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