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7 If 14 yards cost 9s. what is the value of 161 yards? answer 5l 17s. 8 What sum pays for 100 yds. of cloth, at 174s. per yd? answer 861.

9 At 51s. per oz. what are 16oz. of silver worth?

to ?

answer 41 12s 1gr.

10 If Cut. cost 14L. what will 7 C.wt. amount

11 If of an ell English be worth value of 7 ells ?

12 If 8lb. of tobacco cost 4s 9d.

answer 1181 6s 8d. of 19s. what is the answer 71 78 9d.11gr. what is that per lb. P answer 7d.}

13 How much cash will purchase 4 pieces of cloth, each

273 yards, at 15§s per yard ?

per yard?

answer 851 10s 11d. 14 Please to tell the quantity and value of 5 pieces of silk, each 243 yards at 6s Od. answer quantity 85 15 If lb. less by, cost 13s of 2lb.

yds. value 25l 14s 6d. 21gr. d. what cost 14lb. less by answer 41 9s 9 d. 8s. per lb. which being

16 Bought 120lb. of tea, at sold for 70L. required the gain per cent?

answer 351 5s 3d. 3qr.

17. What will 133lb. cost at the rate of 175L, per C.wt.

answer 21 35224 18 If of a ship be worth 731 1s 3d. what part of her may be purchased for 250l 10s. P

answer &

19 If 3 times 3lb: cost 1 time 11. what is the value ofofof 124lb ? answer 7s 6d. 20 A mercer sold 4 pieces of silk, each containing 223yds. at 83s. per yard, what is the amount of his bill? answer 461 9s 11d 21gr. 21 A person having of a ship, sells of his share for 3191. what is the proportional worth of the whole vessel ? answer 5981 2s 6d.

INVERSE PROPORTION.

RULE.

After the necessary preparations, multiply the first and second terms together, and divide that product by the third

term; or,

Invert the dividing term, and multiply them together for the fractional answer. See the last note.

EXAMPLES.

1 What quantity of shalloon that is yd. wide, will line. 71yds. cloth, 11yds. wide?

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2 If 31 yards of cloth, that is 13 yard wide, be sufficient to make a cloak; how much Persian which is but 3 yard wide will be required to line it? answer 4yds. 3qrs. 2na. 3 16 men finishing a piece of work in 28 days: the time is required in which 12 men should do it?

answer 377 days. 4 In exchanging 20 yards of cloth of 14 yard wide, for some of the same quality of 33 yards wide; what quantity of the latter makes an equal barter ? answer 34 yds. 5 If 3 men can perform a service in 4 hours; in what time may ten men effect it?

answer 1hr. 21min. 6 When wheat is at 54 shillings per bushel, if the penny loaf weigh 7oz. what is it per bushel, when the penny loaf weighs 24 oz. P answer 15s 4d. 3qr. 7 If when the price of wheat is 61s. per bushel, the penny loaf weighs 9oz. what must it weigh, when that grain sells at 44s. per bushel ? answer 12oz. 8dr. 8 A piece of tapestry 3 ells Flemish wide, and four long, is to be lined with stuff which is but yds. wide; how many yards are sufficient? answer Gyds. 9 Suppose 275 yards of cloth, that is 14 yard wide, make coats for 130 men; what number of yards of shalloon of yards wide will be requisite to line them?

answer 458 yds. 10 How many yards of baize ell English wide will be sufficient to line 20 yards of camelot, that is yards wide? answer 12yds. 11 A merchant bartering 58C. of sugar at 63 d. per lb. for tea, at 8s. per lb. would know what quantity of the latter article he is to receive ?

answer 43 Lib. 12 What

12 What number of pieces of merchandize, at 2018. per piece, are equivalent to 2404 pieces, at 121s. per piece? answer 149 17 pieces. 13 A lends to B 10031. for 63 months; what sum should Blend A for 35 years to requite his kindness? answer 141 11s 9d. 185gr. 14 How many yards of cloth, at 81s. per yard, must be given for 26 yards, at 5 s. a yard?

J

answer 17yds. 1gr. 3na. 14

THE DOUBLE RULE OF THREE IN VULGAR

FRACTIONS.

RULE.

Prepare the terms, if necessary; then state, and work them agreeably to the directions given in whole numbers. Or,

Invert the dividing terms, and multiply the upper figures continually for the numerator, and those below for the denominator, of the fractional answer.

Note. The Note to case 5, in Reduction, may be applied here.

EXAMPLES.

1 If of a yard of cloth that is tyd. wide cost L. what is the value of yard that is 12 yard wide, being ofthe same quality?

If 3yd.
fyd. S

Styd. 21.

Lyd. }

} | | = | } 17 18 + 1 = ?g=}l.—15s 4d. answer.

Or,

70

3.13s 4d.

Cancelled. 3× × 8 × 8 × 2 If 9 students spend 1031. in 20 students spend in 30 days? 3 The labour of 3 men for 19 the same rate, what must 20 men days?

18 days; what sum will

answer 391 18s 4d. days comes to 8. at have for working 1001 answer 3051 Os 3d. 3

4 If 5 persons drink 74 gallons of beer in a week, quantity will serve 8 persons 22 weeks?

what

answer 280 gallons. 5 Fourteen persons, upon examining into their expences for 20 weeks past, found they had laid out 404. in what time, at the same rate, may 2021. be expended by 46 persons? 56 answer 31193 weeks. 6 If 131. in 2 of a year gain 1. interest, what interest will 501. gain in of a year; and at what rate per cent, per annum?

annum ?

7

answer 21 5s 1d. 24gr. at 105 per cent. 7 If 50l. in 12 of a year gain 21 5s 1d. 23gr. in. what time will 134. gain 17. and at what rate per cent. per answer year, at 105 per cent. 8 When 12 persons use 14 pound of tea per month; how much should a family of 8 persons provide for year? answer 44lb. 9 Two brothers at school compute the expence of their boarding, tuition, &c. for of a year to be 5611. how much will the education of 3 sons for 5 years cost their father at that rate? answer 600L.

DECIMAL FRACTIONS.

DECIMAL Fraction is a part, or parts of a unit, denoted by a point prefixed to a figure, or figures, thus, .4, .45, .456; the first figure after the point denotes SO many tenths of a unit; the second so many hundredths of a unit, or tenths of one tenth, which are equal to, and read as, 45 456

1 100 1000

A mixt number consists of a whole number and a decimal'; thus, 245, 789; which is, 245-780.

As whole numbers, counting from the right to the left, increase in a ten fold proportion; so decimals, counting towards the right, decrease in the same proportion; which is exemplified in the following.

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TABLE.

C. of Millions
∞X. of Millions
Millions

C. of Thousands
X. of Thousands
Thousands
Hundreds

Tens Units

Units

Tenth Part

Hundredth Parts

X. Thousandth Parts
C. Thousandth Parts
Millionth Parts

ca Thousandth Parts

X. Millionth Parts
C. Millionth Parts
M. Millionth Parts

987 6 5 4 3 2 1.1 2 3 4 5

Note. Ciphers, annexed to decimals, neitner increase nor decrease their value; thus, ,25000, and ,25 are equal, but prefixed, decrease them in a tenfold proportion; thus ; .5, 05,.005, all express different decimals, and=10, 150, 1000•

ADDITION OF DECIMALS.
RULE.

Place the numbers according to their value; viz. units under units, tenths under tenths, &c. and add as in addition of integers; putting the point in the sum total exactly under those in the example.

EXAMPLES.

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What is the sum of 450+31.47+376.004+1.08+456+ 76+.05 ? "answer 1315.364 If 2476.8471 + 94.9 + 9.8941 + 867.05 +84.9 + 271.007+5.1008+1.6789 be added together, what is the

sum ?

answer 3811.3779 SUBTRACTION

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