Fractions
1. William has a wrench marked 5/8, but it is too large. Would a 19/32 wrench be smaller?
2. A #6 x 1-in. glue dowel requires that at least a 3/16-inch diameter hole be drilled. Will a ¼-in. drill bit make a large enough hole?
3. A #6 x 1-in. glue dowel requires a minimum hole depth of 29/32-in. Is a 15/16” hole deep enough?
4. Which is smaller, a ½-in. socket or a 5/8-in.?
6. Is a 7/32-in. wrench larger or smaller than a 7/16-in. wrench?
7. A dishwasher that is 22¼ in. wide is to be placed in an opening that is 22 5/16 in. wide. Will it fit?
8. What is the overall thickness of a countertop made of 1 3/8-inch plywood and 5/16- inch marble?
9. In a certain wall, the studs (interior supports of an outside wall) are 3¾-inch thick. The inside wallboard is 5/8-inch thick and the outside covering is 2 3/16-inch thick. What is the total thickness of the wall?
10.How much total rebar is needed to make the following cut lengths (disregard cutting loss): 7¾-inch, 8 1/16-inch, 7 5/8-inch?
11.Most concrete pads are 4 inches thick; digging to 6 inches gives enough room to lay a good base for the pad. The 2” of the base area will be filled with gravel and fine sand. After compacting the base material with a tamper, you find that the base fill is 1 13/16-inches thick. How much more thickness of base material must be added so that when the 4-inches of concrete are added, the overall depth is 6-inches?
12.If a set of stair steps is 13 risers high and each riser is 7 ¼ in. high, what is the total rise of the steps?
13.A rule of thumb used in constructing stairways is the rise and the run (tread) should always add up to 17 inches. Applying this rule, what should the length of the tread for a stairway be if the rise is 7 7/8”?
14.A drill bit advances 1/16 in. for each complete turn. How many turns are needed to drill a hole 1 7/8 in. deep?
15.How many 2 ¼ in. long pegs can be cut from a dowel that is 1 yard long? (Disregard cutting loss.)
16. How many 2 ¼ in. long pegs can be cut from a dowel that is 1 yard long if 1/16 in. is wasted on each cut?
17.Rough lumber that is 6 in. wide finishes to be 5 5/8 in. How many finished 2” x 6” boards placed side-by-side are in needed to make a picnic table that is 42 in. wide?
18.Find the distance between 3 ½ in. and 6 ¼ in.
19.Find the distance between 14 7/8 in. and 12 5/8 in.
Decimals
1. Two measurements of an object are recorded. If the measures are 15.724 in. and 15.71 in., find which measurement is smaller.
2. A metric washer has an inside diameter of 0.368 cm. Will it fit a bolt that has a diameter of 0.31 cm?
3. A small fencing job requires $48.95 for concrete, $89.06 for fence posts, and $192.81 for fence rails.
a. Estimate the cost by rounding each amount to the nearest ten dollars.
b. Find the exact cost of materials for this project.
c. If labor is figured at $18.25/hour and the job takes 13.75 hours, find the cost of labor. (Round answer to nearest penny.)
d. Determine the total cost for this job (materials and labor.)
4. The outside diameter of a small circular pond including the brick walkway is 7.28 meters (m). If the brick walk surrounding the pond is 1.75 m wide, find the actual diameter of the pond.
5. To build a small pole shed, 18 pieces of steel rod are needed. Each steel rod is 12.125” long. What total length of steel rod needed for this job?
6. On a particular job, 105 feet of conduit will be cut into 7.6-foot lengths. How many 7.6-foot lengths of conduit can be cut from this larger piece?
7. A piece of angle iron is 7.2 feet long and needs to be cut into eight pieces. Assuming that there is no waste, what is the length of each piece after cutting?
8. If eight 1 ½” ratcheting clamps cost $12.58, find the cost of each clamp. (Round answer to the nearest penny.)
9. To find the depth of an American Standard screw thread, the number of threads per inch is divided into 0.6495. Find the depth of thread of a screw that has eight threads per inch. (Round to the nearest ten-thousandths.)
10.A stack of 24 sheets of Plexiglas is 3 inches high.
a. What is the thickness of one sheet to the nearest thousandth of an inch?
b. What is the thickness of one sheet expressed as a fraction of an inch? (In other words, convert your answer from 13a. into an equivalent fraction.)
11.½” thick drywall weighs 1.7 lbs/ft2.
a. How much does a 4’ x 8’ sheet of ½” thick drywall weigh if its area is 32 ft2?
b. If there is a 500 lb. load limit to a trailer, how many whole sheets of drywall can be hauled without going over the load limit?
12.The thickness of a sheet of rigid insulation is two and six hundred twenty-five thousandths of an inch.
a. Write this thickness as a decimal number.
b. Write this decimal as an equivalent mixed number.
Percents
1. An order of building supplies totaled $388.59.
a. What is the amount of sales tax on this order is the tax rate is 5.5%? (Round answer to nearest penny.)
2. A salesperson at a lumber company receives a 7% commission on total sales. If the salesperson is paid $672 in commission for her sales this week, find the total sales made.
3. A contractor makes a profit of $1,250 on a $15,382.50 job. What is the percent profit? (Round answer to nearest tenth of a percent.)
4. Mirth Construction will give customers a 10% discount for inside work scheduled November thru January. If a bathroom remodeling job for January is quoted at $2,875, how much savings will there be with the discount? (Round answer to nearest penny.)
5. If 15% extra flooring is needed to allow for waste when boards are laid diagonally, how much total flooring should be ordered to cover 1,995 board feet of flooring? (Round answer to nearest whole number.)
6. Slightly damaged paneling is discounted 25% off the regular price. If the regular price is $14.95 per sheet, what is the savings per sheet? (Round answer to nearest penny.)
7. A contractor ordered 700 board feet of lumber for a job that required 650 board feet. What percent of the required lumber was ordered for waste? (Round answer to nearest tenth.)
8. When earth is dug, it usually increases in volume or expands by 20%. How much earth will a contractor have to haul away if 205 ft3 are dug?
9. A dust collector with a 1½ hp motor regularly sold for $299.99. Currently, it is listed in a sales advertisement for $279.00. Find the percent decrease in price. (Round answer to nearest tenth.)
10.A 16 ½” drill press costs $749. It has a selling price of $964.58. Find the mark up percent for the drill press. (Round answer to nearest tenth of a percent.)
11.Two years ago, a forty-foot roll of R-11 insulation was priced at $10.50. The same insulation now sells for $11.75. Find the percent increase. (Round answer to nearest tenth of a percent.)
12.If a lumberyard applies a markup of 21% on a ten-foot 2” x 6” pressure treated pine lumber that costs $6.29, what will be the selling price? (Round answer to nearest penny.)
13.A bundle of 20-year fiberglass shingles is on sale for $8.44 while a bundle of 25-year fiberglass shingles sells for $10.29. Find the percent increase in price for the
additional 5-year warranty. (Round answers to nearest tenth of a percent.)
Measurements
Helpful Hint: If you are working on a project with a partner and using two different measuring tapes, take the time to check that both tapes are in sync. Sometimes if the hook end of an older tape happens to get bent, it may throw off the measurement as much as a sixteenth of an inch. That error can be enough to cause problems if you need to do precision work. To double check two metal measuring tapes for accuracy, mark a line at a certain distance on a board, draw the tapes out and compare readings.
Source: www.craftsman.com
1. A blueprint calls for the length of a part to be 14.875 inches with a tolerance of ±0.05 in. What are the upper and lower limits for this part?
2. The blueprint specification for a sheet of metal to be 0.375 in. thick with a tolerance of ±0.001 in. What are the upper and lower limits for this sheeting?
3. Find the upper and lower limit dimensions of an object whose blueprint dimension is 7 3/8 in. long with a tolerance of ±1/16 in.
4. To promote water run-off, a concrete pad needs a slight slope. One-quarter inch of drop per foot of length is usually sufficient.
a. If a concrete pad is 23.5 ft long, find the total drop, in inches, needed to promote water run-off according to this ratio? (Round answer to 3-decimal places.)
b. Convert the answer from (a.) to a fraction.
5. Convert the following measurements into the indicated unit. (Round answers to 2 decimal places.)
a. 2 feet 3 inches = ________ feet
b. 10 feet 8 ½ inches = ________ feet
c. 412 square inches = ________ square feet
e. 850 square feet = ________ square yards
f. 5925 square feet = ________ square yards
g. $69.50/sq. ft. = $________ /sq. in.
h. $29.95/sq. yd. = $________ /sq. ft.
i. 2 1/3 yd = ________ in.
6. A rug 15 ft 3 in. long must fit in a room whose length is 13 ft 9 in. How much should be trimmed from the rug to make it fit the room?
Formulas
1. The following is a description of a horse barn that was listed on a website: The basic 36 ft x 60 ft horse barn has 12 ft x 12 ft stalls with a 12 ft-wide center aisle.
a. Draw a rough sketch of the floor plans for this barn, which allow for the greatest number of stalls.
b. If a more precise drawing was made using 0.25” = 1 ft, what would the length and width of the barn be in the scaled drawing?
2. In drawing plans to make a wooden hand plane, the block plane view is 3 ½ ” long representing an actual 10 ½” piece of wood. If the plan shows a width measuring ½ ” in the drawing, find the width of the actual hand plane. (Assume a similar scale is used for all drawings.)
3. On a house plan, ½ in. represents one foot. Find the dimensions of the family room, in feet, that measures 5 3/8 in. by 6 ½ in. in the house plan.
4. If it takes Tim 4 ¾ minutes to sand a small board, how many similar sized boards can he sand in 2 ¼ hours?
5. If four bundles of 50-year shingles weigh 300 lbs., how much will 97 bundles weigh? (Round answer to nearest pound.)
6. Given an 8-sided polygon (octagon):
a. Find the sum of the interior angles for the octagon.
b. If all angles are equal in size, determine the measure of each interior angle.
c. If all exterior angles are equal in size, determine the measure of each exterior angle.
7. Given a 10-sided polygon (decagon):
a. Find the sum of the interior angles for the decagon.
b. If all angles are equal in size, determine the measure of each interior angle.
c. If all exterior angles are equal in size, determine the measure of each exterior angle.
8. If the pitch of a roof must be 5:12, how much rise should there be over a run of 54 ft?
9. If the pitch of a roof must be 3:12, how much run should there be with a rise of 7 ft?
Geometry
1. A rectangular-shaped bedroom that measures 15.9 ft by 10.8 ft needs to be carpeted. a. Determine how many square feet of carpeting is needed for this room.
(Round to 2 decimal places.)
b. Determine how many square yards of carpeting is needed for this room. (Round to 2 decimal places.)
2. A rectangular-shaped parcel of land measures 720.5 ft by 2,110.5 ft.
a. Find the area of this parcel in square feet. (Round answer to nearest tenth.)
b. Find the area of this parcel in acres rounded to nearest tenth of an acre. (Remember, 1 acre = 43,560 sq. ft.)
3. A picture frame has outside measurements of 36 in. by 28 in. How many inches of picture frame molding are needed to make this frame?
4. How much edge molding is needed to surround a stainless steel kitchen sink that measures 36 in. by 25 ½ in?
5. Find the number of feet of lumber needed for the base plates around the perimeter for
the building shown. 9 ft 8 in
5 ft 6 in 11 ft 9 in
15 ft 3 in
6. Using the building layout in #5, determine how many 2 ft by 4 ft ceiling tiles will be required to cover the ceiling of this building.
7. Wood flooring is to be installed in a room that measures 18 ft. by 24 ft. There is a tiled entryway measuring 6 ft. by 3 ft. in the room that will not need to be included. How many square yards of flooring is needed for this room?
8. Fiberglass roofing shingles are sold in bundles. The number of bundles needed to cover a square (100 ft2) depends on the overlap when the shingles are installed. If the overlap allows 4 in. of each shingle to be exposed, then four bundles are needed per square. With a 5-in. exposure, 3.2 bundles are needed per square.
a. Find the number of bundles for a 4-in. exposure if the roof measures 25 ft. x 35 ft.
b. Find the number of bundles for a 5-in. exposure for a roof measuring 30 ft x 20 ft. (Round to nearest tenth.)
9. Determine the amount of Formica needed, in square inches, to cover a trapezoidal table top that measures 36 inches on the shorter base, 48 inches on the longer base and has a distance of 24 inches between the bases (height.)
10.Determine the number of 4’ x 8’ sheets of drywall needed to cover the walls of a room with dimensions 9.5 ft. wide by 12.75 ft long with 8 foot high ceilings, ignoring reduction to area by windows and doors. (Include a 5% addition for cutting/waste.)
11.A gable on a house has a rise of 10 ft 2 in. and a span of 38 ft. 5 in. What is its area in square feet? (Round to 2 decimal places.)
10 ft. 2 in.
38 ft. 5 in.
12.Determine the number of 4’ x 8’ sheets of drywall needed to cover the ceiling of a room that measures 12.8 ft. x 18.2 ft. (Include a 5% addition for cutting/waste.)
13.How many square feet of wood are needed to build a box with dimensions 24” wide, 12” deep, and 15” high. (Assume that wood is needed for all six surfaces.)
14.A deck project calls for rectangular-shaped concrete pads measuring 16 inches x 16 inches x 6 inches. For this particular project, 12 pads will be needed.
a. Calculate the cubic feet of concrete needed for the project. (Round to 1 decimal place.)
b. Since concrete is sold in cubic yards, convert the answer in (a.) to cubic yards. (Hint: 27 cu. ft. = 1 cu. yd.) (Round to 1 decimal place.)
c. How much concrete should be ordered for this deck project if a 10% waste factor is included? (Round to nearest ½ cu. yd.)
15.A cylindrical-shaped concrete pad is to be made with a diameter of 12 inches and a height or thickness of 6 inches.
a. Calculate the cubic feet of concrete needed to make one of these pads. (Round to 2 decimal places.)
b. Since concrete is sold in cubic yards, convert the answer in (a.) to cubic yards. (Hint: 27 cu. ft. = 1 cu. yd.) (Round to 3 decimal places.)
c. Find how many 80 lb. bags of packaged concrete mix will be needed to make seven 12-inch diameter cylindrical pads 6 inches thick, assuming one 80 lb. bag of concrete mix makes 2/81 cu. yd. of concrete.
16.If you want to make a measuring box to hold exactly 1 cubic foot of dry ingredients, what would be the inside dimension of the height, width and depth in feet?
17. A product flyer states that 4 ½ - 48” x 79” panels cover 100 sq. ft. Is this correct? Find the total square footage of 4 ½ of these panels.
18.Determine the total lateral area (vertical sides), in square feet, of a calf barn using the following diagrams (2 of the 4 sides shown):
Side view 10’ End view 10’ 20.5’
72’ 36’
19.Find the area, in square feet, of the end wall of a solar calf nursery shown below:
8 ft. 6 ft.
20.The two end walls of a solar calf nursery will be built, using the dimensions shown in the previous problem. The back wall will be rectangular-shaped with a length of 30 feet and height of 6 feet. The front of the solar calf nursery will be left open.
a. Calculate the total area of the three sides of this building.
b. One end will have a door that measures 32-inches wide and 80-inches high. Find the area of the door in square feet, rounding answer to one decimal point.
c. Subtract the door area from the total area for this building found in (a.)
d. Add 10% of the total area less the door for waste. (Round to 1 dec. place.)
e. Determine the number of 4’ x 8’ sheets of plywood needed to side this building using the answer found in (d.)
f. 5/8” grooved, textured plywood sells for $23.99 per 4’ x 8’ sheet. Find the price of siding this building using this plywood.
21.Determine the pitch of the roof with a rise of 4 ft and a run of 24 feet. (Recall, roofers usually express pitch with a denominator of 12.)
22.Determine the pitch of the roof with a rise of roof with rise of 9 ft and a run of 15 feet.
23.How long a rafter is needed for the gable of the house in the figure? (Round answer to the nearest tenth.)
16’ ? 21’
24.Find the missing dimension in the diagram. (Round answer to the nearest tenth.)
? 25.5’
Statistics
1. Find the mean for the following measurements: 13.31 ft, 13.2 ft, 12.97 ft and 13.09 ft. (Round to 1 decimal place.)
2. The following are weekly over-time totals for the last six weeks: 6.5 hrs., 14.5 hrs., 14 hrs., 3.75 hrs., and 7.25 hrs.
a. Find the mean weekly overtime total. b. Find the median weekly overtime total.
Finance
1. Your cost of materials for the installation of a hardwood floor is $1,773.72. If you use a 15% mark up rate, determine the selling price of the flooring for the customer. (Round answer to nearest penny.)
2. If a plastic roof vent costs a lumberyard $4.03 and it sells for $5.49, what is the mark- up rate? (Round to nearest tenth.)
3. Three bundles of 35-year shingles cover 100 sq. ft. and sell for $13.98/bundle. Four bundles of 50-year shingles cover 100 sq. ft. and sell for $13.88/bundle.
a. Find the price/sq. ft. for the 35-year shingles. (Round to nearest cent.)
b. Find the price/sq. ft. for the 50-year shingles. (Round to nearest cent.)
4. One gallon of aluminum roof coating sells for $6.84. A 5-gallong pail of the same product sells for $26.74.
a. Find the price/quart for the 1-gallon size. (Round to nearest cent.)
b. Find the price/quart for the 5-gallon size. (Round to nearest cent.)
5. A package of tongue and groove knotty cedar planking is prices at $14.44. If the package contains 14 sq. ft., find the price/sq. ft. (Round answer to nearest penny.)
6. A 48” x 32” piece of wainscot paneling is on sale for $5.95. Find the price/sq. ft. rounded to the nearest penny.
7. Complete the order form. For this order, apply a 12% discount based on the subtotal and use a 5.5% tax rate.
Quantity Description Unit Price Amount