Transcript 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