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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 40.18 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 125

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 ? Aos. Whole gain 541 Os Od Oqr.

} Gain

per cent. 85 14.3 1.7+

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OF THE SQUARE ROOT. Q. What is a Square ? Ă. Any number multiplied by itself produces a square, Q. What is the Extraction of the Square Root?

A. If a square be given to find one side, it is called the extraction of the Square Root.

Q. How is the given Square to be prepared for extraction?

A. By pointing off at every two figures, from the units place, both ways for a resolvend.

Q. What is a Surd ?.

A. It is an imperfect Square, or such a number whose Square Root can never be exactly found.

EXAMPLES. 1 What is the Square of 17.1? Answ. 292. 41 2 What is the Square of.09 ? Answ. .0081 3 What is the Square of .0094?. Answ..00008336 4 What is the Square Root

Answ. 68.649 + of 4712.81261? 5 What is the Square Root

Answ. 98.553 + of 9712.718651? 6 What is the Square Root

Answ. 1.78106+ of 3,1721812 ? 7 What is the Square Root ,

Answ. 1,1822+ of 1.3976121? 8 What is the Square Root

Answ. 27.6007+ of 761.801216? 9 What is the Square Root

Answ. .02759+ of 0007612816? 10 What is the Square Root

Answ. 2.000016+ of 4,000067121?

11 There is an army consisting of a certain number of men, who are placed rank and file, that is, in the form of a Square, each side having 47.2 men; I demand how

many men the whole

square

contains ? Ans. 222784 men, 12 The floor of a certain great room is tdade exactly square, each side of which contains 75 feet? I demand how many Square feet are contained therein? Ans. 5625 feet.

13. Suppose 12 544 Soldiers are to be put into rank and file, in the form of an equal square ; I demand how many soldiers will be in the front,and how many deep? Ans 112.

14 A certain square pavement contains 197 136 square stones ail of the same size; I demand how many are contained in one of its sides ? Ans. 414..

15 The wall of a town is 17 feet high, which is sur. rounded by a moat, of 20 feet in breadth; I demand the length of a ladder which shall reach from tle outside of the moat to the top of the wall i Answer 26.2+feet. OF THE SQUARE ROOT OF A VULGAR FRAC

TION.

Q. How is the Square Root of a Vulgar Fraction extracted ? A. Reduce the Fraction to its lowest terms.

2 Extract the Square Root of the Numerator for a new Numerator, and the Square Root of the Denominator for a new Denominator..

3 If the fraction be a Surd, reduce it to a Decimal, and then extract the Square Root from it.

4 The Decimal Fractions must consist of an eyen num. her of places, as two, four, &c.

EXAMPLES.

1 What is the Square-Root of ? Answer {.
2 What is the Square-Root of 466? Answer
3 Vhat is the Square-Root of joil Answers

Surds.
4 What is the Square-Root of 3197? Answer .71528+
5 What is the square-Root of ? Answer .87447 +
6. What is the Square-Root of ? Answer.72414+

OF THE SQUARE-ROOT OF A MIXT NUMBER.

Q. How is the Square-Root of a mixt number extracted?

A. ! Reduce the Fractional part of the mixt number to its lowest term.

2 Reduce the mixt vumber to an improper fraction.

3 Extract the Roots of the Numerator and Denominator, for a new Numerator and Denominator.

4 If the mixt number given be a Surd, reduce the fractional part to a Decimal, and annex it to the whole number, and extract the Square-Root from the whole.

EXAMPLES." 1 What is the Square-Root of 373 ? Answer 64 2 What is the Square-Root of 1728? Answer 5* 3 What is the Square-Root of 532? Answer 2.

SURDS. 4 What is the Square-Root of 7614 ? Answer 8.7649 + 5 What is the Square-Bdot of 778? Answer 2.79617

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