If the given quantity or divisor consists of 4, 4, or 3.

Rule.

Multiply the given quantity by 4, adding to the product 1 for, 2 for 1, 3 for 2; and it will give the divisor, which divide with as before, and the quotient multiply by 4, will give the answer.

25. Suppose à person in trade to clear 10351. 9s. 03ď. in 10 years equally, what was his yearly increase of for tune? Answ. 987. 12s. 3±d.

26. Suppose another to clear 5187. 8s. 03d. equally in 83 years, what was his yearly profit? Answ. 591. 4s. 11d.

QUESTIONS shewing the Use of this DIVISION.

Quest. 1. A piece of broad cloth containing 24 yards, cost 181. 6s. what did it cost d yard?

Answ. 15s. 3d.

2. Bought 39 of butter, for 497, 14s. 6d. what did it

cost Cut.? Answ. 11. 5s. 6d.

3. If a hogshead of wine cost 167. 16s, what was it gallon? Answ. 5s. 4d.

4. If 27 C. of sugar cost 477. 13s. 9d. what cost 1Cwt. ? Aw. 1 15s. 3, d.

1

5. If a Cwt. of sugar cost 31. 10s. what is it .

Answ. 74d.

6. If I held 120 acres of land, and my yearly rent is 87%. what do I pay an acre? Answ. 14s. 6d.

7. If a reckoning of 6. 14s. 2d. be to be paid by 35 persons, what must they pay a piece? Answ. 3s. 10d.

8. A man dying left his estate worth 10002. betwixt his wife and 3 sons, viz. to his wife; to the eldest son, and the remainder to the second and third, share and share alike: what is the share of each? Answ. The wife 3331. 6s. 8d. the first son 2507. the second and third sons 2081. 6s. 8d.

5

9. Three merchants, A, B and C, have a ship in company: A hath B, and C ; and they receive freight 2281. 16s 8d. It is required to divide it among the owners according to their respective, shares ? Answ. A's share

1431 Os. 5d. B's 571. 4s. 2d, and C's 287. 12s. 1d.

11

10. Four merchants have a ship in company, viz. A 1, B, C, and D, and they let it out a voyage to the West Indies en freight, at 221 10s. 8d. P month; she performs the voyage in 18 months; what is each man's share of the freight? Answ. A's 1391. 88. 6d. B's

101. 8s. C's 881. 14s. 6d. and D's 76l. 1s.

11. A father left, among 5 sons an estate consisting of 5001. in cash, with 5 bills, each 481. 10s. 6d he ordered 201. to be laid out on his funeral, and his debts to be paid, amounting to 1647. the rest he leaves among his sons, thus, to the eldest, and to the other four equal shares; what is the share of each son? Answ. 1861. 4s. 2d. the

eldest, and the others 937. 12s. 1d. a piece..

12. A privateer having taken a prize worth 10257. it is divided into 100 shares, of which the captain is to have 11; 2 lieutenants, each 5; 12 midshipmen, each 2; and the remainder is to be divided equally among the sailors who are 120 in number? Answ. Captain's share 1121.

15s.

15s. lieutenant's 517. 5s. a midshipman's 207. 10s. and a sailor's 4t. 10s. 114d.

13. Ten pounds a quarter is allowed to five anditors of a fire office. They attend about seven times in the quarter, and the absentees' money is always divided equally among such as do attend. A and B on these occasions never miss; C and D are twice in a quarter absent, and E only twice: At the payment what had each man to receive?

CHAP. VI..

REDUCTION.

EDUCTION is the changing a number of a higher

Ror greater denomination to a lesser; likewise a

ber of divers denominations to the lowest of them, and the contrary, viz. to change a number of a lesser denomination to a grea er.

I.

To bring a number of a higher or greater denomination: to a lower or less.

Rule.

Multiply the given number of the higher by that num ber which one of the greater contains of the less,

1.

27

20 shillings 17.

540 shillings.

So 271. will be reduced into 510 shillings; for if 27 be multiplied by 20 (the shillings in a pound) the product is 540: in ĺke manner 540 shillings may be reduced into 6480 pence : for if 540 be multiplied by 12 (the pence in 1 shilling) the 6480 product is 6480.

12 pence shilling.

II.

To bring a number of divers denominations to the lowest mentioned.

Rule.

To the product found (last) still add the odd number of the same denomination.

So 3641. 15s. 5d.

thus: 3647. multi

plied by 20 (be

cause 20 shillings

Application.

may be reduced into 87545 pence,

1. S. d.

364 15 5

make one pound,) Mult. by 20 shil. in 17. and add 15s.

makes 7280,

to

which, adding 15s.

7295 shill. in 364/. 15s.

the sum is 7295 Mult. by 12 peuce in 1s. and add 5d.

shillings; which

shillings, being

multiplied by 12

(the pence contain

87545 pence in 364/, 15s, 5d.

ed in a shilling) produce 87540 pence, to which add the 5 odd pence, the sum is 87545 pence.

Note. The practical method of reducing the pounds is thus say O is nothing, but 5 is 5, (the units of the shillings,) then say twice 4 is 8, and I (the ten shillings in 15) is 9, &c.

III.

To bring a number of a lesser denomination to a greater,

Rule.

Divide the given number by that which one of the greater contains of the less; the quotient is the answer.

Application.

So 540 shillings may be reduced

210)5410 to 271 For if I divide 540 by 20, (the shillings in 1 pound) the quotient will be 27.

Answ. 271.

Note.

Note. If after division any thing remains, the remainder is of the same name or denomination with the dividend. For it is the remaining part of the dividend after the divi sor is taken away as often as possible.

Examples.

In 87545 pence how many pounds?

· 12) 87545

First, I divide 87545 pence by 12, (because 12 pence) make a shilling) and thereby get the quotient 7295 shillings and there rcmain 5 odd pence over i. Again dividz ing 7295 shillings by 23, the quoti ent is 3647, and 15 remain, viz. 15 odd shillings: So 87545 pence are reduced to 364l. 15s. 5d.

210) 7205 5d, rem,

3647. 15s, 5d.

Note. The bringing a greater name to a lesser is called Reduction descending, and bringing a less to a greater Reduction ascending..

Reduction descending and ascending mutually prove each other, as may appear by comparing the preceding operations.

Questions concerning Reduction.

2. What is Reduction?

A. The bringing a greater denomination to a lesser, called Reduction descending; or a less to a greater, called Reduction ascending.

2. How is Reduction performed?

4. The greater to the less is brought, when I have multiplied,

But to the greater to reduce the less, I must divide. 2. If there is a remainder after I divide?

A. The remainder is of the same name with the divi deud.

2. How is Reduction proved?

4. Reduction descending, and Reduction ascending, prove each other..

1. Money.