166. Shingles are sold in bundles of 250 each. Allowing for waste, the usual estimate of the number of shingles per square is shown in the following table.

Ex. A gable roof is 40' long and 20' on each side. How many shingles laid 4" to the weather must be bought to

cover it?

4 2 40 × 20 × 2 100

= 16 squares.

length x width x no. sides
no. square ft. in a square

16 × 1000 = 16000 shingles (by table).

167. In flooring, a waste of about of the total amount of lumber required is allowed for the "tongue and groove."

Use cancellation when possible :

1. I wish to floor a room 20′ × 16'.

How much will the material cost at $30 per thousand square feet?

2. How many bundles of shingles 16" x 4" will be required to cover a roof 120' x 40' ?

3. At $4 per thousand how much will it cost to shingle a roof 100' x 30', allowing 800 shingles to the square?

4. Find the cost, at $40 per thousand square feet, of the tongued and grooved flooring for a room 30' x 20'.

168. Lumber is sold by the 1000 (M) board feet. foot is 1 ft. long, 1 ft. wide, and 1 in. thick.

NOTE. Boards less than 1" thick are counted as 1" thick.

A board

169. In making extensions in bills of lumber, point off 3 places and multiply by the price per 1000 feet, using aliquot parts and cancellation.

At $22 per M what is the cost of 60 pieces of hemlock 16' x 6' x 2''?

5

16 × 6 × 2 × 60 × 22

= $21.12

12

Divide by 12 because the width is expressed in inches.

Make the extensions in the following bill of lumber :

8 ft. long, 4 ft. wide, and 4 ft. high, and contains 128 cu. ft.

NOTE. A cord foot is 1 ft. of the length of such a pile.

Use cancellation :

1. How many cords of wood in a pile 40' x 20' x 8'?

2. At $5 per cord, how much will it cost to fill with wood a shed 25' x 15' x 18'?

171. Stone is measured by the cubic yard, or by the perch (243 cu. ft.).

172. Bricks are estimated by the M. 22 common bricks laid in mortar are counted for each cubic foot of wall.

NOTE. Allowance is always made for openings in ordering material and in making contracts.

SPECIAL METHODS

173. To find the number of bricks in a wall, multiply the number of cubic feet in the wall by 22.

174. To find the number of perches of stone, in a wall, divide the number of cubic feet in the wall by 243.

1. How many perches of stone in a wall 15' x 8' x 8'?

2. How many bricks will be required to erect the four walls of a flat building 60' × 40′ × 20', an allowance of 200 cu. ft. being made for the openings and corners, and the walls being 12" thick?

DIFFERENCES IN TIME

175. Two methods are employed in finding the difference in time between two dates:

1. Exact number of days.

Find the exact number of days from Feb. 2, 1912, to June 4, 1912. 29, number days in February

2

27, number days left in February

31, number days in March

30, number days in April

31, number days in May

4, number days in June 123 da.

2. Compound subtraction.

What is the difference in time between Oct. 24, 1909, and May 8, 1911?

May is the 5th month in the year, October the 10th month. The subtraction is performed by the method of denominate numbers. (1 mo. = 30 days)

APPLICATION TO MANUAL TRAINING

107

Find the difference in time between the following dates: 3. From Jan. 23 to Nov. 15 of the same year. (Not a leap year.)

4. From Dec. 13, 1910, to April 3, 1912. (Compound subtraction.)

5. From May 10, 1900, to Jan. 5, 1904. (Compound subtraction.)

6. From Jan. 1, 1913, to Dec. 25, 1913.

APPROXIMATIONS USED IN BUSINESS

176. To find the number of bushels of grain in a bin, multiply the capacity in cubic feet by .8.

177. To find the number of heaped bushels of fruit or vegetables in a bin, multiply the capacity in cubic feet by .63.

178. To find the number of gallons in a cistern or reservoir, multiply the capacity in cubic feet by 7.48.

Find the approximate number of bushels of (a) grain, (b) apples, in the following bins:

1. 12' x 10' x 8'

2. 20' x 15' x 10'

3. 16' x 8' 4" x 7'

4. 18' 3" x 15' 9" x 12' 4"

Find the approximate number of gallons in the following: 5. A cylindrical cistern, diameter 4', depth 20'.

6. A cylindrical cistern, radius 3', depth 15'.

7. A reservoir, 100 rd. × 60 rd. × 50'.

APPLICATION OF PRACTICAL MEASUREMENTS TO

MANUAL TRAINING

1. A room 32′ x 28' is laid off so as to accommodate 20 pupils in manual training. Allowing one fifth of the floor space for the teacher's use in demonstration work, how much floor space is allowed per pupil?

2. Find the total cost of the following manual training tools and supplies:

5. At 26 per board foot, what will the material cost for making the table shown in the illustration? Add expense of sanding at 2 per board foot for all lumber used.