9169
16
24’24’5’5’
Unit 3Unit 3Construction Construction
Mathematics ReviewMathematics Review
Add, subtract, multiply, and divide fractionsAdd, subtract, multiply, and divide fractions Convert between improper fractions & Convert between improper fractions &
mixed fractionsmixed fractions Add, subtract, multiply & divide decimal Add, subtract, multiply & divide decimal
fractionsfractions
Add, subtract, multiply, and divide fractionsAdd, subtract, multiply, and divide fractions Convert between improper fractions & Convert between improper fractions &
mixed fractionsmixed fractions Add, subtract, multiply & divide decimal Add, subtract, multiply & divide decimal
fractionsfractions
Learning ObjectivesLearning Objectives
Page 23Page 23
FractionsFractions
written with one number over the top of written with one number over the top of anotheranother– numeratornumerator– denominatordenominator
1616
UNIT 3page 23UNIT 3
page 23
99
Proper FractionsProper Fractions
numerator is numerator is lessless than denominator than denominator
7167
163434
UNIT 3page 23UNIT 3
page 23
Improper FractionsImproper Fractions
numerator is numerator is greatergreater than denominator than denominator
5454
19161916
UNIT 3page 23UNIT 3
page 23
Using FractionsUsing Fractions
whole numbers can be changed to fractionswhole numbers can be changed to fractions
UNIT 3page 23UNIT 3
page 23
Using FractionsUsing Fractions
example:example:
66
6161
xx 4444
== 244
244
change into fourthschange into fourths
UNIT 3page 23UNIT 3
page 23
Using FractionsUsing Fractions
mixed numbers can be changed to fractions by mixed numbers can be changed to fractions by changing the whole number to a fraction with changing the whole number to a fraction with the same denominator as the fractional part & the same denominator as the fractional part & adding the two fractionsadding the two fractions
UNIT 3page 24UNIT 3
page 24
Using FractionsUsing Fractions
example:example:
convert 3 5/8 to an improper fractionconvert 3 5/8 to an improper fraction
UNIT 3page 24UNIT 3
page 24
33 5858
== 3131
8888
++ 5858
xx == 248
248
++ 5858
== 298
298( )
Using FractionsUsing Fractions
improper fractions can be reduced to a improper fractions can be reduced to a whole or mixed number by dividing the whole or mixed number by dividing the numerator by the denominatornumerator by the denominator
UNIT 3page 24UNIT 3
page 24
Using FractionsUsing Fractions
example: reduce to lowest proper example: reduce to lowest proper fractionfraction
44 1414
174
174
17 ÷ 4 =17 ÷ 4 ===
UNIT 3page 24UNIT 3
page 24
174
174
Using FractionsUsing Fractions reducing fractions to lowest form by reducing fractions to lowest form by
dividing the numerator and the denominator dividing the numerator and the denominator by the same numberby the same number
UNIT 3page 24UNIT 3
page 24
3434
6868
6868
== 2222
÷÷ ==
UNIT 3page 24UNIT 3
page 24Using FractionsUsing Fractions
example: reduce to the example: reduce to the
lowest fractional formlowest fractional form
6868
using fractionsusing fractions
fractions can be changed to higher terms by fractions can be changed to higher terms by multiplying the numerator & denominator multiplying the numerator & denominator by the same numberby the same number
UNIT 3page 24UNIT 3
page 24
Using FractionsUsing Fractions
example: example: changed to higher terms changed to higher terms
10161016
5858
5858
== 2222
xx ==
UNIT 3page 24UNIT 3
page 24
5858
Adding FractionsAdding Fractions
denominatorsdenominators mustmust all be the sameall be the same find the find the LLeast east CCommon ommon DDenominator (enominator (LCDLCD)) then add the numeratorsthen add the numerators convert to mixed numberconvert to mixed number
UNIT 3page 24UNIT 3
page 24
Adding FractionsAdding Fractions
example:example:
UNIT 3page 24UNIT 3
page 24
5165
16++ 3
838
++ 11321132
== ??32
What is the least common denominator?
What is the least common denominator?
Adding FractionsAdding Fractions
example:example:
5165
16xx 2
222
== 10321032
3838
xx 4444
== 12321232
UNIT 3page 24UNIT 3
page 24
5165
16++ 3
838
++ 11321132
== ??32
What must you multiply to get a common denominator?
What must you multiply to get a common denominator?
Adding FractionsAdding Fractions
example:example:
11321132
10321032
12321232++ ++ ==
33323332
1321
3211oror
UNIT 3page 24UNIT 3
page 24
5165
16++ 3
838
++ 11321132
== ??32
Add & convert to a mixed numberAdd & convert to a mixed number
Adding FractionsAdding Fractions
take 15 minutes & do take 15 minutes & do Activity Activity
3-13-1 on on page 24page 24
UNIT 3UNIT 3
Subtracting FractionsSubtracting Fractions
denominatorsdenominators mustmust all be the sameall be the same find the find the LCD LCD ((LLeast east CCommon ommon DDenominator)enominator) subtract the numerators & retain the common subtract the numerators & retain the common
denominatordenominator convert to mixed numberconvert to mixed number
denominatorsdenominators mustmust all be the sameall be the same find the find the LCD LCD ((LLeast east CCommon ommon DDenominator)enominator) subtract the numerators & retain the common subtract the numerators & retain the common
denominatordenominator convert to mixed numberconvert to mixed number
UNIT 3page 25UNIT 3
page 25
Subtracting FractionsSubtracting Fractions
example:example: 3434
-- 5165
16 == ??1616
UNIT 3page 25UNIT 3
page 25
What is the least common denominator?
What is the least common denominator?
Subtracting FractionsSubtracting Fractions
example:example: 3434
-- 5165
16 == ??
3434 xx
4444
== 12161216
1616
UNIT 3page 25UNIT 3
page 25
Change so the
denominator is 16
Change so the
denominator is 16
3434
Subtracting FractionsSubtracting Fractions
example:example: 3434
-- 5165
16 == ??
5165
1612161216
-- ==7
167
16
1616
UNIT 3page 25UNIT 3
page 25
Subtract numerators & retain the common denominator
Subtract numerators & retain the common denominator
Subtracting FractionsSubtracting Fractions
take 15 minutes & do Activity 3-2 on page 25take 15 minutes & do Activity 3-2 on page 25
UNIT 3UNIT 3
Multiplying FractionsMultiplying Fractions
change all mixed numbers to improper change all mixed numbers to improper fractionsfractions
multiply all numeratorsmultiply all numerators multiply all denominatorsmultiply all denominators reduce to lowest termsreduce to lowest terms
UNIT 3page 25UNIT 3
page 25
Multiplying FractionsMultiplying Fractions
example:example:example:example: 1212
xx 1818
xx ??33 44 ==
1212
xx 258
258
xx 4141 ==
UNIT 3page 25UNIT 3
page 25
Change all mixed numbersto improper fractions
Change all mixed numbersto improper fractions
Multiplying FractionsMultiplying Fractions
example:example:example:example: 1212
xx 1818
xx ??33 44 ==
UNIT 3page 25UNIT 3
page 25
Multiply all numerators and thendenominators to get the answer
Multiply all numerators and thendenominators to get the answer
10016
10016
1212
xx 258
258
xx 4141 ==
Multiplying FractionsMultiplying Fractions
example:example:example:example: 1212
xx 1818
xx ??33 44 ==
10016
10016 ==
4164
1666 == 1414
66
UNIT 3page 25UNIT 3
page 25
Reduce the fraction to lowest terms
Reduce the fraction to lowest terms
Multiplying FractionsMultiplying Fractions
take 15 minutes & do take 15 minutes & do Activity 3-3Activity 3-3 on on page page 2525
UNIT 3UNIT 3
Dividing DecimalsDividing Decimals
identical to dividing whole numbers, except identical to dividing whole numbers, except that the that the pointpoint must be properly placed must be properly placed
count number places to right of the count number places to right of the divisordivisor add this number to the right in the add this number to the right in the dividenddividend
& place decimal point above in the & place decimal point above in the quotientquotient
UNIT 3page 28UNIT 3
page 28
Dividing FractionsDividing Fractions
example: example: 36.5032 ÷ 4.12 = 36.5032 ÷ 4.12 = ??4.124.12 36.50 3236.50 32.. . .
. . 88
-3 296-3 2962 4722 472
3 5433 543
6 6
-2 472-2 47200
-32 96-32 96
88
UNIT 3page 28UNIT 3
page 28
Dividing FractionsDividing Fractions
take 15 minutes & do Activity 3-7 on page 29take 15 minutes & do Activity 3-7 on page 29
UNIT 3UNIT 3
Area MeasurementArea Measurement
areaarea– area of a floor, wallsarea of a floor, walls– square feet, yards, meterssquare feet, yards, meters
length x width length x width use same unitsuse same units two sides must be the sametwo sides must be the same
UNIT 3page 29 - 30
UNIT 3page 29 - 30
Square & RectangularSquare & Rectangular
example:example: area of a room area of a room
10’ x 12’ = 120 sf10’ x 12’ = 120 sf
UNIT 3page 29UNIT 3
page 29
76” x 12’ 5” = ? 76” x 149” = 11324 sq inchesor 11324 ÷ 144 = 78.64 sf
76” x 12’ 5” = ? 76” x 149” = 11324 sq inchesor 11324 ÷ 144 = 78.64 sf
Triangular AreaTriangular Area
example:example:
5 (height) x 24 (base) = 120 sf5 (height) x 24 (base) = 120 sf
24’24’
5’5’
UNIT 3page 30UNIT 3
page 30
Triangular AreaTriangular Area
multiply the multiply the basebase times the times the heightheight then then divide the sum by divide the sum by 22
example:example:
24’24’
5’5’
5 (height) x 24 (base) = 120 sf120 sf ÷ 2 = 60 sf5 (height) x 24 (base) = 120 sf120 sf ÷ 2 = 60 sf
UNIT 3page 30UNIT 3
page 30
Circular AreaCircular Area
circumference - distance around the circlecircumference - distance around the circle
UNIT 3page 30 - 31
UNIT 3page 30 - 31
Circular AreaCircular Area UNIT 3page 30 - 31
UNIT 3page 30 - 31
diameter - length of line running between two points and passing through the center circlediameter - length of line running between two points and passing through the center circle
diameterdiameter
Circular AreaCircular Area UNIT 3page 30 - 31
UNIT 3page 30 - 31
radius - one-half the length of the diameterradius - one-half the length of the diameter
radiusradius
Circular AreaCircular Area
pipi ( () is used when determining the area or ) is used when determining the area or volume of a circular object. volume of a circular object.
pi is the pi is the ratioratio of the of the circumferencecircumference to the to the diameterdiameter and is equal to and is equal to 3.14163.1416
UNIT 3page 30 - 31
UNIT 3page 30 - 31
Circular AreaCircular Area
area of a circle =area of a circle = x r2 (radius) x r2 (radius)
UNIT 3page 30 - 31
UNIT 3page 30 - 31
Circular AreaCircular Areaexample area of a patio example area of a patio
30’30’
Area = x 15’2Area = x 15’2
Area = 3.1415 x (15’ x 15’) Area = 3.1415 x 225 sf Area = 706.86 sf
Area = 3.1415 x (15’ x 15’) Area = 3.1415 x 225 sf Area = 706.86 sf
rr
UNIT 3page 30 - 31
UNIT 3page 30 - 31
x r2x r2Area = Area =
Volume MeasurementVolume Measurement
volume is a cubic measurevolume is a cubic measure volume is found by multiplying area by depthvolume is found by multiplying area by depth
UNIT 3page 31UNIT 3
page 31
Volume MeasurementVolume Measurementexample: example: volume of concrete for volume of concrete for a a 4”4” thick patio that is thick patio that is 706.86 sf 706.86 sf
706.86 sf x 4” ( 0.334 ) = 235.38 ft3706.86 sf x 4” ( 0.334 ) = 235.38 ft3
put in cubic yardsput in cubic yards
235.38 ÷ 27 = 8.71 yrds3235.38 ÷ 27 = 8.71 yrds3
UNIT 3page 31UNIT 3
page 31
convert inches to decimal feet 4”/12” = ( 0.334 )
convert inches to decimal feet 4”/12” = ( 0.334 )
Test Your KnowledgeTest Your Knowledge
take 15 minutes and do problems on take 15 minutes and do problems on page page 3131
UNIT 3UNIT 3
Problems in ConstructionProblems in Construction
Take 30 minutes & complete Take 30 minutes & complete Activity 3-8Activity 3-8 on on page 33page 33
END OF UNIT 3END OF UNIT 3
UNIT 3UNIT 3