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OF DIVISION OF DECIMALS. Q. How are Decimals divided ? .1. As whole Numbers are.

Note 1. The Decimal places of the Divisor and Quoriont must always be equal to those in the Dividend,

2. If there be more Decimals in the Diviser than in the Divadend, unner' (is rilany Cyphers as you please to the Dividend, sq $1.s to be equal ai least to the Divisur.

3 of Decimal Places ure wonting in the Quotient, they must be supplied with Cyphers to the Decimal Point.

4. Observe the satile Note here, which is given in Division of Pidgar Fractions.

2. Ilow are the following examples to be proved? 1. By Multiplication.

EXAMPLES 1 Divide -19.4 by 37.5 7 Divide 9. by .7124 2 Divide 47121.1 ly 47. 8 Divide 9. ů Divide 4.18 by .1812 9 Divide 14. by 47.31 4 Divisle .76121 by 41. 10 Divide 1. by 863. 5 Divide .612812 lay 7.21 1 Divide .01281 by .12 o Divide .121819 by .721 12 Divide.00012:12 by.018

by .9

OF REDUCTION OF DECIMALS.

GASE 1.

Q. How

W do you reduce à Vulgar Fraction to a De. vinal?

14. Divide the upper Term by the lower.
Note i. Both Terms are to be esteemed whole Numbers.

2 By this case, Tables containing the Decima! Parts of an Ilieger ure constructed.

EXAMPLES.

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23

to a decimal.

Facit 19230764 2 Reduce to a Decimal.

Facit ,1785714+Reduce 11 of 1: io a Decimal. Facit .6043956 to 4 Reduce 7s 6d to the Decimal of a pound. Facit 3751.

5 Reduce 10s 9d to the Decimal of a pound. Facit -5854167-1..

Neduce 24 Grains to the Decimal of a lb. Troy. Facit (0:1666-4.

7. Reduce 14 drams to the Decimal of a lb. Avoirdupois. Facit .0546875 lb.

8. Reduce 4 C. 2 qts. to the Decimal of a ton. Facit 225 T.

9. Reduce 14 C. to the Decimal of a ton. Facit .7 ton.

10. Reduce 174 drams to the decimal of an C. Facit .0060686+C.

11 Reduce 4 inches to the Decimal of a yard. Facit .1111111+yard.

12 Reduce 76 yards to the Decimal of a mile. Facit ,043181+ mile.

13. Reducé a mile to the Decimal of a league. Facit 33333333+ league.

14 Reduce 3 qrs. 2na. to the Decimal of a yard. Facit .875 yd.

15 Reduce 4 perches to the Decimal of an acre. Facit 025 acre.

16 Reduce pint to the Decimal of a gallon Facit .125 gal.

17 Reduce 1 gallon of wine to the Decimal of a hhd. Facit .015873+bhd.

18 Reduce 7 minutes to the Decimal of a day. Facit .0048611+day.

19 Reduce 2 days to the Decimal of a week. Facit .2857142+ week.

20 Reduce 72 days to the Decimal of a year. Facit .1972602 + year.

CASE 2.

Q. How do you find the proper quantity of a Decimal Fraction in the known parts of an Integer?

A. Multiply it by the common parts of the Integer.
Q. How do you prove Questions in this case ?
A. By Case 1.

EXAMPLES.

1. What is the proper quantity of .76 of a Pound ? Ans. 158 2d 1.6qr:

2. What is the proper quantity of 861 of a C. weight? Ans. 3 qrs. 121b. 6oz. 14.592dr.

3. What is the proper quantity of .461 of a shilling? Ans 5d. 2.128 qrs.

4. What is the proper quantity of .761. of a hhd. of wine ? Ans. 47 gals. 3 qts. 1.344 pt.

5 What is the proper quantity of .17 of a tun of wine ? Ans 62 gals. 3.36 qts.

6 What is the proper quantity of .761 of a day? Ans. 18 hrs. 15 min. 50.4 sec.

7. What is the proper quantity of .7 of a pound of silver? Ans. 8 oz. 8 dwts.

8. What is the proper quantity of .71 of 4 oz. of gold ? Ans. 2 oz. 16 dwts. 19.2 gr.

9 W bat is the proper quantity of .67 of a league ? Ans. 2 miles, c fur. 3 poles, 1 yd. o feet, 3 in. 1.8 b. c.

10. What is the proper quantity of .712 of a furlong? Ans. 28 poles, 2 yards, 1 foot, 11.04 in.

11 What is the proper quantity of .07 of a barrel of ale ? Ans. 2 gals. 1.92 pt.

12 What is the proper quantity of .4712 of an ell Eng. lish? Ans. 2 qrs. 1.424 na.

13 What is the proper quantity of .72 of a hhd. of Beer? Ans. 38 gals. 3.52 qts.

14 What is the proper quantity of .61 of a tun of wine ? Ans. 2 hhds. 27 gals. 2 qrts. 1.76 pt.

15 What is the proper quantity of .092 of 3 acres, 2 roods ? Ans. 1 rood, 11.52 poles.

16 What is the proper quantity of .461 of a chaldron of coals? Ans. 16 bush. 2.384 pecks. i7 What is the proper quantity of .712 of 3 qrs.

of corn ? Ans. 17 bush. 2.816 qrs.

18 What is the proper quantity of .3 of a year? Ans. 109 days, 12 hrs.

19. What is the proper quantity of .5 of an hour ? Ans. 30 min.

20 A certain Tenant hired an House for 9 years, at 12.41. per annum; how much was due at the end of the term ? Ans. 1111 12s. Note 1, To this Case is referred Case 4'in Practice, p. 55.

EXAMPLES.

1286 at 4s. Ist 4 21. 2d 1286

Facit 2571 4s. ;

257.2

20

4

2 Addition and Subtraction of Decimals of different denominations may easily be performed, after the Decimals are reduced to their proper quantities.

EXAMPLES

1 What is the sum of .481 and 16s reduced to their proper quantities ? Ans. 9s 9.12d.

2 What is the sum of .17 lb. Troy and .84 oz ? Answ. 2 oz 17 dwt 144 gr.

3 Wbat is the sum of .17 ton .19 C .17 qr. and .7 lb. ? Àns. 3 C 2 qrs 15.5-4 Ib.

4 What is the difference between .171 and .7s ? Answ. 2s8d 1.6 qrs.

5 What is the difference between .41 days and .16 hrs ? Ans. 9 hrs 40 min 48 sec.

OF THE. SINGLE RULE OF THREE DIRECT IN DECIMALS.

Q How do you prove the following questions ?

A. By changing their order.

EXAMPLES.

1 If 1.4 lb of mace cost 14.58 what cost 75.31 lb ? Ans. 381 198 110 3,52qrs.

2 If 1.6 C. of Sugar cost 32 12.76s what cost 3 hhds. each 11 C 3 qrs 10.12 lb Ans. 801 15s 3d 3.36 qrs.

3 If 1.5 oz. of Silver be worth 7.8s what is the value of 9.7 1b ? Ans. 301 59 3d 1.44 qr.

4 If 1.47 C. of Sugar be worth 4.52 what is 1.7lb wor at that rate ? Ans il.ld.

5 If i pint of wine cost 1.2s what cost 12.5 hhds? Ans. 3781.

6 If 8.4 lb of Tobacco cost 16s 4.6d what cost 3 bhds. each 4 C. 2 grs 7.4 lb ? Ans. 1491 12s 3d 2qrs.

7 If a yard of cloth cost 12.33 what cost 3 pieces, each 21.5 yards ? ins. 397 138 4 2d.

8 A man bought a piece of cloth for 6l 13.12s. I demand how many Yards there were in the same, when he gave after the Rate of 4s 2.9d per yard ? Answer 31.569 Yards.

9 A man bought 5.8 tuns of oil for 60.4! but by misfortune it chanced to leak out 50.9 gallons ? I demand how he must sell the rest per gallon to be no loser ? Answer 10.27d per gallon.

10 Two men bartered, A had 40.7 yards of linen, for *which B

gave

him 25.6 ells of Holland, at 4.5s per ell; I demand the price of the linen per yard ?·Ans.2s 9d 3.8qr.

11 A Grocer bought 7.6 C of sugar, at 40.1s per C. and sold the same out at 4.5 per lb I demand whether he gained or lost, and how much ? Ans. 14s 5d 1.12 qr gain.

12 A Brewer made a quantity of Beer, which cost him 90.41 and afterwards sold it out at 26.7s per barrel, by which he gained 10l. I demand the quantity that was brewed ? Ans. 75 barrels 7.4+gals.

13 A Grócer bought 3 C 1.5 qr of cloves, at the rate of 2.758 per lb. and sold them for 601 11s od what did he gain or lose by the bargain ? Ans. he gained 8l 12s

14 A Merchant bought 436 yards of Cloth for 8.5s per yd. and sold it again at 10.758 per yard, what did he gain by the sale thereof ? Ans. 491. is gain.

15 A owes B 296.851 but he compounds for 7.5s in the pound, what must B receive for his debt? Ans. 1111 6s 4d

2 qrs.

i6 Bought 3 hhds of Tobacoo, each weighing 4 C 1.9 qrat 5.61 per C. which I sold out at 71 169 per C. what did I gain by the whole ? Ans. 291 108 8d 1.0 qr.

17 A Jeweller bought a Diamond for 60 guineas, and after it was neatly cut, weighed 1.50z which he sold again for 3.25s per grain: 1 deinand how much he gained by the said Diamond; and also at what rate per cent he made his gain? Aas. Whole gain 541 Os od Oqr.

Gain

per cent. 85 14.3 1.7+

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