31. Summary of short methods of division.

1. To divide by 10, move the decimal point one place to the left.

2. To divide by 100, move the decimal point two places to the left, and so on for other powers of 10.

3. To divide by 5, multiply by 2 and divide by 10.

4. To divide by 25, multiply by 4 and divide by 100. 5. To divide by 125, multiply by 8 and divide by 1000. 6. To divide by 331, multiply by 3 and divide by 100.

WRITTEN EXERCISE

1. State a short method of dividing by 663, or 20o. 2. State a short method of dividing by 163, or 10o.

3. State a short method of dividing by 121, or 100.

18. 39,888÷125.

4959 ÷ 331. 17. 67,400 ÷ 125.

16. 4936125. 19. Divide by 25: 13,428, $37,642, $135,621, $427,693. 20. Divide by 125: 17,200, $68,300, $276,400, $317,500. 21. Divide by 331: 69,720, $32,960, $48,750, $276,320. 22. At 25 a yard, how many yards of cloth can be bought for $37.25?

23. At 331 a yard, how many yards of cloth can be bought for $98?

24. Divide 3,742,697 by 25, by long division, and see how many seconds it takes. Do the same by the short method stated above. Write the time with the answer.

ORAL EXERCISE

1. To multiply by number? To divide by

is the same as to divide by what is the same as to multiply by what number? Illustrate on the blackboard.

2. Multiply by : 48, 250, 380, 460, 666, 1110, 1234.

3. Divide by : 70, 35, 60, 300, 450, 700, 1450, 8112.

4. To multiply by is the same as to divide by what number? To divide by is the same as to multiply by what number? Illustrate on the blackboard.

5. Multiply by : 36, 90, 63, 45, 75, 300, 123, 321. 6. Divide by : 30, 70, 50, 25, 80, 400, 2000, 4211. 7. Multiply by : 30, 60, 90, 33, 63, 300, 600, 1230. 8. Divide by : 20, 12, 16, 10, 60, 100, 200, 500, 1000. 9. Multiply by : 8, 16, 32, 48, 64, 84, 100, 200, 1000. 10. Divide by : 9, 11, 21, 25, 60, 70, 91, 125, 250, 800. 11. Multiply by 3: 8, 16, 20, 32, 40, 44, 48, 60, 80, 444. 12. Divide by 2: 9, 12, 15, 21, 30, 60, 66, 90, 120, 300. 13. Since , what is the short method of multiplying by ? of dividing by ?

=

14. Multiply by : 21, 31, 34, 123, 112, 321, 132, 125. 15. Divide by : 22, 300, 34, 160, 444, 664, 486, 1010. 16. Since .4, state a short method of multiplying and of dividing by . Do the same for and .

17. Multiply by : 30, 60, 66, 120, 600, 720, 840, 1200. 18. Because .121 what is the short method of multi

plying by .12?

19. At 12 a yard, what will 16 yd. cost? 72 yd.?

doz. eggs cost?

yd, of silk cost?

yd. of silk cost?

yd. of lace cost?

yd. of lace cost? yd. of velvet cost?

25. At 789 a yard, what will 26. At $18.60 a dozen, what will doz. spoons cost? 27. At 121 a yard, how much cloth will $1.50 buy? 28. How much will 12 doz. forks cost at $16 a dozen? 29. How much will 64 doz. eggs cost at 169 a dozen? 30. At 16 a pound, how much will 34 lb. of meat cost? 31. At 24 a pound, how much will 23 lb. of meat cost? 32, At 64 a pound, what will lb. shelled almonds cost? What will 2 lb. 4 oz. cost?

33. At 36 a dozen, how much must a dealer pay for 22 doz. small bottles of mucilage?

34. At $19.20 a dozen, how much must a dealer pay for 1 doz. fountain pens? for 2 doz.?

35. At 15 mi. an hour, how far will an automobile travel in 20 min.? in 40 min. ? in 30 min.?

36. At 12 a dozen, how many dozen eggs will $9.25 buy? How many dozen will $12.50 buy?

37. At 35 mi. an hour, how far will a train travel in 12 min.? in 24 min.? in 36 min.? in 48 min.?

38. At 47 mi. an hour, how far will a train travel in 12 min.? (12 min. hr.) How far in 15 min. ?

=

33. At 121 a yard, how much cloth will $876 buy?

34. At 12 a gross, how many gross will $17.75 buy?

of paper fasteners

35. At 33 a hundred, how many photograph cards can be bought for $1.83?

36. At 663 a gross, how many gross of pens can be bought for $24?

37. At yd. each, how many strips of ribbon can be cut from a piece 27 yd. long?

38. When a train is traveling at the rate of 32 mi. in 40 min., what is its rate per hour?

39. When a horse is trotting at the rate of mi. in 3 min., what is his rate per hour?

MEASURES

32. Tables for reference. Although these tables have been learned, they are here inserted for reference and review.

TABLE OF LENGTH

12 inches (in.) = 1 foot (ft.).
3 feet = 1 yard (yd.)»

5 yards or 16 feet = 1 rod (rd.).

320 rods or 5280 feet 1 mile (mi.).

The hand (4 in.) is used in measuring the height of horses at the shoulder. Sailors use the fathom (6 ft.) and cable length (120 fathoms) for measuring depths, and the knot (nautical mile, 1.15 common or statute miles, or 6080.27 ft.) for distances. furlong ismi., a league is 3 mi., and a cubit is 18 in.

TABLE OF SQUARE MEASURE

A

144 square inches (sq. in.)

=

square foot (sq. ft.).

9 square feet = 1 square yard (sq. yd.). 30 square yards = 1 square rod (sq. rd.). 160 square rods = 1 acre (A.).

640 acres = = 1 square mile (sq. mi.).

Carpenters, architects, and mechanics often write 8" for 8 in., and 5' for 5 ft. In this book both of these forms are used.

TABLE OF CUBIC MEASURE

1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.).

27 cubic feet = 1 cubic yard (cu. yd.).

A perch of stone or masonry is usually considered as 1 rd. long, 1 ft. high, and 11 ft. thick, and it contains 244 cu. ft. It varies, however. A cubic yard of earth is considered a load.