EXAMPLES.

20 sec.?

1 pint?

1. What is one fourth of 33 wk. 5 da. 23 hr. 21 min. 8 wk. 3 da. 5 hr. 50 min. 20 sec. 2. What is one seventh of 24 bushels, 1 peck, 4 quarts, 3 bu. 1 pk. 7 qt. 1 pt. 3. Divide 109 acres, 74 square rods by six: what is the result? 18 A. 39 sq. rd. 4. What is one ninth of 973 gal. 1 pt.? 108 gal. 1 pt. 5. What is one twelfth of 48 hundred-weight, 64 pounds, 8 ounces? 4 cwt. 5 lb. 6 oz. 6. What is one eighteenth of 41 pounds, 3 ounces Troy weight? 2 lb. 3 oz. 10 pwt. 7. Divide 28 Ib. 10 3 2 3 1 1 gr. by nine: what is the result? 3 lb. 2 3 3 3 2 9 gr. 8. What is one thirteenth of 186 sq. yd. 5 sq. ft. 50 sq. in.? 14 sq. yd. 3 sq. ft. 26 sq. in. 9. What is one twenty-second of 144 da. 44 min. 16 sec.? 6 da. 13 hr. 7 min. 28 sec. 10. A farmer divided 1540 A. 140 sq. rd. into 20 lots: how much land in each lot? 77 A. 7 sq. rd. 11. A man walks 35 mi. 40 rd. in 8 hours: how far did he walk in 1 hour? 4 mi. 125 rd. 12. A dozen silver spoons weigh 6 oz. 4 pwt.: what is the weight of one spoon? 10 pwt. 8 gr. 13. I cut 25 C. 108 cu. ft. of wood in 12 da.: how much did I cut in 1 day? 2 C. 19 cu. ft. 1152 cu. in.

14. The weight of ten boxes of books was 2 T. 15 cwt. 65 lb. what is the weight of each? 5 cwt. 56 lb. 8 oz. 15. A vintner put a hogshead of California wine, containing 63 gallons, in 144 bottles: how much did he put in each bottle? 1 qt. 1 pt. 2 gi.

16. A barrel of flour was divided among 16 persons: how much did each receive?

12 lb. 4 oz.

17. A farm of 364 acres, 116 square rods was divided equally among six children: how much did each re60 A. 126 sq. rd.

ceive?

18. If 43 2 12 gr. was divided into 29 equal doses, what was the weight of each?

13.8 gr. 19. How many castings weighing 67 lb. each can be made from 16 cwt. 8 lb. of iron?

PROMISCUOUS EXAMPLES.

24.

1. A farmer sold 158 bu. 2 pk. of rye, 1040 pk. of corn, 197 bu. 1 pk. 5 qt. of wheat: how much grain did he sell? 615 bu. 3 pk. 5 qt. 2. A man owning 1040 A. 80 sq. rd. of land, sold 998 A. 23 sq. rd: how much had he left? 42 A. 57 sq. rd. 3. A has 57 bu. 1 pk. 3 qt. of oats, B has 6 times as much how much have both? 401 bu. 1 pk. 5 qt.

4. If a locomotive run 210 mi. 156 rd. in 9 hours, how far will it run in one hour? 23 mi. 124 rd. 5. What is the weight of 154 hogsheads of sugar, each weighing 11 cwt. 91 lb.? 91 T. 14 cwt. 14 lb. 6. What cost 165 firkins of butter, each containing 56 lb., at 38 cents a pound? $3511.20

7. Reduce 3 wk. 5 da. 41 sec. to seconds. 2246441 sec. 8. A man owns 156 A. 90 sq. rd. of land, which he divides into lots, each containing 6 A. 42 sq. rd.: how many lots are there?

9. A grocer buys 587 gal. of molasses at 42 sells it for 51 ct. a gal.: how much does he gain?

25 lots.

ct., and

$52.83

10. What cost 172 bags of coffee, each weighing 78 lb., at 32 cents a lb. ?

$4293.12

11. How much silver will it take to make six dozen solid table-spoons, each spoon weighing 10 penny-weights, 14 grains? 3 lb. 2 oz. 2 pwt.

12. An Illinois farmer raised 1045 bushels of potatoes, which he placed in 418 barrels: how many potatoes in

each barrel?

13. Reduce 14500 pints to gallons.

2 bu. 2 pk. 1812 gal. 2 qt.

14. How many times will a wheel, 18 ft. 4 in. in circumference, turn in going 15 miles?

4320.

15. How many cubic feet in a block of marble 14 ft. long, 6 ft. wide, and 3 ft. high? 252 cu. ft. 16. A boy lives 105 rd. from school, which he attends twice a day, five days in a week: how far will he travel in attending school 4 weeks? 26 mi. 80 rd. 17. How many rods of hedge are required to surround a field 2 miles square?

2560 rd. 18. How long will 112 bu. of oats last a horse that eats 7 qt. a day?

512 da.

19. At the rate of $6.50 per cord, what is the value of a pile of wood 18 feet long, 4 feet wide, and 16 feet high? $58.50

20. How long will 3 barrels of flour last a family that uses 24 lb. 8 oz. a week?

24 wk. 21. A vintner had 149 gal. 2 qt. of wine; he sold one half at 4 cents a pt.: how much did it bring?

$23.92

22. How many stoves, each weighing 1 cwt. 36 lb., can be made from 17 pigs of cast iron, each weighing 1 cwt. 28 lb. ?

16.

23. In a mass of ore weighing 47 lb. 8 oz. 12 pwt., one half is silver, 1 lb. 6 oz. 8 pwt. is gold, and the rest of the mass consists of refuse: what is the weight of the refuse? 22 lb. 3 oz. 18 pwt. 24. How many minutes in the first three months of the year 1876?

131040 min.

25. Five silver vases of the same size were sold for $456.75, at 35 cents a pwt.: what was the weight of each? 1 lb. 1 oz. 1 pwt.

26. A jeweler has gold enough to make 90 rings, each weighing 8 pwt. 16 gr. how many rings can he make, if he make each 1 pwt. 2 gr. heavier? 80 rings.

27. A travels 4 mi. 127 rd. less per day than B, who travels 89 mi. 190 rd. in 10 days: how far will A travel, while B is traveling 44 mi. 255 rd.? 22 mi. 260 rd.

QUESTIONS FOR REVIEW.

For what is Dry Measure used? Give the table. What is the standard unit? What is the English quarter? The chaldron? Give the rule for Reduction from higher to lower denominations. From lower to higher. Proof. For what is Avoirdupois Weight used? Give the table. How is the standard Avoirdupois pound determined? For what is Long Measure used? Give the table. What is the standard of length? For what is Land or Square Measure used? What is a square? What is meant by a square foot? A square yard? By 3 feet square? By 3 square feet? What is a rectangle? What is the area of a figure? The unit of measure? Give the rule for finding the area of a rectangle. When the area and one side are given, how find the other side? Give table for Square Measure.

For what is Cubic Measure used? What is a cube? A cubic yard? How are the cubic contents of a rectangular solid found? Give the table for Cubic Measure. What is said of the cord? The cord foot? For what is Liquid Measure used? Give the table. For what is Time Measure used? Give the table. What is the exact length of a solar year? Do all years have 365 days? Was 1800 a leap year? 1876? 1878? Name the months in their order. Which months have 30 days? Which 31 days? For what is Troy Weight used? Give the table. What is the standard unit of weight? For what is Apothecaries' Weight used? Give the table. What other measures of length are used? Give the table. Describe a Surveyor's Chain. For. what is Circular Measure used? Give the table. Give the Miscellaneous Table.

Define Addition of Compound Numbers. Give the rule. Define Subtraction of Compound Numbers. Give the rule. Define Multiplication of Compound Numbers. Give the rule. Define Division of Compound Numbers. Give the rule.

PROPERTIES OF NUMBERS:

DEFINITIONS.

83. Integers are divided into two classes, prime and composite.

A Prime Number is one that can be exactly divided only by itself and one; as, 1, 3, 5, 7, 11, etc.

A Composite Number is one that can be exactly divided by some other number; as, 4, 6, 8, 9, etc.

NOTE.-Two numbers are prime to number that will exactly divide both. each other; 8 and 15 are prime to each posite number.

each other when 1 is the only Thus, 4 and 5 are prime to other, though each is a com

84. A Factor of a number is a number that will exactly divide it. Thus, 3 is a factor of 6, 9, 18, etc.

A Prime Factor of a number is a prime number that will exactly divide it. Thus, 3 is a prime factor of 24; and 5 of 30.

A Composite Factor of a number is a composite number that will exactly divide it. Thus, 4 is a composite factor of 24; and 6 of 30.

A Divisor of a number is a number that will exactly divide it. Thus, 3 is a divisor of 12; and 5 of 10.