to lowest form by
dividing the numerator and the denominator
by the same number
Using Fractions
example: reduce
6 to the
8
lowest fractional form
6 = 6 ÷2
8 ÷2
8
=
3
4
UNIT 3
page 24
using fractions

UNIT 3
page 24
fractions can be changed to higher terms by
multiplying the numerator & denominator
by the same number
UNIT 3
page 24
Using Fractions

example: changed
5 = 5 x2
8 x2
8
5
to higher terms
8
10
=
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

Adding Fractions
example:
UNIT 3
page 24
5
3
11
+
+
=
16 8
32
What is the least
common denominator?
?
Adding Fractions
example:
UNIT 3
page 24
5
3
11
+
+
=
16 8
32
?
What
you multiply
a
5 x 2must10
3 x 4 to get
12
=
=
16 common
2
8
4
32 denominator?
32
Adding Fractions
example:
UNIT 3
page 24
5
3
11
+
+
=
16 8
32
?
Add & convert to a mixed number
33
10
12
11
+
+
=
32
32
32
32
1
or 1
32
Adding Fractions

take 15 minutes & do Activity
3-1 on page 24
UNIT 3
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

Subtracting Fractions
example:
5
3
=
4 16
UNIT 3
page 25
?
What is the least
common denominator?
Subtracting Fractions
example:
5
3
=
4 16
3
Change
so the
4
denominator is 16
3
4
x
4
4
12
=
16
?
UNIT 3
page 25
Subtracting Fractions
example:
5
3
=
4 16
UNIT 3
page 25
?
Subtract numerators & retain
the common denominator
12 - 5
16
16
=
7
16
Subtracting Fractions
take 15 minutes & do Activity 3-2
on page 25
UNIT 3
Multiplying Fractions
change all mixed numbers to improper
fractions
 multiply all numerators
 multiply all denominators
 reduce to lowest terms

UNIT 3
page 25
Multiplying Fractions
example:
1
1
x 4 =
x 3
8
2
UNIT 3
page 25
?
Change all mixed numbers
to improper fractions
1
25 x 4
x
2
8
1
=
Multiplying Fractions
UNIT 3
page 25
?
1
1
x 4 =
x 3
8
2
Multiply all numerators and
then
denominators to get the answer
example:
1
25 x 4
x
2
8
1
100
=
16
Multiplying Fractions
example:
1
1
x 4 =
x 3
8
2
Reduce the fraction
to lowest terms
100
4
= 6
16
16
=
1
6
4
UNIT 3
page 25
?
Multiplying Fractions

UNIT 3
take 15 minutes & do Activity 3-3 on page
25
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

Dividing Fractions
example: 36.5032 ÷ 4.12 =
8 .8 6
4.12. 36.50.32
-32 96
3 543
-3 296
2 472
-2 472
0
?
UNIT 3
page 28
Dividing Fractions
take 15 minutes & do Activity 3-7
on page 29
UNIT 3
Area Measurement

area
– area of a floor, walls
– square feet, yards, meters
length x width
 use same units
 two sides must be the same

UNIT 3
page 29 - 30
Square & Rectangular
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
UNIT 3
page 29
Triangular Area
UNIT 3
page 30
example:
5’
24’
5 (height) x 24 (base) = 120 sf
Triangular Area
UNIT 3
page 30
multiply the base times the height then
divide the sum by 2
example:

5’
24’
5 (height) x 24 (base) = 120 sf
120 sf ÷ 2 = 60 sf
Circular Area

UNIT 3
page 30 - 31
circumference - distance around the circle
Circular Area
UNIT 3
page 30 - 31
diameter - length of line running between two points and
passing through the center circle
diameter
Circular Area
radius - one-half the length of the diameter
radius
UNIT 3
page 30 - 31
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

Circular Area

area of a circle =
UNIT 3
page 30 - 31
 x r2 (radius)
Circular Area
example area of a patio
Area
Area
Area
Area
Area

x r2
=
=  x 15’2
= 3.1415 x (15’ x 15’)
= 3.1415 x 225 sf
= 706.86 sf
UNIT 3
page 30 - 31
Volume Measurement
UNIT 3
page 31
volume is a cubic measure
 volume is found by multiplying area by depth

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
Test Your Knowledge

UNIT 3
take 15 minutes and do problems on page
31
Problems in Construction

UNIT 3
Take 30 minutes & complete Activity 3-8
on page 33
END OF UNIT 3