ORAL PROBLEMS FOR REVIEW.

440. 1. At 3 cts. a yd., what will 5 mi. of telegraph wire cost? 2. My neighbor's farm is mile square; how many acres did it contain?

3. Bought 40 acres of land at 75 cts. per sq. rod, and sold it so as to double my money; required my gain?

4. At 25 cts. a gallon, what is a family's milk bill for 60 days, taking 2 qts. daily?

5. If a man lives 2 miles from the City Hall, how many miles will he travel in 6 days, making 1 trip a day?

6. The length of a blackboard is 6 ft., its width 4 ft.; how many sq. yards does it contain ?

7. If a garden is 5 rods long and 4 rods wide, how many rods in its perimeter ?

8. If oz. of spice costs 8 cents, what will 2 pounds cost? 9. At $1 a sq. yard, what will it cost to carpet a room 18 feet long and 15 ft. wide?

10. A stationer paid $1.25 a gross for pencils, and sold them for a cent apiece; how much did he gain on 5 gross ?

11. In a certain school are 72 girls, and of the pupils are boys; how many pupils in the school?

12. The surface of a cube is 150 sq. inches; what is the surface of one side?

13. What fraction of a semi-circumference is 45 degrees? 14. How many writing books of 36 pages each can be made from a half ream of paper?

15. How many days in 7 of the longest months?

16. A can do a job in 2 days, B in 3 days; what part will each do in one day?

17. How long will it take both to do the same job working together?

18. How many yards of carpeting & yd. wide, will carpet a room 18 ft. square?

19. How many sq. yards in the pavement of a street 60 ft. wide and 800 ft. long?

20. How many suits of clothes can be made from 648 yards, allowing 4 yds. to a suit?

WRITTEN PROBLEMS FOR REVIEW.

441. 1. How many acres in a piece of land 184 rods long and 96 rods wide?

2. What will 16568 cu. feet of wood cost, at $31⁄2 a cord?

3. How many dollars can be made out of 50 lb. 9 oz. of silver, allowing 4123 grains to a dollar?

4. How many cubic inches in a box whose length is 30 inches, its breadth 18, and its depth 15 inches?

5. How many cubic inches in a block of marble 43 inches long, 18 inches broad, and 12 inches thick?

6. How many cubic feet of air in a school-room 16 feet long, 15 feet wide, and 9 feet high?

7. How many cubic feet in a pile of wood 16 feet long, 6 feet wide, and 5 feet high? How many cords?

8. How many cords of wood in a pile 140 feet long, 4 feet wide, and 6 feet high?

9. At 50 cts. per decister, what will a ster of wood cost?

10. What will a metric ton of hemp cost, at 25 cts. per kilo? 11. At 6 cts. per liter, what cost a hektoliter of milk? 12. How many square yards in the four sides of a room 18 feet long, 17 feet wide, and 14 feet high?

13. How many square yards of plastering will it take to cover the four sides and the ceiling of a room 18 feet square, and 15 feet high?

14. How many yards of muslin 3 qrs. wide, are equal to 36 `yds. brocatelle, which is 13 yard wide?

15. How many yards of silk 3 qrs. wide, will 51 yds. of cambric line, which is 14 yd. wide?

16. What will it cost to pave a street 3 mi. 115 rods long, and 2 rods wide, at $15 a square rod?

17. A man having 15 acres and 60 rods of land, laid it out in lots each containing 12 sq. rods, and sold the lots at $150 apiece; how much did he realize for his land?

18. What is the worth of a pile of wood 18 ft. long, 10 ft. high, and 9 wide, at $34 a cord?

19. How many times will a wheel of a railroad car, 9 ft. in circumference, turn round in going 1500 miles?

20. How long would it take a cannon ball, flying at the rate of 8 miles per minute, to reach the moon, a distance of 240000 miles?

21. The velocity of light is 11875000 miles per minute, and it takes 8 minutes for it to pass from the sun to the earth; how far from the sun is the earth; and how many weeks would it take to travel this distance, 30 miles an hour?

22. How many bricks will it take to pave a sidewalk 75 feet long and 8 feet wide, each brick being 8 inches long and 4 inches wide?

23. Required to reduce 5 mi. 6 fur. 23 rods 5 yd. and 8 in. to inches, and prove the operation.

24. Allowing 1 shingle to cover 24 sq. inches, how many shingles will be required to cover the roof of a house 50 feet long, the rafters on each side being 29 feet long?

25. How many farms of 160 A. in a township 6 miles square? 26. How many bricks will it take to build a prison 60 feet long, 25 feet wide, and 48 feet high, whose walls are 1 foot thick, the bricks 8 in. long, 4 in. wide, and 2 in. thick?

27. If the pendulum of a clock vibrates 65 times per minute, how much time will it gain in a common year?

28. How many years would it take to count a billion, counting 60 a minute, working 10 hours a day, and allowing 365 days to a year?

QUESTIONS.

418. What is a plane figure? 419. The perimeter of a plane figure? 420. The area?

421. What is a rectangle? 423. The dimensions of a rectangular figure? 424. How find the area of rectangular surfaces? When the area and one side are given, how find the other?

425. What is a rectangular solid? 427. The contents? 428. The dimen

sions?

430. What are the dimensions of a cord of wood? 431. How many cubic feet does it contain? Cord feet?

432. How is stone masonry estimated? Brickwork?

433. What is a board foot? 434. A board inch? How many board feet in a cu. foot? 435. How are sawed and hewn timber estimated? Round timber? 436. How find the contents of boards, plank, etc.?

438. How find the contents of cubical bins, cisterns, etc.?

442. 1. When a number is divided into a hundred equal parts, what is one of the parts called? Two of the parts? Five? Ten?

2. A man paid $100 for a horse and sold it for $105; how many dollars did he gain? How many hundredths of the cost did he gain?

3. What part of $100 is $5 ? (Art. 226.)

4. If I pay $100 for a sofa and sell it for $94, how many dollars shall I lose? How many hundredths of the cost?

443. The number of hundredths gained or lost is called the Rate per cent.

444. Per Cent, means by the hundred, or simply hundredths.

Thus, 3 per cent is 3 hundredths of a number; per cent is 5 hun. dredths, etc.

445. The Sign of Per Cent is %. Thus, 4% means 4 per

cent.

446. The process of calculating by hundredths is called Percentage.

5. A farmer lost 8 sheep out of every 100 of his flock; what per cent of them did he lose?

6. A man gave away $10 out of every $100 of his income; what per cent of his income did he give away?

7. A teacher having a class of 150 pupils, promoted 10% of them; how many were promoted?

447. Per cent is expressed by decimals, by %, or by fractions.

448. Since hundredths occupy two decimal places, every per cent requires, at least, two decimal figures. Hence, if the given per cent is less than 10, a cipher must be prefixed to the figure denoting it. Thus, 2% is written .02; 6%, .06, etc.

NOTES.-1. A hundred per cent of a number is equal to the number itself; for 108 is equal to 1.

2. In expressing per cent, when the decimal point is used, the words per cent and the sign (%) must be omitted, and vice versa. Thus, .05 de notes 5 per cent, and is equal to 15 or 2; but .05 per cent or .05% denotes of 16, and is equal to 1000 or 2000.

100

449. To read any given Per Cent, expressed Decimally.

Call the first two decimal figures per cent; and those on the right, decimal parts of 1 per cent.

NOTE.-Parts of 1 per cent, when easily reduced to a common fraction, are often read as such. Thus, .105 is read 10 and a half per cent; .0125 is read one and a quarter per cent.

Read the following as rates per cent:

8. .06.052; .085; .094.

9. .012; .174; .0836; .154.