s. di

grs.

20 a =960S

EXAMPLES.

1 Reduce 155 8d. to the decimal of a pound; also, 395se 12lb. 6oz. 14,592dr. to that of an C.wt.

S.

15 8=754960)754,00(7854166£.+facit.

6720

2 Reduce 73 6d. to the decimal of a pound. facit,375.

3 Reduce 9d to the decimal of a pound.

9375

4 Reduce 10s 94.4 to the decimal of a pound.

5385416+

5 Reduce 24 grains to the decimal of a lb.

,0041666+

9

6 Reduce 14 drams to the decimal of a lb. avoirdupois.

Reduce 4C 2qr. to the decimal of a ton.

8 Reduce 76 yards to the decimal of a mile.

Reduce 39r. 2nd to the decimal of a yard. 10 Reduce 4 perches to the decimal of an acre. 1 Reduce pint to the decimal of a gallon. 12 Reduce 7 minutes to the decimal of a day. 13 Reduce 3G.wt. zgr. 14lb. to C.wt. 14 Reduce 7yds. 2qr. 3na. to yards. 15 Reduce 134 1R. 14P. to acres. 16 Reduce 30. 1w. 5da. to months.

facit 30546875 facit,225

CASE 3.

To reduce a decimal fraction to its value;

RULE.

Multiply it by the known parts of the integer.

Note. To find the value of any decimal of a £. by infpection; double the first figure after the point for fhillings, adding one, if the Lecond be 5 or upwards; the fecond, if lefs than 5, or its excefs above 5, call tens, and the third units of farthings, abating one when above 12, and two if above 36.

EXAMPLES.

What is the value of,7854166 of a pound? ,7854166

By inspection.
,7854166

20

. 15,7083320

$.15 8, 2

142 The Single Rule of Three in Decimals.

11 What is the value of ,092 of 3A. 2R?

answer 1R. 11,52per.

12 What is the value of ,3 of a year?

answer 109da. 13hr. 48min.

13 What is the value of,6875 of a yard?

answer 2qr. 3na.

14 What is the value of ,3375 of an acre?

answer 1R. 14per.

15 Find the value of ,785 of a £. by inspection.

answer 15s Sd

16 Find the value of ,875 of a £. by inspection.

answer 17s 6d.

17 What is the value of a tenement for nize years, at 12,41. per annum? answer 111/ 12s. 18 Sold 25 yards of superfine scarlet cloth, at 2,751. per yard; what was its value?

answer 681 15s. 19 What is the sum of ,48 of a £. and,16 of a shilling?

answer 9s 9,12d.

20 What is the sum of,17 of a lb. troy, and ,84 of an answer 2017dwt. 14,4gr.

02.15
21 What is the sum of,177.,190.wt.,17gr. ,7lb.

answer 3C. wt. 2qr. 15,54lb.

22 What is the sum of 78 acres, and ,67 rood?

answer 3R. 31,6per.

23 What is the difference between 177 and 7s.?

answer 2s 8d. 1,6qr. 24 What is the difference between ,41 days, and ,16 of an hour? answer 9hr. 40min. 48sec.

THE SINGLE RULE OF THREE IN DECIMALS.

The operation both in direct and inverse proportions are agreeably to those rules in page 59, and 63, having regard to placing the points.

DIRECT PROPORTION.

EXAMPLES.

If 1,4lb. of mace cost 14,5s. what cost 75,31? s. lb. £. s. d. gr.

lb.

་་

As 1,4 14,5 : : 75,31. 38 19 11 3,52 answer,

z If 1,6C. of sugar sell for 31 12,76s. what is the proportional cost of 3hhds. each 11C, 3gr. 10,12.

answer 801 15s 3d. 3,36qr.

3 If 1,50%. of silver be worth 7,8s. what is the value of 9,716.? answer 30l 5s 3d. 1,44gr. 4 If 1,47 C. of sugar be worth 4,51, what is that for 1,716?

answer 11,1d. 5 Sold 12,5hhds. of wine, at 1,25. per pint; query the

amount?

6 Bought 3 pieces of cloth, each per yard; please to cast up the cost. 7 If 8,4lb. of tobacco cost 16s 4,6d. 3hhds. each 4C. 2qr. 7,4lb.

answer 3781.

21,5 yards, at 12,35. facit 391 135 4,2d. what is the value of answer 149/ 125 3d.

8 How many yards are in a piece of cloth which brings 61 13,12s. at 45 2,6d. per yard? answer 31,569yds. 9 Bought 5,8 tons of oil for 60,41. whereof 50,9 gallons leaked out; what must the rest be sold for per gallon, that the purchaser may be no loser? answer 10,27d. 10 A grocer bought 7,6C.wt. of sugar, at 40,1s. pèr C.wt. which he sold at 4,5d. per lb. whether did he gain or lose, and how much? answer gained 14s 5d. 1,12qr.

11 Bought 3C. 1,5gr. of cloves, at 2,75s. per lb. which was sold for 60l 11s 6d. query the gain? answer 81 125. 12 When a merchant buys 436 yards of cloth at 8,5s. per yard what will he gain by disposing of it at 10,755. per yard? answer 491 18.

13 A owes B 296,851. but compounds for 7,5s in the £. what sum must B receive? answer 111/ 6s 4d. 2qr.

14 How many English ells of linen may be bought for 25 18s 1d at 7s 9d. per yard? answer 53E 1gr. 15 If a yard of ribband sell for 4,5 cents, how many dollars will buy 345 yards? ans. 15,525, i.e. 15D. 524c. D.d. c. m

16 When 675 yards cost

be had for 38 mills?

12,8 2 5, how many yards may answer 2 yards.

D. d. c.

17 If 19 yards of calico bring 25,7 5 yards come to?

what will 435,5 D. d. c.m.

answer 590,2 1770. 18 What

144

The Single Rule of Three in Decimals.

18 What must be paid for 7 yds. of broad cloth, at 51. dollars per yard? ansiver 40,5625D. or 40D. 561 cts. 19 How does broad cloth sell per yard, when 73 yards cost 40D. 56 cents? answer 5,5D. 20 The French foot is just 1,068ft. English; how tall then would a 6ft. Philadelphian be at Paris?

answer but 5,618ƒ7..

INVERSE PROPORTION.

EXAMPLES.

How many men can do as much work in 4 of a month, as 16 could in a month and a half?

mo. men. mo. men.

As 1,5: 1 6:,4: 60 answer.

2 If, when wheat flour is as high as 6. per C.wt the half penny cake weighs 1,13330%. what should be the weight of it, when flour is only 1,81251. per C.wt.?

answer 3,750%.=30%, 12dr. 3 If a board be,75 foot broad, what length will it require to measure 12 square feet? answer 15ft. 4 How much Persian ,75yd. wide, will line 25,5 yards of five quarter cloth? answer 42,5 yds. 5 A had 40,7 yards of linen, for which B gave him 25,6 ells of Holland, valued at 4,5s. per ell; how was A's linen rated per yard? answer 2s 9d. 3,8qr.

6 How many dollars of 7,5s. each, should be given in exchange for 100 French guineas, at 34,5s? answer 460 7 What sum has A at interest, when it yields as much in 7 months, as B's 450l. do in 15? answer gool.

THE DOUBLE RULE OF THREE IN DECIMALS.

Questions in this rule are wrought as in whole numbers, placing the points agreeably to the preceding directions.

EXAMPLES.

I If 3 men receive 8,91. for 19,5 days labour; how much must 20 men have for 100,25 days?

If