1. Construction Math
This presentation gives examples of scenarios one would use math in construction situations.

2. Math Using Whole Numbers
You need 3,540 board feet to complete a job. You currently have 132 boards that are 12’ long.
How many board feet do you currently have?
How many more 12’ long boards do you need to reach the 3,540 board feet that you need?

3. Answers
132 x 12 = 1584 bd. ft.
= 1956
1956 ÷ 12 = 163 more 12’ boards
To solve for part A you multiply the number of boards you have by the length of the boards. You have 132 boards times 12 ft. which equals 1584 board feet
To solve for part B you subtract the amount of board feet that you have from the amount that you need, thus 3,540 – equals You will then divide that number by the length of each piece of wood. When you divide 1956 by 12, you discover that you need 163 more 12 foot boards in order to have 3,540 board feet.

4. Math Using Whole Numbers
52’
Foundation A
33’
For the foundation above, find
The perimeter.
How many concrete blocks are required to build 8 ft. tall basement walls? 8” 8”
16”

5. Answers (33 ft. x 2) + (52 ft. x 2) = 170 ft.
170 ft. x 12 in. = 2040 in.
2040 in. ÷ 16 in. = blocks
8 ft. x 12 in. = 96 in.
96 in. ÷ 8 in. = 12 blocks
127.5 blocks x 12 blocks = 1,530 blocks total
To find the answer for part A, you need to add all the side lengths together. Since the foundation is a rectangle, you know that the two vertical sides are equal and the two horizontal sides are equal. Therefore, you can multiply 33 ft. times 2 and add it to the 52 ft. times 2 which will give you 170 ft.
Part B. requires several steps. First, you need to determine your perimeter in inches. Therefore you multiply the number of feet in your perimeter by 12 inches. Which is 170 time 12 equaling 2040 inches as your perimeter.
Now that you know the length of the perimeter in inches, you must find out many 16 inch blocks you need to complete a perimeter around the foundation.
Therefore, you need to divide the length of the perimeter in inches by the length of one block, which is 2040 in. divided by 16 inches equaling 127 and a half blocks needed to complete a perimeter.
Next, you need to determine how many 8 inch tall blocks you need to complete an 8 ft. wall. You need to determine how many inches are in 8 ft. by multiplying 8 ft. by 12 in. which gives you 96 inches. Now you need to figure out how many blocks are needed to reach 96 inches. Therefore you divide 96 inches by 8 inches which tells you that you need 12 8 inch blocks to build a 8 ft. tall wall.
Finally you need to determine the total number of blocks needed by multiplying the number of blocks needed to form a perimeter by the number of blocks needed to build a 8 ft. tall wall. Giving you 127 and a half blocks times 12 blocks which equals 1,530 blocks total.

6. Math Using Fractions
If inch on a drawing represent 1 foot, how many inches on the drawing would represent 18 feet?

7. Answer
18 x = = in.
To find how many inches 18 feet in a drawing would be, multiply 18 by one fourth which gives you 4 and a half inches

8. Math Using Fractions
Two rooms are each 12 feet by feet, and a third room measures feet by 8 feet. How many square feet of hardwood flooring will be required to cover the floors of the three rooms?

9. Answer
2(12 x ) = 2 1 ( x ) = = 348 sq. ft.
( x 8) = ( x ) = = sq. ft.
= =
= sq. ft.
To find the area of a rectangle, you multiply the length times the width. There were two rooms that were 12 ft. long by 14 and a half feet wide. Therefore, you multiply 12 time 14 and a half and then multiply that answer by 2 which should give you 348 square feet.
For the other room, you multiply its length by its width giving you 10 and one third times 8 which should give you 82 and two thirds square feet.
To determine the total number of square feet needed, you add the square footage of all three rooms together giving you 348 square feet plus 83 and two thirds square feet. To add fractions, you must convert each fraction to have the same denominator. In this case, 3 is the easiest choice. Therefore, you must convert 348 to one thousand forty four thirds and 82 and two thirds to 2 hundred forty eight thirds. Now you can add the two fractions which should give you twelve hundred ninety two thirds, equaling four hundred thirty and two thirds square feet.

10. Math Using Fractions
How many inch wide boards does it take to cover a surface 222 inches wide?

11. Answer
222 in. ÷ in. = ÷ 37 8
÷ = x = = 48 boards
The find the number of 4 and 5 eighths inch wide boards needed cover a surface 222 inches wide, you divide the total width by the width of one board. Since we are dealing with a fractional width, you must convert both widths to fractions giving you 222 over one feet divided by 37 eighths.
To divide fractions you must multiply the dividend by the reciprocal of the divisor. In this case you would multiply 222 over one by 8 thirty sevenths giving you 1,776 / 37ths which converts to 48 boards.

12. Math Using Decimals
A job is estimated to cost $1, The actual materials cost is $ and the labor and overhead costs come to $ How much profit does the contractor expect for the job?

13. $158.97 is the profit. Answer 1,250.75 - 495.42 755.33 - 596.36 158.971,
$ is the profit.
To find how much profit the worker will earn, you must subtract the materials and labor costs from the estimate given to his customer. In this problem, you should find that the worker earns $ as profit.
Remember when subtracting decimals, always make sure you line up the decimal points.

14. Math Using Decimals
A counter is estimated to need 81.9 board feet of material. If the material costs $3.15 per board foot, what is the total cost?

15. Answers
81.9 x
$257.99
To determine the total cost of the materials needed, you multiply the number of board feet by the cost per board foot. To determine where the decimal should go in the answer, count how many digits follow the decimals in the numbers you multiplied together. You need to make sure your answer has that number of digits after the decimal. In this case, the answer should have three digits after the decimal. You get 257 and nine hundred eighty five thousandths when you multiply 81 and 9 tenths by 3 and fifteen hundreths. However since we are dealing with the cost of something, you round the answer to the nearest cent giving you 257 dollars and ninety nine cents.

16. Math Using Decimals
How many whole pieces of 2.25 inch by 6 ft. face flooring are required for a closet inches by 6 ft. when the flooring is laid parallel to the length of the closet?
How many whole pieces of 2 and a quarter inch by 6 ft. face flooring are required for a closet 34 and three quarter inches by 6 ft. when the flooring is laid parallel to the length of the closet?

17. = 16 Whole Pieces of Flooring
Answer
= 16 Whole Pieces of Flooring
You must first distinguish between the length and the width because the pieces must run parallel to the length of the closet. In this case, the length would be 6 feet which is also how long your flooring is and the width would be 34 and 3 quarter inches
Now you need to determine how many pieces of the flooring you need to cover the width (the 34 and 3 quarter inches). Therefore, you need to divide the width of the closet by the width of the floor pieces giving you 34 3 quarter inches divided by 2 and a quarter inches.
If there is a decimal in denominator when dividing, move the decimal right until there is no longer any digits after the decimal. You must also move the decimal same number of places for the in the numerator.
In this problem, you must move the decimal in both the numerator and the denominator 2 places to the right because the denominator (2 and a quarter) had 2 digits after the decimal.
When you divide 34 and 3 quarter inches by 2 and a quarter inches the quotient is 15 and forty four hundreds meaning you need 16 whole boards to cover the closet floor.

18. Converting Decimals to Fractions
Find the approximate thickness in common fraction form of a piece of siding that is inch thick.
Four thousand 3 hundred seventy 5 ten thousandths of an inch thick

19. Answer
= 4,375 10,000 = 4,375 ÷ 25 10,000 ÷25 =
= 175 ÷ ÷25 = inch thick
To find the simplest fractional form of four thousand three hundred seventy five 10 thousandths of an inch, you first convert the number to an non-simplified fraction. The easiest fraction to convert it to is four thousand three hundred seventy five over 10,000.
Now you must start to simplify the fraction. You can easily see that both the numerator and the denominator are divisible by 25. Therefore, you can divide both the numerator and the denominator by 25 which gives you one hundred seventy five four hundredths.
Again, you can see that both the numerator and the denominator are still divisible by 25 so you can divide both by 25 again, giving you seven sixteens of an inch. This will be your answer because it cannot be simplified any further.

20. Decimals and Percentages
The total area to be covered with insulation board is 1,250 square feet. How much should be ordered if 8% of the area is added for waste?

21. Answer
8% = = 0.08
1,250 x 0.08 = 100
,250 = 1,350 sq. ft.
1,250 x 1.08 = 1,350 sq. ft.
To calculate the total amount of insulation board needed to be ordered, you must multiply the area that needs to be covered by the percent waste needed. You must first convert the percent to a decimal by dividing it by 100. Now you can multiply. In this case, you multiply 1250 by eight hundredths which equals 100 sq. ft. You must then add the waste area to the actual area.
You add 100 to the 1,250 sq. feet, giving you 1,350 sq. ft.
Or you could just multiply 1,250 by 1 and eight hundredth because when you multiply the number, you are already adding the 1,250 back to the total.

22. Decimals and Percentages
A contractor receives $1,800 profit on a job. If this is 12% of the total charge, what does the owner pay?

23. Answer
12% = 0.12
1,800 ÷ 0.12 = $15,000
To find the total amount the owner pays, divide the amount that the contractor earns by the decimal he earned. Therefore, convert 12% to .12 and then divide 1800 by .12 which gives you $15,000 the total amount of money the owner pays.

24. Decimals and Percentages
The grading on a $145,500 house comes to $2, What percentage of the total cost is this? (Round this answer to the nearest hundredth percent)

25. Answer
2, ,500 = x 100 = 1.72%
To find this percentage, you divide the price of the grading by the price of the house. In this case when you divide 2 thousand five hundred eight and fifty hundredths by 1 hundred 45 thousand, you get one hundred 72 ten thousandths.
To determine the percent you multiply the decimal by 100 which gives you 1. and seventy 2 hundredths %.