Constrution Mathematics Review 9 16 Constrution Mathematics Review 24’ 5’ Unit 3

Unit 3 Construction Mathematics Review Page 23 Learning Objectives Add, subtract, multiply, and divide fractions Convert between improper fractions & mixed fractions Add, subtract, multiply & divide decimal fractions

Fractions 9 16 written with one number over the top of another UNIT 3 page 23 written with one number over the top of another numerator denominator 9 16

Proper Fractions 7 16 3 4 numerator is less than denominator UNIT 3 page 23 numerator is less than denominator 7 16 3 4

Improper Fractions 5 4 19 16 numerator is greater than denominator UNIT 3 page 23 numerator is greater than denominator 5 4 19 16

Using Fractions whole numbers can be changed to fractions UNIT 3 page 23 whole numbers can be changed to fractions

Using Fractions example: UNIT 3 page 23 Using Fractions example: 6 change into fourths 6 1 x 4 = 24

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 example: UNIT 3 page 24 Using Fractions example: convert 3 5/8 to an improper fraction 3 5 8 = 1 + x 24 29 ( )

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 example: reduce to lowest proper fraction UNIT 3 page 24 17 4 17 4 17 ÷ 4 = = 4 1

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 to the lowest fractional form UNIT 3 page 24 6 8 6 8 = 2 ÷ 3 4

using fractions UNIT 3 page 24 fractions can be changed to higher terms by multiplying the numerator & denominator by the same number

Using Fractions 5 8 5 8 = 2 x 10 16 example: changed to higher terms UNIT 3 page 24 5 8 example: changed to higher terms 5 8 = 2 x 10 16

Adding Fractions denominators must all be the same 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 5 16 3 8 11 32 + + = 32 What is the least UNIT 3 page 24 5 16 3 8 11 32 ? example: + + = 32 What is the least common denominator?

What must you multiply to get a Adding Fractions UNIT 3 page 24 5 16 3 8 11 32 ? example: + + = 32 What must you multiply to get a common denominator? 5 16 x 2 = 10 32 3 8 x 4 = 12 32

Add & convert to a mixed number Adding Fractions UNIT 3 page 24 5 16 3 8 11 32 ? example: + + = 32 Add & convert to a mixed number 11 32 10 12 + = 33 32 1 32 or

Adding Fractions UNIT 3 take 15 minutes & do Activity 3-1 on page 24

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 UNIT 3 page 25 Subtracting Fractions example: 3 4 5 16 ? - = 16 What is the least common denominator?

Subtracting Fractions UNIT 3 page 25 3 4 5 16 ? example: - = 16 Change so the denominator is 16 3 4 3 4 x = 12 16

Subtracting Fractions UNIT 3 page 25 Subtracting Fractions example: 3 4 5 16 ? - = 16 Subtract numerators & retain the common denominator 5 16 12 - = 7 16

Subtracting Fractions UNIT 3 take 15 minutes & do Activity 3-2 on page 25

Multiplying Fractions UNIT 3 page 25 change all mixed numbers to improper fractions multiply all numerators multiply all denominators reduce to lowest terms

Multiplying Fractions UNIT 3 page 25 example: 1 2 1 8 ? x 3 x 4 = Change all mixed numbers to improper fractions 1 2 x 25 8 4 =

Multiplying Fractions UNIT 3 page 25 1 2 1 8 ? example: x 3 x 4 = Multiply all numerators and then denominators to get the answer 1 2 x 25 8 4 = 100 16

Multiplying Fractions UNIT 3 page 25 1 2 1 8 ? example: x 3 x 4 = Reduce the fraction to lowest terms 100 16 = 4 6 1 4 6 =

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 -32 96 8 8 -3 296 6 -2 472 . 4.12 . 36.50 32 . UNIT 3 page 28 ? example: 36.5032 ÷ 4.12 = -32 96 8 8 -3 296 6 -2 472 . 4.12 . 36.50 32 . 3 543 2 472

Dividing Fractions UNIT 3 take 15 minutes & do Activity 3-7 on page 29

Area Measurement area length x width use same units page 29 - 30 area area of a floor, walls square feet, yards, meters length x width use same units two sides must be the same

Square & Rectangular example: area of a room 10’ x 12’ = 120 sf UNIT 3 page 29 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

Triangular Area 5’ 24’ 5 (height) x 24 (base) = 120 sf example: UNIT 3 page 30 example: 24’ 5’ 5 (height) x 24 (base) = 120 sf

Triangular Area 5’ 24’ 5 (height) x 24 (base) = 120 sf UNIT 3 page 30 multiply the base times the height then divide the sum by 2 example: 24’ 5’ 5 (height) x 24 (base) = 120 sf 120 sf ÷ 2 = 60 sf

Circular Area circumference - distance around the circle UNIT 3 page 30 - 31 circumference - distance around the circle

Circular Area diameter UNIT 3 page 30 - 31 diameter - length of line running between two points and passing through the center circle diameter

Circular Area radius radius - one-half the length of the diameter UNIT 3 page 30 - 31 radius - one-half the length of the diameter radius

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 UNIT 3 page 30 - 31 x r2 (radius)  area of a circle =

Circular Area r example area of a patio Area =  x r2 Area =  x 15’2 UNIT 3 page 30 - 31 example area of a patio x r2 Area =  Area =  x 15’2 Area = 3.1415 x (15’ x 15’) Area = 3.1415 x 225 sf Area = 706.86 sf 30’ r

Volume Measurement volume is a cubic measure UNIT 3 page 31 Volume Measurement volume is a cubic measure volume is found by multiplying area by depth

convert inches to decimal feet 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