Module 00102-15 Exam Introduction to Construction Math
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
In the number 25,718, the numeral 5 is in the ___________________. A- tens place B- thousands place C- ones place D- hundreds place
B
One ounce is equal to 28.35 grams. Convert 16 ounces to grams. Round your answer to the nearest tenth.
453.6 grams
Which number is in the denominator spot 3/4
4
Forty-five thousand, six hundred twelve pipe fittings have been ordered for a large project. How would you write this number as a whole number using digits?
45,612
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
Your job as a carpenter pays $20/hour and you worked 40 hours last week. The taxes withheld from your wages were $83 federal tax and $19 state tax. Your total check is....
$698
Add the following numbers together: 811, 901, 88, and 5. The sum is....
1,805
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
A floor for a 4-meter square shed must be fabricated. The area of the floor is_______
16m^2
While the measurement of the individual angles in a triangle can vary, their sum is always_______.
180
On the Fahrenheit scale, ho many degrees are there between the freezing and boiling point of water?
180 degrees
When reduced to its lowest terms, the fraction 12/16 would read as...
3/4
Convert 0.86 into a fraction and reduce the answer to the lowest terms.
43/50
The improper fraction 37/6 can be changed to the mixed number....
6-1/6
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
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
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
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.
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 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.
What does a square have in common with a rectangle?
All four corners are 90 degree angles
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
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.
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.
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
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
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
positive numbers
Numbers that are greater than zero. Example 1, 45, 289
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
whole numbers
Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...
What is the place value of 2 in the number 123,456?
Ten Thousands
In a number such as 52.25, any numbers shown to the right of the decimal point represent_______.
That part of the number that is less than 1.
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
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
An inside measurement can be taken with a tape measure by _______.
adding the length of the tape measure case
The volume of a shape in the metric system is stated in terms of ________
cubic meters
negative numbers
numbers less than zero Example -12, -37, -1287
If an angle is not acute, straight, or obtuse, it must be a(n)_______.
right angle
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
The circumference of a circle represents______.
the distance around the outside
dividend
the number to be divided. Example 16/2=8 16 is the dividend
A package contains 12 electrical locks, each with a unique key. A package is delivered to 16 jobs site superintendents. How many unique keys will result from the distribution?
192
7/8 divided by 7/16=_____. Reduce your answer to the lowest terms
2
One sheet of drywall weighs 48.7 pounds. If 50 sheets are ordered, the total weight of the order would be_____.
2,435.0 pounds
Convert 70 degrees Fahrenheit to Celsius using the following formula: degree Celsius=5/9 (degree Fahrenheit-32). Round your answer to the nearest degree.
21 degrees Celsius
You have 5,814 meters of rope that you need to cut into 27 meter sections. How many 27 meter sections of rope will you be able to create, and how much rope will be left over as waste?
215 sections with 9 meters left over
1/4 + 3/8 =_____. Reduce your answer to the lowest terms.
5/8
The volume of a 9-inch cube is______
729 cu in
Using the formula 1kg = 2.205 lbs, 165 lbs converts to a weight of _______.
74.8 kilograms
723+84=
807
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
In the metric system, each millimeter increment is equal to _______.
1/10 of a centimeter
8/12 - 4/8 =______. Reduce your answer to the lowest terms.
1/6
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
1/4 equals how many sixteenths? A- 2/16 B- 4/16 C- 6/16 D- 8/16
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
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
When converting decimals to a percentage, simply move the decimal point______.
two places to the right
2,638/24
109 r22
12,766-1,483=
11,283
Of the following series of numbers, which is the higher number? 0.04671; 0.04761; 0.4761; 0.4671.
0.4761
Which number is in the numerator 1/4
1
You need to mix 42 kilograms of mortar. Each kilogram of mortar mix requires 0.03 liters of water. how many liters of water do you need? (Round your answer to the nearest tenth of a liter)
1.3 liters
An equivalent fraction to 5/16 is...
10/32
When a number is stated as a percentage, it means that number represents a portion of ________.
100
One cubic meter represents a cube shape that measures 1 meter in all three dimensions. How long is each side in centimeters?
100 cm
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
Given the equation 1/2(b times h), the area of a triangular roof section with a base of 7 feet and a height of 3.5 feet is________.
12.25 sq ft
Convert 612 feet to meters using the following information: 1 meter = 3.28 feet. Round your answer to the nearest one-hundredth
186.59 meters
943,153-436,372=
506,781
7/8 times 3/9 =______. Reduce your answer to the lowest terms.
7/24
66,723+5,784=
72,507