44. How many seconds in 5 hours? in 2 days? in 1 week? 45. How many hours in 5 years? in 12 years? in 170 days?

46. How many rods in 7 acres, and how much would it be worth at 75 cents per rod? Ans. 840D.

47. In 6795 square feet, how many square yards?

Ans. 755. 48. In 78479 mills how many dollars? how many eagles? 49. What cost 60 galls. 1 pt. of wine, at .75D. per gallon? Ans. D45.09.3+ 50. What will 26 yards 2 quarters of cloth cost at D4.75 per yard ? Ans. D125.87.5. 51. Required the value of 25.874 yards; 39 42 yards; 67 yards, 2 nails; 47 yards, 2 quarters, at D3.074 per yard.

52. What cost 91.27 gallons; 218.087 gallons; 8 gallons, 2 quarts; 91 gallons, 3 quarts, at D1.25 per gallon?

53. 47963.0521+897.009+81.81+9.0009+.629108+1.08. 54. What number is that, which being added to 9.0146 will make 20.7092 ?

REDUCTION OF DIFFERENT DENOMINATIONS.

IN Reduction of Different Denominations we have several denominations given to be reduced to a lower denomination, still retaining the same value; it is called compound reduction. The remarks and explanations in simple reduction will apply on the present occasion.

RULE.

1. Multiply the highest denomination by as many of the next less as it requires to make one of that, and add in the second denomination, if any; then multiply by the next less denominafion, and add in, if any; continue in this way through the sum

2. When small denominations are to be reduced to larger denominations, reverse this operation, and begin by dividing in the same manner as you are directed above to multiply; by this reversion of the operatior. the proof is obtained. See the examples.

1. Reduce 5 cwt. 2 qrs. 12 lb. 11 oz. 10 drs. to drams.

4 X

20

2+

22 qrs 28 X

176

44

12+

628 lb.

16 X

3768
628

10048

11+

10059 oz.

16 X

60354

10059

10+

160954 drams.

16)160954 drams.

16)10059+10 dr.

28)628+11 oz.

4)22+12 lb.

cwt. 5+2 qr. proof

5 cwt. 2 qrs. 12 lb. 11 oz. 10 dr.

Explanation. Multiply the 5 cwt. by 4 quarters, and add in the 2 quarters and you have 22 quarters; then multiply 22 quarters by 28 pounds, and add in the 12 pounds, and you have 628 pounds; then multiply 628 pounds by 16 ounces and add in the 11 ounces, and you have 10059 oz. ; then multiply those ounces by 16 drams, and add in 10 drams, and you have 160954, which is the answer; then for the proof you can divide by short or long division, as you like, &c.

2. In 126230400 seconds how many years of 365 days?

Ans. 5 T. 8 cwt. 3 qrs. 24 lbs. 13 oz. 14 drs

4 Reduce 2 cwt. 3 qrs. 17 lbs. to pounds.

5 Bring 16 bushels 1 peck to pecks.
6. Reduce 2 hhds. 10 gallons to quarts.

7. Reduce 18 years, 6 months, to months. 8. Reduce 15 yards, 2 feet, to inches..

222 mo.

564 in.

95 fur. 1859 po.

9. Reduce 3 leagues, 2 miles, 7 furlongs, to furlongs 10. Reduce 11 acres, 2 roods, 19 poles, to poles. 11. In 12 cords of wood how many solid feet and inches? Ans. 1536 ft.; 2654208 in.

2688 ft.

41 w.

12. In 21 cords of wood how many solid feet? 13. In 24796800 seconds, how many weeks? 14. In 20692 square rods, how many acres? 129 A. 1 R. 12 po. 15. In 15840 yards how many miles and leagues? 16. In 51 miles how many furlongs and poles ?

9 m. 3 1.

Ans. 408 fur.; 16320 po 236 yds. 1 qr. 3 na.

17. In 3783 nails how many yards? 18. Bring 892245 ounces into tons. Ans. 24 T. 17 cwt. 3 qr. 17 lb. 5 oz. 19. In 12 hhds. of sugar, each 11 cwt. 25 lb., how many Ans. 241344 oz.

ounces?

20. How many revolutions will the wheel of a steamboat, 27 feet in circumference make, in navigating the Hudson from New York to Albany, supposing the distance 160 miles, with-.. out making any allowance for current or tide? Ans. 31288

21. How many inches between the earth and the sun, the distance being 95,000,000 miles? Ans. 6019200000000. 22. If a cannon ball move at the rate of 1 mile in 7 seconds, how long would it be in passing from the earth to the sun? (Multiply by 7, divide by 60, &e.) Ans. 21yr.31da. 18h. 13m. 20s.

23. Admitting your age to be 16 years, 1 week, 17 days, 20 minutes, 45 seconds, how many seconds old are you? (52w.=ly.) Ans. 505268445s.

24. Reduce 184320 grains to pounds.

Ans. 32 lbs.

25. In 16 tons how many hundred weight? quarters ? pounds? ounces? and drams?

Ans. 320cwt.; 1280qrs.; 32000lbs.; 512000oz.; 8192000drs. 26. In 1332005 grains (apoth.) how many pounds? Ans. 231 lb. 3 oz. 5 gr. 27. In 9173 nails how many yards? Ans. 573 yds. 1 qr. 1 na. 28. In 3 ells French, how many inches? 29. In 34594560 inches how many miles? 30. What is the circumference of the earth in yards?

31. Reduce a solar year to seconds:

Ans. 162. Ans. 546 m.

Ans. 44035200 yds.

Ans. 31556937 sec.

32. In 622080 solid inches how many tons of round timber? Ans. 9 T.

33. In 5529600 cubical inches how many cords. Ans. 25. 34. How many minutes and seconds in one complete revolution of a planet? Ans. 21600 minutes; and 1296000 sec.

35. In 89763 square yards how many acres?

Ans. 18 A. 2 R. 7 po. 101 ft. 36 in. 36. In 5054 pints how many bushels? Ans. 78 b. 3 pk. 7 qts. 37. How many quarters of rice, at 6c. per pound, may be bought for D3.36?

38. How many tuns of wine, at 6 cents a gill, for D483.84.

Ans. 2 qrs. may be bought

Ans. I tun.

39. What is the value of a silver cup weighing 10 oz. 5 pwt. 18 gr. at 5 mills per grain? Ans. 24D. 69c. 40. At 9 cents an hour what will 2 yrs. 6 mo. 3 w. 6 da. 12 h. labor be? Ans. D1873.80. 41. At 320 cents a yard, what will 64 nails of cloth cost?

Ans. D12.80. 42. In 86400 grains how many scruples? drams? and ounces? Ans. 4320 sc.; 1440 dr.; 180 oz

43. In 8903304 barleycorns how many leagues?

Ans. 15 1. 1 m. 6 fur. 28 po. 4 yds.

44. In 20 cords of wood how many solid inches?

Ans. 4423680 in.

Ans. 161280 g

45. In 20 tuns of wine how many gills?
46. In 11378955037 seconds, how many years?

Ans. 360 yrs. 300 da. 20 ho. 50 m. 37 sec. 47. How many barley-corns will reach round the globe, it being 360 degrees? Ans. 4755801600. 48. In running 300 miles, how many times will a wheel 9 ft 2 in. in circumference turn round?

Ans. 172800. 49. How many seconds in 1828 years, allowing 365 days to the year? Ans. 57687292800.

50. What is the cost of a tun of wine at 3 cents per gill? Ans. D241.92.

REVIEW.

When is Compound Reduction used? When several denominations are given to be reduced, how will you proceed? What is the rule? How will you prove questions in this rule?

PROPORTION; OR, SINGLE RULE OF THREE.

THE first idea that naturally presents itself to the mind in the consideration of Proportion, is Ratio, or the connexion existing between Ratio and Proportion; for ratio is a Latin word, and means proportion, although it can only exist between quantities of the same kind. The numbers given are called terms, and may be considered as a divisor and dividend; and the ratio, the required term, as a quotient in a division sum. The terms are written thus, 5: 15, ratio 3; 3×5=15; the ratio of 84: 336 =4, because 84 is contained in 336, 4 times; so may any two numbers of the same kind form a ratio. What is the ratio of 9 to 18? Ans. 2. What is the ratio of 6 to 24? What is the ratio of 11 to 13? Ans. 12. What is the ratio of 100 to 30?Ans. 24: 8: 16; here the ratio is 2, because 2 is in 42, and 8 is in 16-2. 2 10 12 60; here the ratio is 5, because 2 is in 10=5; 12 in 60-5. 16 15: 48: 45; here the ratio is reversed, and will stand thus, 1, first and second terms; 41, the third and fourth terms.

3

:

15

Proportion is a comparative relation of one thing, or number, to another ratio. Proportion, when complete, consists of four numbers or terms, and is a combination of two equal ratios; and the product of the first and fourth terms (which are the extremes) is equal to the product of the second and third terms