Construction Math Fundamentals of Construction. Section 1.0.0 Why is math important in construction?...

Construction MathConstruction Math

Fundamentals of ConstructionFundamentals of Construction

Section 1.0.0Section 1.0.0Why is math important in Why is math important in

construction?construction?

* * Provides accurate communication of Provides accurate communication of measurements of materials, tools, measurements of materials, tools, and/or equipmentand/or equipment

Section 2.0.0Section 2.0.0Whole Numbers: complete numbers Whole Numbers: complete numbers

w/o decimals or fractionsw/o decimals or fractions

1 5 12 368 4,7241 5 12 368 4,724

Non-Whole Numbers:Non-Whole Numbers:

1.5 6 ½ 42.8 0.0061.5 6 ½ 42.8 0.006

Section 2.1.0Section 2.1.0Parts to Whole Numbers: Parts to Whole Numbers: DigitsDigitsUnitsUnitsTensTensHundredsHundredsThousandsThousandsTen ThousandsTen ThousandsHundred ThousandHundred ThousandMillionsMillions

Section 2.1.1Section 2.1.1

Review QuestionsReview Questions

p. 2.3p. 2.3

Section 2.2.0Section 2.2.0 Adding Whole NumbersAdding Whole Numbers

66

+ 3+ 3 99

Section 2.2.1Section 2.2.1 Carrying in AdditionCarrying in Addition 4848 + 64+ 64 112112

Section 2.2.2Section 2.2.2 Review QuestionsReview Questions p. 2-4p. 2-4

Section 2.2.2Section 2.2.2 Problem-Solving (Word Problems)Problem-Solving (Word Problems) If a construction company had 14 If a construction company had 14

workers on one job, 18 on another, workers on one job, 18 on another, and 32 on a third job, how many and 32 on a third job, how many total employees do they have all total employees do they have all together?together?

Section 2.2.2Section 2.2.2 1414 1818 + 32+ 32 64 total workers64 total workers

Section 2.3.0Section 2.3.0Subtracting Whole Numbers:Subtracting Whole Numbers: 3838 - 24- 24 1414

Section 2.3.1Section 2.3.1 Review QuestionsReview Questions p. 2.5p. 2.5

Section 2.3.0Section 2.3.0 Borrowing during subtractionBorrowing during subtraction 3434 - 28- 28 66

Section 2.4.0Section 2.4.0 Multiplying Simple Whole Multiplying Simple Whole

NumbersNumbers 44 x 8x 8 3232

Section 2.4.1Section 2.4.1 Review QuestionsReview Questions p. 2.6p. 2.6

Section 2.4.2Section 2.4.2 Multiplying Larger Whole NumberMultiplying Larger Whole Number 7575 x 16x 16 420420 7575__ 11701170

Section 2.4.3Section 2.4.3 Review QuestionsReview Questions p. 2.7p. 2.7

Section 2.5.0Section 2.5.0 Dividing Whole Numbers:Dividing Whole Numbers: 10 div by 210 div by 2

2 105

100

Section 2.5.1Section 2.5.1 Review QuestionsReview Questions p. 2.8p. 2.8

Section 2.5.2Section 2.5.2 Dividing More Complex Numbers:Dividing More Complex Numbers:

12 345.

2

24 105

8.

969

0

0

7

84

Section 2.5.3Section 2.5.3 Review QuestionsReview Questions p. 2.9p. 2.9

Section 2.6.0Section 2.6.0 Using CalculatorsUsing Calculators AdditionAddition Section 2.6.2Section 2.6.2 REVIEW QUESTIONSREVIEW QUESTIONS p. 2.10p. 2.10

Section 2.6.4Section 2.6.4 SubtractionSubtraction Review QuestionsReview Questions p. 2.11p. 2.11

Section 2.6.5Section 2.6.5 MultiplicationMultiplication Review Questions 2.6.6Review Questions 2.6.6

p. 2.11p. 2.11

Section 2.6.7Section 2.6.7 DivisionDivision Review QuestionsReview Questions Section 2.6.9Section 2.6.9 p. 2.12p. 2.12

Section 2 Review Section 2 Review #s 1-20#s 1-20 p. 2.12-2.14p. 2.12-2.14

Section 3.0.0Section 3.0.0

MeasurementsMeasurements Divisions of an inchDivisions of an inch

Section 3.1.0Section 3.1.0 Review QuestionsReview Questions p. 2.16p. 2.16

Section 4.0.0Section 4.0.0 Fractions – value expressed Fractions – value expressed

with a numerator and with a numerator and denominatordenominator

11 22

Numerator

Denominator

Section 4.1.0Section 4.1.0 Equivalent fractions – different Equivalent fractions – different

numerators and denominators numerators and denominators but having the same valuebut having the same value

44 22 1 1 88 44 2 2

Section 4.1.1Section 4.1.1 Review QuestionsReview Questions p. 2.17p. 2.17

Section 4.2.0Section 4.2.0 Reducing to lowest formsReducing to lowest forms Reduce to lowest terms Reduce to lowest terms

possible by dividing both the possible by dividing both the numerator and numerator by numerator and numerator by the highest number possiblethe highest number possible

Section 4.2.0Section 4.2.0 3 33 3 1 1 99 33 3 3

Section 4.2.1Section 4.2.1 Review QuestionsReview Questions p. 2-18p. 2-18

Section 4.3.0Section 4.3.0 Lowest common denominatorLowest common denominator Find lowest number that will Find lowest number that will

EVENLY divide into both EVENLY divide into both denominatorsdenominators

Section 4.3.0Section 4.3.0 33 55 4 84 8

Which is larger?Which is larger?

or

Section 4.3.1Section 4.3.1 Review QuestionsReview Questions p. 2-19p. 2-19

Section 4.4.0Section 4.4.0 Adding FractionsAdding Fractions Find lowest common denominatorFind lowest common denominator Use that denominatorUse that denominator Add the numeratorsAdd the numerators Reduce to lowest termsReduce to lowest terms

Section 4.4.0Section 4.4.0 33 55 4 4 88

6 5 116 5 11 8 8 88 8 8

Section 4.4.1Section 4.4.1 Review QuestionsReview Questions p. 2-20p. 2-20

Section 4.5.0Section 4.5.0 Subtracting FractionsSubtracting Fractions Done same way as addition, Done same way as addition,

except subtract numeratorsexcept subtract numerators

Section 4.5.0Section 4.5.0 33 55 4 4 88

6 5 16 5 1 8 8 88 8 8

Section 4.5.1Section 4.5.1 Review QuestionsReview Questions p. 2.20p. 2.20

Section 4.5.1Section 4.5.1 Subtracting a fraction Subtracting a fraction from a whole numberfrom a whole number

5 – ¼ = 5 – ¼ =

Section 4.5.2Section 4.5.2 55 - ¼- ¼ 4 ¾ 4 ¾

4 4/4

3/4

Section 4.5.3Section 4.5.3 Review QuestionsReview Questions p. 2-21p. 2-21

Section 4.6.0Section 4.6.0 Multiplying FractionsMultiplying Fractions 4 x 5 = 204 x 5 = 20

8 6 488 6 48

Section 4.6.1Section 4.6.1 Review QuestionsReview Questions p. 2.21p. 2.21

Section 4.7.0Section 4.7.0 Dividing FractionsDividing Fractions Invert (flip) 2Invert (flip) 2ndnd fraction fraction multiply numeratormultiply numerator multiply denominatormultiply denominator simplify simplify

4.7.04.7.0 3 3 1 1 = =

8 2 8 2

3 3 x x 2 2 = = 6 6 = = 3 3

8 1 8 48 1 8 4

Section 4.7.1Section 4.7.1 Review QuestionsReview Questions p. 2.22p. 2.22

Section 4.0.0Section 4.0.0 Review QuestionsReview Questions #s 1-20#s 1-20 p. 2.22-2.23p. 2.22-2.23

Section 5.0.0Section 5.0.0 Reading metric ruleReading metric rule units of tenths units of tenths can be written as decimal can be written as decimal or fractionor fraction

5.0.05.0.0

0.2 0.7 1.0 1.6 2.1 2.7

5.1.15.1.1

Review questions Review questions p. 2.25p. 2.25

Section 5.2.1Section 5.2.1 Review QuestionsReview Questions p. 2.26p. 2.26

Section 5.3.1Section 5.3.1 Review QuestionsReview Questions p. 2.26-2.27p. 2.26-2.27

Section 5.4.0Section 5.4.0 Adding / Subtracting Adding / Subtracting DecimalsDecimals

Rule: align decimalsRule: align decimals Review questionsReview questions p. 2.28p. 2.28

5.4.05.4.0 4.5614.561 + 54.7+ 54.7

4.5614.561 + 54.7+ 54.7 = 59.261 = 59.261

Section 5.5.0Section 5.5.0 Multiplying DecimalsMultiplying Decimals Rule: answer must total Rule: answer must total number of decimal places number of decimal places in answerin answer

5.5.15.5.1

8.28.2

x 1.26x 1.26

10332 10332 (count 3 decimal places)(count 3 decimal places)

= 10.332= 10.332

5.5.15.5.1

Review QuestionsReview Questions p. 2.28-2.29p. 2.28-2.29

5.6.05.6.0 Dividing decimalsDividing decimals if decimal in numerator, keep if decimal in numerator, keep

decimals in linedecimals in line If decimal in denominator, move If decimal in denominator, move

until right of units place. Must until right of units place. Must move same number of places move same number of places for the numerator.for the numerator.

5.6.25.6.2

Review questionsReview questions p. 2.30p. 2.30

5.6.45.6.4

Review questionsReview questions p. 2.30p. 2.30

5.6.65.6.6

Review questionsReview questions p. 2.31p. 2.31

5.7.05.7.0

Rounding decimalsRounding decimals .5 or above, round up.5 or above, round up .499999999999 or below, .499999999999 or below, drop offdrop off

5.7.75.7.7

Review questionsReview questions p. 2.31p. 2.31

5.8.05.8.0

Using calculatorsUsing calculators

5.8.15.8.1

Review questions Review questions p. 2.32p. 2.32

Section 5.0.0Section 5.0.0

Review QuestionsReview Questions #s 1-15#s 1-15 p. 2.32-2.34p. 2.32-2.34

6.0.06.0.0

Conversion ProcessesConversion Processes Decimal Decimal Percentages Percentages Percentages Percentages Decimals Decimals

6.0.06.0.0

decimals decimals percentage = percentage = # x 100# x 100

percentage percentage decimals = decimals = # / 100# / 100

6.1.16.1.1

Review questionsReview questions p. 2.35p. 2.35

6.2.16.2.1 Fractions Fractions decimals decimals set up as division set up as division problem. problem.

Review questionsReview questions p. 2.36p. 2.36

6.3.16.3.1 Converting decimals Converting decimals fractionsfractions Setup with value overSetup with value over

place valueplace value Becomes fraction Becomes fraction reduce reduce

6.4.06.4.0 Converting inches Converting inches

decimalsdecimals divide inches by 12 and divide inches by 12 and

place as decimalplace as decimalEx. 7” = _?_’ 7/12” = 0.583’Ex. 7” = _?_’ 7/12” = 0.583’

Section 6.0.0Section 6.0.0

Review questionsReview questions #s 1-10#s 1-10 p. 2.37p. 2.37

Section 7.0.0Section 7.0.0

WE WILL WE WILL SKIP!!!!!!SKIP!!!!!!

8.0.08.0.0 AnglesAngles

– acuteacute

– rightright

– obtuseobtuse

– straightstraight

– adjacentadjacent

– oppositeopposite

ShapesShapes Triangles – 180 , Triangles – 180 ,

– equilateralequilateral– rightright– isosceles isosceles – scalenescalene

Squares / RectanglesSquares / Rectangles 4 sides, right angles4 sides, right angles diagonalsdiagonals 360360

CirclesCircles 360 360 circumferencecircumference diameterdiameter radiusradius

Pythagorean TheoremPythagorean Theorem

a + b = ca + b = c

2 2 2

AreaArea amount of space a shape amount of space a shape

takes uptakes up measured in square in (sq measured in square in (sq

in) or ft (sq ft)in) or ft (sq ft)

AreaArea

A (square) = l x wA (square) = l x w A (rectangle) = l x wA (rectangle) = l x w A (circle) = Ii rA (circle) = Ii r A (triangle) = ½bhA (triangle) = ½bh

2

AreaArea find areafind area

14’

8’

AreaArea

9’

9’

AreaArea

16’

9’

AreaArea

12’

8.3.18.3.1

Review QuestionsReview Questions p. 2.52p. 2.52