8. How many pints are in 1 tun of wine?

Ans. 2016 pts.

9. How many hours in 33 years, 2 months 12 days; allowing 13 months to a year?

Ans. 289920 h.

10. In 29 yards, 2 quarters, 3 nails, how many Ans. 475 na.

nails?

REDUCTION ASCENDING.

DEFINITION. Reduction is called ascending when it is required to reduce a smaller, to a larger denomination; and it is then performed by division.

Rule. Divide the given denomination by such a number as will make one of the next higher; and the last quotient by such a number as will make one of the next, &c. until you have reduced it to the denomination required.

Examples.

1. Reduce 444165 mills into dollars. 10)444165

10)44416 cts. 5 m.

10)4441 dimes 6 cts.

Ans. 444 dol. 16 cts. 5 m.

2. In 57935 mills, how many dollars, &c. ?

Ans. $57. 93 cts. 5 m.

3. In 524 lb. Avoirdupois, how many cwt. &c. ** Ans. 4 cwt. 2 qrs. 20 lb.

ure ?

4. In 3229 rods, how many acres, square measAns. 20 acres, 29 rods. 5. In 1140480 inches, how many miles, long measure? Ans. 18 miles. 6. In 1585267200 inches how many degrees, each containing 69 miles? Ans. 360 deg. 7. How many cords of wood are in 2560 solid feet? Ans 20 cords.

8. In 2016 pints of wine, how many tuns.

.

Ans. 1 tun.

9. In 289920 hours, how many years; allow

ing 13 months to a year?

Ans. 33 years, 2 mo. 12 d.

10. In 475 nails, how many yards?

Ans. 29 yds. 2 qr. 3 na.

COMPOUND DIVISION. DEFINITION.-Compound Division teaches, by having the price of several things given, to find the price of one.

CASE I.

When the quantity is an even number:

RULE. Divide the price by the quantity, (if there are decimals in the price, point them off according to the rule of division of decimals) the quotient will be the price of one, in dollars and parts.

Examples.

1. If 24 bushels of rye cost $21, how much is 1 bushel of it worth?

2. If 340 bushels of rye cost $456.25 cts. I demand the price of 1 bushel?

Ans. $1. 341310. 3. If 2020 lb., of cheese cost $181.80 cts. what did Ans. 80:09 cts.

it cost per pound?

CASE II.

To find the firice per cwt when there are parts in the quantity, such as cut. gr. &c.

RULE. Reduce the smaller denominations to the decimal of an cwt. (by case 2d in reduction of decimals)

then divide the price by the quantity, as in case Ist; the quotient, pointed according to the rule of decimals, will be the answer,

Examples.

1. If 2 cwt. 3 qr. of sugar cost $45.26 cts. I demand the price of 1 cwt.

Crut. gr. crt. D. cts.

23=2·75)45·26($16.458,5 Ans:

NOTE. In this question 3 qr. reduced to the decimal of a cwt. is equal to 75, which I annexed to the 2 cwt. for a divisor; and divided $45.26 cts. by It, and got 16. dols. in the quotient; I then annexed three cyphers to the remainder, and continued the division, and thereby got the remaining part of the quotient, viz. 458

50

2. If 15 cwt. 2 qr. of rice were sold for $54.25 cts. ; I demand the price of 1 cwt. Ans. $3.5 dimes. 3. If 3 cwt. 2 qr. 14 lb. of iron cost $16.67·5; I demand the price per cwt.

Ans. 84.6 dimes.

CASE III.

When Cwt. qrs. and lb. are given to find the price per lb.

RULE. Find the price per cwt. by case 2d; then divide the price per cwt, by 112, the quotient will be the price per lb.

Examples.

1. If 3 cwt. 2 qr. 14 lb. of iron cost $16.67 cts. 5 m. I demand the price per pound.

Cut. gr. lb.

c. m.

3 2 14 3.625)16.675(46÷112041. Ans.

Crot D. c. m. D. d.

14500

21750

21750

2. If 20 cwt. 3 qrs. 14 lb. of iron, cost $43.50 cts.

what did it cost per lh, ?

Ans. 03 cts. 51 m.

CASE IV.

To divide by fractional parts.

RULE. To divide by fractional parts, is the same as multiplying by them; (see case 5th, compound multiplication.)

Examples.

1. What is the value of of an house, which is worth $3000 ? 3000×3 9000÷4 $2250. Ans.

CASE V.

When the number of shares are unequal. RULE. Divide the sum by the number of simple shares, the quotient will be the share of the first, which multiply by so many as the second has more than the first, and thus continue till you have found all the shares. PROOF. Add all the shares together, and if the sum is equal to the sum divided, the work is right.

Examples.

1. Divide $373.50 cts. among, A. B. and C. in such a manner, that B. may have twice as much as A. and C. twice as much as B.

7 number of simple shares. $373.50 7853.355, A's. A's, $53.35 × 2 106 70 10, B's. B's, $106.70 x 2213.4020, C's.

PROOF. $373.50 cts.

and

2. Divide $1089.33 cents among 4 persons, give the second, three times as much as the first; the third, four times as much as the second, and the fourth 5 times as much as the third.

Ans. A's $14.33+; B's $42.99; C's $171.96† ; and D's $859.80 cts. ; twenty five cts. being lost in fractions.

CASE VI.

When the shares are not equal, but increase by a certain ratio, as 1, 2, 3, 4, 5, &c.

RULE.-Divide the sum by the number of persons, the quotient is a mean, or middle share; from the middle share subtract the ratio, the remainder is the next share that is less; from the last found share subtract the ratio until you have found all the shares that are less; to the middle share add the ratio, the sum is the next share that is larger; to the last found share add the ratio till you have found all the shares that are larger.

Examples.

1. Divide $600 among 5 persons, and as often as A. has 2, give B. 4, C. 6, D. 8, and E. 10 dolls.

2. Divide $640 among

persons in such a manner, that the second shall have one more than the first, the third one more than the second, &c.

Ans. A's share, 888-429; B's $89.429,; C's$90.429 ; D's, $91.42; E's,$92-429; F's, $93.42; G's$94.429. Divide $1600 among four persons, in such a manner, that as often as the first has one, give the second 2, the third 3, the fourth 4 dolls.

1600.00 4400.00 the middle share.

400.00 + 50 cts. half ratio=400-50 C's share.

400:50 + 100 cts. ratio

401.50 D's share.

$1600.00

Proof.