Module 00102 Intro to Construction Math
A general contractor ordered three different sized windows to complete a job on a residential home. She ordered a bow window 36'' x 36'' that cost $874; one double-hung 25'' x 34'' window that cost $67; and one double-hung window 54'' x 24'' that cost $93. If she budgeted $1,250 for windows, how much will she have left after buying them?
$ 216
In calculating a bid for a roof restoration, a contractor estimates $850 for lumber, $460 for roofing shingles, and $170 for hardware. What is the total cost for the materials portion of the bid?
$1480
Brazil's currency is called the real and is identified with the R$ symbol. A plumbing contractor allots R$10,236 to complete three residential jobs. If Job 1 will cost R$2,477, Job 2 will cost R$2,263, and Job 3 will cost R$3,218, how much money remains to handle unexpected costs?
$2278
Which number is in the numerator 1/4
1
2,638/24
109 r22
12,766-1,483=
11,283
A supervisor sends a trainee to the truck for 180 special fasteners. The fasteners come in bags of 15. How many bags will the trainee bring back?
12 bags
One plumbing job requires 45 meters of PVC pipe, and a second job requires 30 meters. The pipe comes in 6-meter lengths only. How many sections should the plumber buy? How much pipe will be left over, assuming that there are no errors?
13 with 3 meter left over
An HVAC contracting company sent out three work crews to complete three installations over the past week. If Crew One worked 10-, 9-, 11-, 12-, and 9-hour days, Crew Two worked 9-, 12-, 12-, 9-, and 9-hour days, and Crew Three worked 12-, 12-, 10-, 9-, and 11-hour days, how many total hours did the three crews work for the week?
156
Which number is in the denominator spot 3/4
4
943,153-436,372=
506,781
66,723+5,784=
72,507
723+84=
807
Russia's currency is called the ruble and is identified with the Rub symbol. An electrical contractor has Rub 850,360 in the business's bank account. After depositing Rub 119,980 in payments made by clients and paying out Rub 79,205 in wages, how much remains in the account?
891,135
3/4 equals how many sixty-fourths? A- 48/64 B- 50/64 C- 52/64 D- 54/64
A
Look at the following description of a number. This number would be written as ___________________. Digit in the hundreds place: 9 Digit in the ones place: 4 Digit in the thousands place: 3 Digit in the tens place: 6 A- 3,964 B- 4,693 C- 30,964 D- 39,064
A
equation
A mathematical sentence that shows that two expressions are equivalent. Example 2*2=4 and 1*4=4 so 2*2=1*4
decimal
A number with one or more digits to the right of the decimal point example 1.25 .25 is the numbers to the right of the decimal point
If a crane rental company charges $800 per day, $3,400 per week (5 days), and $10,500 per month, A- How much would it cost to rent the crane for 3 days? B- How much would it cost to rent the crane for 12 days? C- How much would it cost for one month and 11 days?
A- $2,400 B- $ 8,400 C- $18,100
Without using a calculator, determine the decimal equivalent of 13.9%. A. 0.139 B. 0.013 C. 0.009 D. 1.39
A- 0.139 Sometimes decimals need to be expressed as percentages, or percentages as decimals. See Section 3.3.1
Find the lowest term for each of the following fractions: A- 2/16= B- 2/8= C- 12/32= D- 4/8= E- 4/64=
A- 1/8 B- 1/2 C- 3/8 D- 1/2 E- 1/16
The dimensions around the perimeter of an irregular shaped concrete form are 11 5/16", 36 ½", 44 1/8" and 16 ¼". What is the distance around the perimeter of this form? A. 108 3/16" B. 107 ½ " C. 108 9/16" D. 107 9/16A
A- 108 3/16'' First convert all fractions that are not already sixteenths to equivalent sixteenths: 36 ½ = 36 8/16, 44 1/8 = 44 2/16, and 16 ¼ = 16 4/16. Add all numbers together: 11 5/16 + 36 8/16 + 44 2/16 + 16 4/16 = 107 19/16. 19/16 = 1 3/16. Add 1 3/16 to 107 for 108 3/16. See Section 2.1.1 for finding equivalent fractions and Section 2.3.0 for adding fractions.
A worker applies two coatings to a pipe. The first coating is 51.5 nanometers thick, and the second coating is 89.7 nanometers thick. How thick is the combined coating? A. 141.2 nanometers B. 144.2 nanometers C. 145.02 nanometers D. 142.12 nanometers
A- 141.2 51.5 nanometers + 89.7 nanometers = 141.2 nanometers See Section 3.2.1
A bricklayer lays 649 bricks the first day, 632 the second day, and 478 the third day. Without using a calculator, determine how many bricks the worker laid during the three-day period. A. 1,759 B. 1,760 C. 1,770 D. 1,769
A- 1759 Total bricks laid = 649 bricks + 632 bricks + 478 bricks = 1,759 See Section 1.2.0
The number matching the words two thousand, six hundred eighty-nine is _____. A. 2,689 B. 6,289 C. 2,286 D. 20,689
A- 2689
3.53 ´ 9.75 = _____ A. 34.42 B. 48.13 C. 36.14 D. 12.28
A- 34.42 3.53 ´ 9.75 = 34.4175, rounded up to 34.42. See Section 3.2.2
Change these improper fractions to mixed numbers: A- 35/8 B- 97/16 C- 13/4 D- 14/5 E- 48/16
A- 4 3/8 B- 6 1/16 C- 3 1/12 D- 2 4/5 E- 3
An insulating company has 400 rolls of insulation that must be equally distributed to 5 different job sites. Without using a calculator, determine how many rolls of insulation will go to each site. A. 80 B. 208 C. 20 D. 8
A- 80 400 rolls insulation ÷ 5 sites = 80 rolls per site See Section 1.3.0
Full productivity is achieved when a crew pours and finishes 65 cubic yards of concrete in a day. The superintendent on the project has promised the crew a bonus if it can exceed its daily requirement by 125%. How much concrete in cubic yards, must the crew pour and finish to achieve this goal? A. 82 B. 90 C. 105 D. 75
A- 82 By pouring and finishing 82 cubic yards in a day, the crew will slightly exceed the 125% threshold: 65 ´ 125% = 65 ´ 1.25 = 81.25. See Section 3.3.1.
Rounded to the nearest thousandth, the number 82.17420118 is _____. A. 82.174 B. 82.1742 C. 82.2 D. 82.175
A- 82.174
The three angles in an equilateral triangle are _____ angles. A. acute B. adjacent C. right D. obtuse
A- acute The acute angles are equal and are all less than 90 degrees. See Sections 6.1.0 and 6.2.3, Figures 24 and 28.
Metric rulers are typically divided into _____. A. centimeters and millimeters B. meters and kilometers C. centimeters and meters D. millimeters and meters
A- centimeters and millimeters
A four-sided shape with four 90-degree angles is a ____. A. rectangle B. rhombus C. parallelogram D. pyramid
A- rectangle
A painter must paint the floor in a circular entry that has a diameter of 14 feet. A gallon of the paint he will use can cover 250 square feet. Will one gallon of paint be enough to complete the job? A- yes B- no
A- yes A gallon will provide more than enough coverage. Use the area of a circle formula A = p ´ r² where pi is a constant 3.14, and r is the radius of the circle: A = 3.14 ´ 7² = 3.14 ´ 49 = 153.86 sq. ft. See Section 6.3.0.
An HVAC contractor must install ductwork in six identical homes in a small development. She has calculated that each home will require about 215 square feet of galvanized sheet metal to fabricate all the required ducts in each house. The shop supervisor has set aside 1,400 square feet of sheet metal for the project. Has he set aside enough sheet metal to complete the job? A- yes B- no
A- yes Enough material is available. The problem can be solved two ways: 1,400 ¸ 6 = 233.3 sq. ft. per job available; 215 ´ 6 = 1,290 sq. ft. needed. See Section 1.3.0.
1/4 equals how many sixteenths? A- 2/16 B- 4/16 C- 6/16 D- 8/16
B
A project supervisor estimates that a commercial building will require sixteen thousand, five hundred feet of copper piping to complete its restroom facilities. Written as a whole number, this value is ___________________. A- 1,650 B- 16,500 C- 160,500 D- 16,000,500
B
An estimate for a commercial flooring job requires one thousand, six hundred ninety-three square meters of carpet to complete the first floor. Written as a whole number, this value is ___________________. A- 163 B- 1,693 C- 10,693 D- 16,093
B
Find the lowest common denominator for the following pairs of fractions: 1/4 and 3/16 A- 8 B- 16 C- 18 D- 20
B
Find the lowest common denominator for the following pairs of fractions: 1/4 and 3/8 A- 4 B- 8 C- 12 D- 18
B
Find the lowest common denominator for the following pairs of fractions: 4/32 and 5/8 A- 64 B- 32 C- 16 D- 8
B
How many concrete blocks like the one shown in Figure 1 are required to erect a 2' high wall for the foundation shown in Figure 2 Assume there is no waste. Round the answer up to the nearest whole number. (Hint: Multiply the distance around the foundation by 12 to change it from feet to inches first.) A- 336 blocks B- 504 blocks C- 514 blocks D- 528 blocks Concrete block is 16'' long 8'' high and 8'' wide
B
In the number 25,718, the numeral 5 is in the ___________________. A- tens place B- thousands place C- ones place D- hundreds place
B
A chimney is located 5 feet away from the vent connection on a furnace. The furnace manufacturer states that the vent connector must have at least ¼" per foot of upward slope per foot of horizontal distance between the furnace and the chimney. In the distance between the furnace and the vent, what is the minimum change in elevation that is required from where the vent connector pipe is attached to the furnace to where it connects to the chimney? A. 1 ¼' B. 1 ¼" C. 5' D. 5"
B- 1 1/4'' With a ¼" per foot slope requirement, the pipe must have at least 1 ¼" change in elevation: 5' ´ ¼" per foot = 5/4 = 1 ¼". See Section 2.4.0.
If the total square footage of the area to be tiled is 2250 sq. ft., how many tiles (2 sq. ft. each) would be required to complete this job? A. 4,500 B. 1,125 C. 2,250 D. 3,000
B- 1,125 If each tile is 2 sq. ft., it would take 1,125 tiles to cover the floor: 2,250 ¸ 2 = 1,125. See Section 6.3.0.
Perform the following calculation and reduce the answer to its lowest term: 3/8 + 9/16 = _____. A. 7/8 B. 15/16 C. 3/4 D. 12/16
B- 15/16 3/8 ´ 2/2 = 6/16 6/16 + 9/16 = 15/16 See Section 2.3.0
Asphalt roofing shingles are typically sold by the square, with a square covering 100 square feet. A contractor must shingle a roof that measures 65.5' ´ 35'. How many squares will be required to cover this roof? A. 26 B. 23 C. 25 D. 33
B- 23 The job requires 23 squares. First find the area of the roof: 65.5' ´ 35' = 2,292.5 sq. ft. Next, find the number of squares: 2,292.5 ¸ 100 = 22.925 squares = 23 (rounded up). See Section 3.2.2.
A rectangular concrete form is 4' long, 3' wide, and 2' deep. What is the volume of this form? A. 1.89 cu. yd. B. 24 cu. ft. C. 24 sq. ft. D. 27 cu. ft.
B- 24 cu ft The volume of a cube is calculated by multiplying the length by the width by the depth: 4 ´ 3 ´ 2 = 24 cu. ft. See Section 6.4.2.
Perform the following calculation and reduce the answer to its lowest term: 11/32 - 2/8 = _____. A. 1 9/32 B. 3/32 C. 1/8 D. 9/32
B- 3/32 2/8 ´ 4/4 = 8/32 11/32 - 8/32 = 3/32 See Section 2.3.0
A length of pipe is 5.5 meters long. How many 1.2-meter lengths of pipe can be cut from that one length of pipe? A. 4.5 B. 4 C. 5 D. 6
B- 4 5.5 ¸ 1.2 = 4.58 lengths of pipe. However, only four of the required length pipes can be cut from the 5.5-meter length. See Section 3.2.3.
A 1,200-gallon tank is 62% full when it contains _____ gallons. A. 800 B. 744 C. 650 D. 456
B- 744 Convert the percentage to a decimal and multiply the tank capacity by that decimal value: 1,200 ´ 0.62 = 744. See Section 3.3.1.
The lowest common denominator for the fractions 8/64 and 8/32 is _____. A. 32 B. 8 C. 24 D. 16
B- 8 Find the lowest common denominator possible between them, which means reducing the fractions to their lowest terms. See Section 2.1.3
A driver is given $600.00 in cash and told to pick up 130 sheets of sheetrock at $4.15 per sheet. He is also told to up pick extra pails of joint compound if he has enough cash left. Each pail of joint compound costs $29.50. Does the driver have enough cash left over to pick up 4 pails of joint compound? A- Yes B- No
B- No Not enough cash is left over to pick up 4 pails of joint compound: 130 ´ $4.15 = $539.50 and $600.00 - $539.50 = $60.50 cash left. $29.50/pail ´ 2 pails = $59.00, so there is enough for 2 pails but not 4 pails. See Section 1.3.0.
An open top concrete tank is available to a construction crew to store water. The job site has a daily requirement for 5,000 gallons. The cylindrical tank is 20' in diameter and is 12' deep. Is this tank large enough to meet the needs of the construction site? Note: A gallon of water has a volume of 1.33 cu. ft. A- yes B- no
B- no Use the volume of a cylinder formula V = p ´ r² ´ h where pi is a constant 3.14, r is the radius of the cylinder, and h is the height of the cylinder: V = 3.14 ´ 10² ´ 12 = 3.14 ´ 100 ´ 12 = 3,768 cu. ft. Since each gallon of water occupies 1.33 cu. ft., there is no way that this tank can handle the 5,000 gallon-per-day requirement. See Section 6.4.3.
To convert a measurement in centimeters to meters, you simply move the decimal point _____. A. three places to the right B. two places to the left C. three places to the left D. four places to the right
B. two places to the left When converting from a smaller value to a larger one, the decimal point must move to the left. See Section 5.1.2
2/16 equals how many thirty-seconds? A- 1/32 B- 2/32 C- 4/32 D- 8/32
C
3/16 equals how many thirty-seconds? A- 2/32 B- 4/32 C- 6/32 D- 8/32
C
An engineer estimates that the total cost to install a building's HVAC system will be three hundred twenty-two thousand nine hundred seven dollars. Written as a whole number, this value is ___________________. A- $3,297 B- $300,297 C- $322,907 D- $322,000,907
C
Each laborer earns $12.00 per hour. Alfredo's weekly timecard shows 28 hours worked, Bob's card shows 40 hours of work, and Jane's card shows 38 hours of work. Excluding any deductions, how much money must be set aside to pay these three laborers? A. $1,420.00 B. $1,368.00 C. $1,272.00 D. $1,500.00
C
Find the lowest common denominator for the following pairs of fractions: 2/6 and 3/4 A- 6 B- 8 C- 12 D- 16
C
It costs a painting contractor $2.37 per square foot to paint a wall. What will it cost to paint an 864.5 square foot wall? Round to the nearest cent. A. $2,848.88 B. $2,888.86 C. $2,048.87 D. $204.88
C- $2048.87 864.5 square feet ´ $2.37 per square foot = $2,048.865, rounded up to $2,048.87. See Section 3.2.2
89.435 ÷ 0.05 = _____ A. 447.175 B. 17.887 C. 1788.7 D. 4.47175
C- 1788.7 89.435 ÷ 0.05 = 1,788.7. See Section 3.2.3
A contractor must tile a floor that measures 50' ´ 45'. What is the total square footage of the area to be tiled? A. 2,100 sq. ft. B. 2,475 sq. ft. C. 2,250 sq. ft. D. 2,500 sq. ft.
C- 2,250 sq ft The area of a rectangle = length ´ width. The area of the tile floor is 2,250 sq. ft.: 50' ´ 45' = 2,250 sq. ft. See Section 6.3.0.
A worker has been asked to deliver 15 scaffolds to each of 26 different sites. Without using a calculator, determine how many scaffolds the worker will deliver. A. 240 B. 120 C. 390 D. 375
C- 390 15 scaffolds ´ 26 sites = 390 scaffolds See Section 1.3.0
Without using a calculator, convert 14.75 to its equivalent fraction expressed in lowest terms. A. 29 5/20 B. 14 7/4 C. 59/4 D. 14 75/100
C- 59/4 14.75 = 1475/100 = 1475 ÷ 25/100 ÷ 25 = 59/4. See Section 3.3.3
A supplier delivered a total of 1,478 feet of cable for a job. Due to a delay, the electricians installed only 489 feet. Without using a calculator, determine how many feet of cable remain. A. 1,099 B. 978 C. 989 D. 980
C- 989 1,478 feet dash- 489 feet installed = 989 feet of cable remaining See Section 1.2.0
Put the following decimals in order from smallest to largest: 0.402, 0.420, 0.042, 0.442 A. 0.442, 0.420, 0.402, 0.042 B. 0.042, 0.402, 0.442, 0.420 C. 0.042, 0.402, 0.420, 0.442 D. 0.420, 0.042, 0.442, 0.402
C. 0.042, 0.402, 0.420, 0.442 It is relatively simple to tell if one decimal value is larger or smaller than another. It is really no different than determining if one whole number is larger than another. See Section 3.1.2
3/4 equals how many eighths? A- 2/8 B- 4/8 C- 5/8 D- 6/8
D
Find the lowest common denominator for the following pairs of fractions: 1/8 and 1/2 A- 3 B- 5 C- 7 D- 8
D
Given the number 92,475, which digit is in the ten-thousands place value column? A- 2 B- 4 C- 7 D- 9
D
Of the numbers listed, which one has the lowest value? A. 0.6500 B. 0.0025 C. 0.0133 D. 0.0001
D- 0.0001 The lowest value is the number with the greatest number of zeros immediately to the right of the decimal. See Section 3.1.0, Figure 4.
The decimal equivalent of 2/5 is _____. A. 0.25 B. 4.0 C. 0.33 D. 0.40
D- 0.40 2 ¸ 5 = 0.40. See Section 3.3.2.
A measurement on a drawing states that a distance is 45.5 yards. What is the same distance in inches? A. 4,550" B. 15.17" C. 1,620" D. 1,638''
D- 1638'' One yard equals 36 inches. 36" per yard ´ 45.5 = 1,638". See Section 5.1.1, Table 2.
Which of the following fractions is an equivalent fraction for 3/8? A. 3/64 B. 6/64 C. 36/64 D. 24/64
D- 24/64 3/8 ´ 8/8 = 24/64 See Section 2.1.1
When 0.60 is converted to a fraction, it becomes _____. A. 5/16 B. 1/3 C. 5/8 D. 3/5
D- 3/5 0.60 = 60/100 = 6/10 ¸ 2/2 = 3/5. See Section 3.3.3.
How many 1 ¼' by 4' pieces can you cut from a 4' ´ 8' sheet of plywood? A. 4 B. 5 C. 3 D. 6
D- 6 Six pieces can be cut from the sheet with a ½' by 4' piece remaining as scrap: 1 ¼ ' ´ 6 = 7 ½'. See Section 2.4.0.
Which of the following fractions is equivalent to ½? A- 4/8 B- 32/64 C- 8/16 D- All of the above
D- All of the above
The dimensional units feet and inches often appear as the symbols ' and " in construction drawings and calculations.
Example 5' feet and 5'' inches
When measuring objects, its fine if all measurements are not measured using the same denominator. Doing this doesn't make comparing, adding, and subtracting fractional measurements any easier. True or False
False When measuring objects, try to record all measurements using the same fractions—in sixteenths of an inch, for example. In other words, use the same denominator for each measurement. Doing this makes comparing, adding, and subtracting fractional measurements easier.
equivalent fractions
Fractions that have the same value Examples 1/2, 2/4, and 4/8 are all the same amount when the fractions are reduced to the lowest common denominator
the correct order to solve problems is what?
MDAS ("My Dear Aunt Sally") multiplication, division, addition, and subtraction for more difficult problems use PEMDAS, Please Excuse My Dear Aunt Sally The P represents parentheses, and the E represents exponents then multiplication, division, addition, and subtraction
whole numbers
Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...
positive numbers
Numbers that are greater than zero. Example 1, 45, 289
remainder
The amount left over when one number is divided by another.
divisor
The number by which another number is divided. example 16/8=2 8 is the divisor
A fraction divides whole numbers into parts. Fractions often appear as two numbers separated by a slash or a horizontal line, such as 1/2 True or False
True
The slash or horizontal line means the same thing as the ÷ sign. Think of a fraction as another way to write a division problem. The fraction 1/2 means 1 divided by 2, or one divided into two equal parts. This fraction is spoken as "one-half." True or False
True
A centimeter is 1/100 of a meter, while a kilometer is equal to 1000 meters. True or False
True The metric system is logically arranged, and the prefix of the unit represents its order of magnitude. See Section 5.0.0
improper fraction
a fraction whose numerator is larger than the denominator
mixed number
a number made up of a whole number and a fraction
fraction
a portion of a whole number represented by 2 numbers. The upper number in the fraction is called the numerator and the bottom number in a fraction is called a denominator
negative numbers
numbers less than zero Example -12, -37, -1287
quotient
the answer to a division problem Example 16/8=2 2 is the quotient
product
the answer to a multiplication problem. Multiplying 2 numbers to get the product. Example 2*5=10 10 is the product
difference
the answer to a subtraction problem. Subtracting 2 numbers to find the difference. Example 7-5=2 2 is the difference
sum
the answer to an addition problem. Adding 2 numbers together to get the sum. Example 2+5=7 7 is the sum
dividend
the number to be divided. Example 16/2=8 16 is the dividend
In the division problem 5/8÷3/4, the answer is _____. A. 5/6 B. 3/8 C. 1/2 D. 4/5
A- 5/6 5/8 ¸ ¾ = 5/8 ´ 4/3 = 20/24 = 5/6. See Section 2.4.0.
