(31.) How much cloth will it require to make 52 coats, allowing to each 2 yds., 1 qr. 2 na.?

Ans. 123 yds., 2 qrs., 0 na. (32.) There are 14 piles of wood, each containing 7 C., 114 ft.; what is the whole quantity ? Ans. 110 C. 60 ft. (33.) What is the weight of 20 chests of tea, each weighing 4 cwt., 1 qr., 12 lbs.? Ans. 87 cwt., 0 qr., 16 lbs.

REVIEW.

When the multiplier exceeds twelve, what is the rule? When the multiplier consists of three or more figures, what is the rule?

COMPOUND DIVISION.

THIS rule is the reverse of Compound Multiplication: it shows how often a given quantity is contained in another of different denominations. Multiplication and Division will reciprocally prove each other; and this should be generally practised.

GENERAL RULE.

1. If the divisor does not exceed twelve, proceed as in Short Division of whole numbers.

2. Divide the first denomination on the left-hand by the divisor; multiply the remainder, if any, by the number of the second denomination contained in a unit of the first, and add the second to the product; divide as before.

3. When the divisor is a composite number, and is greater than twelve, divide by the factors successively.

4. When the divisor is a prime number greater than twelve, divide by the whole divisor as in Long Division. Proof, by Multiplication.

REVIEW.

What is Division the reverse of? What two rules will prove each other? Why will they prove each other? What should be generally practised? 1. When the divisor does not exceed twelve, what will you do? 2. How will you divide the first denomination? 3. When the divisor is a composite number, how can you divide? 4. How will you

divide when the divisor is a prime number? Proof. What is a prime number? Ans. A prime number is one which can be measured only by itself or a unit, as 3, 7, 23, &c. What is a perfect number? Ans. A perfect number is equal to the sum of all its aliquot parts.

h. yr. m. w. da.

h.

(3.) 14) 26 8 3 4 6(1 10 3 4

19+4 Ans.

12 X
14)152+8
14

12

4X 14)51+3

42

9

7X

14)67+4

Explanation.-14 in 26, once and 12 over: 12 x 12 mo.+8 mo.=152 14-10 mo. and 12 over; 12×4 w. +3=51÷14=3 w. and 9 over; 9×7 +4=67÷14=4 days and 11 over; 11 x 24 h.+6=270÷14-19 h. and 4 over. Then, to prove it, multiply the quotient by the divisor, and add in the remainder, and you produce the dividend.

56

11

24X

44

22

14)270+6

14

130

126

(4.) 9 lbs., 6 oz., 11 dwt.÷4.

Ans. 2 lbs., 4 oz., 12 dwt. +3. (5.) 11 lbs., 4 oz., 1 dr., 2 scr., 12 grs.÷5.

Ans. 2 lbs., 3 oz., 1 dr., 2 scr., 18 grs.+2.

(6.) 6 cwt. 1 qr., 11 lbs., 4 oz.÷3.

Ans. 3 cwt., 0 qr., 13 lbs., 1 oz.+1. 4.

(7.) 4 T., 6 cwt., 14 lbs. 12 oz., 8 dr.

Ans. 1 T., 1 cwt., 17 lbs., 11 oz., 2 dr.

(8.) 14 L., 2 m., 4 fur., 8 po.-5.

Ans. 2 L., 2 m., 7 fur., 9 po. +3.

(9.) 9 L., 1 m., 3 fur., 0 po., 4 yds. 6.

Ans. 1 L., 1 m., 5 fur., 33 po., 2 yds.+3. ́

(10.) 25 m., 5 fur., 25 po., 2 yds., 2 ft.-7.

Ans. 3m., 5 fur., 15 po., 0 yd., 1 ft.+ 1. ́ (11.) 5 fur., 17 po., 3 yds., 2 ft., 8 in., 2 bar.-c.-8. Ans. 27 po., 1 yd., 0 ft., 6 in., 1 bar.-c.

(12.) 27 A., 1 R., 9 po., 12 ft.÷9.

Ans. 3 A., 0 R., 5 po., 8 ft.+6.

(13.) 70 C., 94 ft., 1294 in.÷10.

(14.) 27 yds., 2 qrs., 3 na.÷11.

Ans. 7 C., 9 ft., 820 in. +6.

Ans. 2 yds., 2 qrs., 0 na.+3.

(15.) 45 hhds., 25 galls., 3 qts., 1 pt.÷12.

Ans. 3 hhds., 49 galls., 1 qt., 1 pt. +3.

(16.) 119 bush., 2 pks., 4 qts.-8.

Ans. 14 bush., 3 pks, 6 qts., 1 pt.

(17.) 25 yds., 1 qr., 3 na.÷7.

(18.) 42 yrs., 6 mo., 3 W.,

Ans. 3 yds., 2 qrs., 2 ña.+1. 8 da., 9 h.-9.

Ans. 4 yrs., 8 mo., 3 w., 0 da., 22 h.+3. (19.) 41 sig., 4°, 17, 18"8. Ans. 5 sig., 4°, 17, 9"+6., (20.) 480 cwt., 3 qrs.÷28. Ans. 17 cwt., 0 qr., 19 lbs. (21.) 50 T., 12 cwt., 3 qrs., 8 Ibs.÷45. ́

Ans. 1 T., 2 cwt., 2 qrs., 0 lb. +36.

Ans. 5 cwt., 1 qr., 20 lbs. +4.

(26.) Divide 225 bush., 2 pks., 6 qts., among 4 persons. Ans. 56 bush., 1 pk., 5 qts.+2,

(27.) Divide 576 A., 2 R., 18 po., among 7 men.

0

Ans. 82 A., 1 R., 14 po. (28.) Divide a hogshead of wine equally among 20 perAns. 3 galls., O qt., 1 pt.+4=1 gi. nearly. (29.) If it require 3 yds. to make a coat, how many coats can be made from 72 yds., of broadcloth ?

sons.

Ans. 24 coats.

(30.) What will be the share of 1 man, if 250 T., 12 cwt., 28 lbs., be equally divided among 75 men?

Ans. 3 T., 6 cwt., 3 qrs., 8 lbs.+72. (31.) What time will you require to walk 500 m., at the rate of 25 m. a-day? Ans. 20 da. (32.) If 20 loads of hay contain 42 T., 5 cwt., what is the weight of each load? Ans. 2 T., 2 cwt., 1 qr.

MISCELLANEOUS QUESTIONS IN THE COMPOUND RULES.

(1.) If a man can travel in one day 20 m., 4 fur.; another day 25 m., 3 fur., 18 po.; another day 22 m., 4 fur., 36 po., required the distance. Ans. 71 m., 1 fur., 14 po. (2.) In 3 tracts of Michigan land, the 1st contains 240 A., 2 R., 5 po.; 2d, 268 A., 3 R., 25 po.; 3d, 468 A., 2 R., 20 po.; required the number of acres in the 3 tracts.

Ans. 978 A., 0 R., 10 po. (3.) Add 2 cwt., 1 qr., 25 lbs. ; 4 cwt., 1 qr., 16 lbs.; 6 cwt., 2 qrs., 8 lbs. ; 21 cwt., 3 qrs., 20 lbs.; 15 cwt., 2 qrs., 18 lbs., together. Ans. 51 cwt., 0 qr., 3 lbs. (4.) Bought 3 casks of vinegar; the 1st contained 18 galls., 2 qts, 1 pt., 2 gi.; 2d, 21 galls., 2 qts., 0 pt., 3 gi.; 3d, 24 galls.; 3 qts., 1 pt., 2 gi.: required the quantity in the 3 casks. Ans. 65 galls., 0 qts.. 1 pt., 3 gi. (5.) Bought a piece of broadcloth containing 42 yds., 2 qrs., 3 na.; and sold 2 suits from it, each containing 5 yds., qr., 2 na.: how much have I remaining of the piece? Ans. 31 yds., 3 qrs., 3 na. (6.) If I should sell A. 6 galls., 1 qt., 1 pt.; B. 7 galls., 2 qts., 0 pt., of molasses, from a cask containing 93 galls., 2 qts., 1 pt., how much would remain ?

1

Ans. 79 galls., 3 qts., 1 pt.

(7.) From 70 bush. take 54 bush., 1 pk., 3 qts.

Ans. 15 bush., 2 pks., 5 qts.

(8.) From 8 sq. yds. take 5 ft., 96 in.

Ans. 7 yds., 3 ft., 48 in.

(9.) From 2 lbs., troy, take 8 oz., 12 dwt., 18 grs.

Ans. 1 lb., 3 oz., 7 dwt., 6 grs.

(10.) From 2 galls. take 1 qt., 1 pt., 1 gi.

Ans. 1 gall., 2 qt., 0 pt., 3 gi.

(11.) Required the weight of 4 chests of tea, each weigh

ing 2 cwt., 1 qr., 12 lbs.

Ans. 9 cwt., 1 qr., 20 lbs.

(12.) Required the weight of 5 hhds. of sugar, each weighing 5 cwt., 1 qr., 14 lbs. Ans. 26 cwt., 3 qrs., 14 lbs.

(13.) In 14 pieces of sheeting, each containing 31 yds., 2 qrs., 1 na., how many yards in all?

Ans. 441 yds., 3 qrs., 2 na.

(14.) A farmer has 5 bins of wheat, containing 47 bush., 1 pk., 4 qts., 1 pt. each; how much in all?

Ans. 236 bush., 3 pks., 6 qts., 1 pt.

(15.) From 1 yr., 6 mo. take 9 m., 2 w., 2 da.
Ans. 8 mo., 1 w.,

5 da. (16.) Bought 3 loads of cord-wood, the 1st contained 1 C., 42 ft.; 2d, 1 C., 92 ft.; 3d, 1 C., 86 ft.: how much in all? Ans. 4 C., 92 ft. (17.) From 7 galls., take 1 gall., 1 qt., 1 pt., 1 gi.

Ans. 5 galls., 2 qts., 0 pt., 3 gi.

(18.) From 4 A., 2 R., 6 po., take 36 po.

Ans. 4 A., 1 R., 10 po.

(19.) Multiply 2 yds., 2 qrs., 2 nạ., by 61.

Ans. 160 yds., 0 qr., 2 na.

(20.) 740 A., 3 R., 4 po.+672 A., 0 R., 16 po.

Ans. 1412 A., 3 R., 20 po.

COMPOUND REDUCTION.

IN Simple Reduction but one denomination is given; whereas in Compound Reduction, several denominations are given to be reduced to one denomination, still retaining the same value: as, 1 pound, 5 ounces, avoirdupois, would be 21 ounces, because in 1 pound there are 16 ounces+5 ounces 21 ounces: 21 oz. 1 lb., 5 oz.

=

=

RULE.

1. Multiply the highest denomination by as many of the next less as it requires to make one of that, and add in the