130 The Single Rule of Three in V. Fractions. 7 If 14 yards cost 9s. what is the value of 16 yards? answer 51 175.

8 What sum pays for 100yds. of cloth, at 17s. per yd.?

9 At 5s. per oz. what are 1611oz.

10 If C.wt. cost 14 to?

answer 861. of silver worth?

answer 4 12s 1gr. what will 7 G.wt. amount

answer 118/ 6s 8d.. of 19s. what is the answer 71 78 9d 13qr. 12 If 8lb. of tobacco cost 4s 9d., what is that per lb.

11 If of an ell English be worth 335 value of 7 ells?

answer 7d.

13 How much cash will purchase 4 pieces of cloth, each 27 yards, at 155s. per yard? answer 851 10s 11d. 14 Please to tell the quantity and value of 3 pieces of silk, each 24 yards, at 6s od. per yard?

answer quantity 85 yds. value 251 14s 6d.2}qr. 15 If lb. less by, cost 13d. what cost 14b. less by of 2lb.? answer 41 91 93zd. 16 Bought 120lb. of tea, at 8s. per lb. which being sold: for 70l. required the gain per cent.?

answer 351 55 3d. 3gr. 17 What will 133lb. cost at the rate of 17. per C.wt. answer 21 38. 717 18 If of a ship be worth 734 is 3d. what part of her may be purchased for 250/ 10s..

19 1f 3 times 3lb. cost 1 time 11 of of of 124lb.?

answer

what is the value

answer 7s 6d. 20 A mercer sold 4 pieces of silk, each containing 22 yds. at 8s.. per yd. what is the amount of his bill? answer 461 9s 11d. 21qr. 21 A person having of a ship, sells of his share for 319. what is the proportional worth of the whole vessel ? answer 5981 25 6dé

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 answers See the last note.

EXAMPLE S.

·I What quantity of shalloon that is yd. wide, will line Tyds. of cloth, 1yd. wide?

First 7 yds. I

yd. yd. yd. yd.

Second, 1= yds.} As 1 .. 12 : 1 - 15 answer.

3 15 4

Or cancelled;

--= 15 yds.

22 8

2 If 34 yards of cloth, that is 13 yard wide, be sufficient to make a cloak; how much Persian, which is but yards wide, will be required to line it? answer 4yds. 3grs. zna. 3 16 men finishing a piece of work in 28 days: the time is required in which 12 men should do it?

answer 37 days. 4 In exchanging 20 yards of cloth of 14 yards wide, for some of the same quality of yards wide;

the latter makes an equal barter ?
If 3 men can perform a service in 4

5

what quantity of answer 34 yds. hours; in what answer ihr. 21 min.

132 The Double Rule of Three in V. Fractions.

12 What number of pieces of merchandize, at 201s. per piece, are equivalent to 240 pieces, at 12s. per piece?

answer 1497 pieces. 13 A lends to B 10037. for 63 months; what sum should Blend A for 3 years, to requite his kindness?

answer 141 11s 9d. 135gr. 14 How many yards of cloth, at 8s. per yard, must be given for 26 yards, at 5s. a yard?

answer 17yds. 1gr. 3na.+4.

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 cafe 5, in reduction, may be applied here.

EXAMPLES.

1 If of a yard of cloth that is yds. wide, cost . what is the value of yard that is 14 yard wide, being of the same quality?

Or,
Cancelled.

• } 7518 ÷ 31=3438=31=135 4d. answer.

2 If 9 students spend 103. in 20 students spend in 30 days?

18 days; what sum will

20

answer 391 18s 40.37 days comes to 8+1. at have for working 1004 answer 3051 os 84.39

+ If 5 persona drink 7 gallons of beer in a week, what 4 quantity will serve 8 persons 224 weeks? ans. 280 gallons.

5 Fourteen persons upon examining into their expences, for 20 weeks past, found they had laid out 40%. in what time, at the same rate, may 2013 be expended by 46 persons? 56 answer 31195 weeks. 6 If 131. in 2 of a year, gain 1. interest what interest will 50l. gain in, of a year; and at what rate per cent. per annum? ans. al 58 id. 23qr. at 10 per cent. 7 If 50l. in of a year gain 21 55 1d. 23gr. in what time will 133 gain and at what rate per cent. per annum? answer year, at 10% per cent. 8 When 12 persons use 1 pound of tea per month; how much should a family of 8 persons provide for

·12

9 Two brothers at school compute the boarding, tuition, &c. for of a year to much will the education of 3 sons for 5 father at that rate?

year? answer 411. expence of their be 56. how years cost their answer 6ool.

DECIMAL FRACTIONS.

DECIMAL Fraction is a part, or parts, of a unit;

A 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,,o, tooo.

4

56

A mixt number consists of a whole number and a decimal ; thus, 245, 789; which is, 245 73.

789
이

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.

TABLE.

C. of Millions
X. of Millions
Millions

C. of Thousands
X. of Thousands
Thousands

Hundreds

-Tenth Part

Tens Units
-Units

9

X. Thousandth Parts

Hundredth Parts

C. Thousandth Parts
Millionth Parts

Thousandth Parts

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

98

Note. Ciphers annexed to decimals neither 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 TOO, 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.