38. A note drawn June 20th, 1846; how long will it have existed April 10th, 1848? Ans. 1 y. 9 m. 21 d. 39. The United States were declared to be free and independent July 4th, 1776; how long to Jan. 1st, 1849?

Ans. 72 y. 5 m. 28 d. 40. Columbus discovered the island of St. Salvador on the 11th of Oct., 1492; how long to the 4th of July, 1848 ?

Ans. 355 y. 8 m. 23 d.

41. Find the difference of time between Jan. 10th, 1840, and March 4th, 1848. Ans. 8 y. 1 m. 23 d. 42. Find the difference of time between June 16th, 1842, and Oct. 12th, 1848. Ans. 6 y. 3 m. 26 d. 43. Find the difference of time between July 20th, 1843, and Nov. 6th, 1848. Ans. 5 y. 3 m. 17 d. 44. The art of printing was discovered a. D. 1440; how long to July 4th, 1848 ? Ans. 408 y. 7 m. 4 d.

45. Henry was born Feb. 20th, 1838; how old was Henry March 8th, 1849 ? Ans. 11 y. and 16 d. 46. George Washington was born on the 22d of Feb., 1732; he departed this life on the 14th of Dec., 1799: how old was he when he died? Ans. 67 y. 9 m. 22 d.

COMPOUND MULTIPLICATION.

COMPOUND MULTIPLICATION is a short method of finding the amount of any compound quantity, taken a given number of times.

I. To multiply by a number that does not exceed 12. RULE 1.-Set down the given sum or quantity, with the multiplier under the lowest denomination.

2.-Multiply the lowest denomination by the multiplier, and divide the product by as many as will make one of the next higher; set down the remainder, and add the quotient to the next product, (as in Addition,) and so on through all the denominations.

3. The largest denomination is done like Simple Multiplication.

What is Compound Multiplication? What is the rule for working Compound Multiplication-1st? 2d? 3d?

PROOF.-Multiply by a number one short of the real number, and to the product add once the given quantity.

2. Multiply £4 16s. 31d. by 2; by 3; by 4; by 5.

3. Multiply £16 14s. 41d. by 6; by 7; by 8; by 9; by 10; by 11; by 12.

4. Multiply 4 lbs. and 6 oz. Troy wt., by 2; by 3; by 4; by 5; by 12.

Ans. 9 lbs.; 13 lbs. 6 oz.; 18 lbs. ; 22 lbs. 6 oz.; 54 lbs.

5. Multiply 6 lbs. 4 oz. 10 dwts. and 16 grs. by 6; by 7; by 8. 38 lbs. 3 oz. 4 dwts.; 44 lbs. 7 oz. 14 dwts. 16 grs.;

Ans. 51 lbs. 5 dwts. 8 grs.

6. Multiply 6b 23 43 by 6; by 9; by 12.

Ans. 37b 33; 55lb 103 43; 74lb 63.

7. Multiply 12 cwt. 2 qrs. 14 lbs. 10 oz. by 5; by 9.

Ans. 63 cwt. 17 lbs. 2 oz ; 113 cwt. 2 qrs. 19 lbs. 10 oz. 8. Multiply 22 yds. 1 qr. and 2 na. by 4; by 5; by 6; by 7, by 8; by 9; by 10; by 11; by 12, and prove your work.

9. Multiply 12 ells Eng. 2 qrs. and 3 na. by 5; by 7; by 10. 10. Multiply 6 ells Fr. 3 qrs. by 4; by 5; by 10; by 11; by 12.

11. Multiply 12 mi. 4 fur. and 15 po. by 6; by 7; by 9; by 10.

12. Multiply 12 acres 1 rood and 24 po. by 2; by 3; by 4; by 5.

13. Multiply 6 sq. yds. 5 ft. and 24 in. by 6; by 9; by 12 Ans. 39 yds. 4 ft.; 59 yds. 1 ft. 72 in.; 78 yds. 8 ft. 14. Multiply 12 tons 10 ft. (round timber) by 5; by 7; by 9.

15. Multiply 16 cords and 30 ft. by 4; by 5; by 6; by 12. S 64 cd. 120 ft.; 81cd. 22 ft.; 97cd. 52 ft.;

Ans.

{

194 cd. 104 ft.

16. Multiply 24 gal. 2 qts. 2 gills by 2; by 3; by 4; by 6. 17. Multiply 26 bush. 3 pks. and 5 qts. by 7; by 11; by 12. 18. Multiply 4 y. 4 m. 3 w. and 3 d. by 6; by 9; by 10. 19. Bought 10 cords of wood at £2 6s. 8d. per cord; how much for the whole ? Ans. £23 6s. 8d. 20. Bought 12 yards of cloth at £1 3s. 6d. per yd.; how much for the whole ? Ans. £14 2s. 6d.

II. When the multiplier is a composite number, and neither of the factors exceeds 12.

RULE.-Multiply the given sum or quantity by one of the factors, and the product thence arising by the other factor.

PROOF.-Reverse the factors, take others, or apply the rule for proof, Case I.

22. Multiply £5 6s. and 21d. by 18; by 24; by 42; by 56. 23. How many gallons in 48 barrels? in 72? in 81 ? 24. Bought 96 bushels of wheat at 8s. and 61d. per bushel; how much for the whole ? Ans. £41.

25. Bought 132 tons of coal at £2 2s. 4d. per ton; how much for the whole ? Ans. £279 8s.

How do you multiply by a composite number? How do you prove the work?

II. When the multiplier exceeds 12, and is not a composite number as before.

RULE 1.-Take two numbers whose product comes the nearest to the given multiplier, and work as in the last

case.

2. To the result add as many times the given quantity as is required to make up the deficiency.

PROOF.-Reverse the factors or take others.

27. Multiply £4 12s and 41d by 23; by 29; by 37.

28. Multiply 2 y. 4 m. 2 w. and 3 d. by 37; by 46.

29. How many yards in 57 pieces of muslin, allowing each piece to contain 24 yds. 2 qrs. and 2 na. ?

Ans. 1403 yds. 2 qrs. 2 na. 30. Find the value of 46 barrels of pork at £4 4s. 6d. per barrel. Ans. £194 7s.

IV. To multiply compound quantities by large multipliers. RULE 1.-Multiply the given sum or quantity by 10, and the product thence arising by 10; and if there are thousands in the multiplier, multiply by 10 again.

2. Then multiply the given sum or quantity by the units, the first product by the number of tens, the second product by the number of hundreds, etc. Add all together for the total product. (See Example 31.)

PROOF.-Multiply the multiplier by each denomination.

What is the rule for working when the multiplier exceeds 12, and is not a composite number? How do you prove the work?

How do you multiply compound quantities by large numbers-1st? 2d1 How do you prove the work?

32. Multiply £2 2s. 4d. by 174; by 186; by 2392.

Ans. £368 6s.; £393 14s.; £5063 1s. 4d.

33. Multiply 1 cwt. 1 qr. 14 lbs. by 163; by 284.

Ans. 224 cwt. 14 lbs.; 390 cwt. 2 qrs. 34. Find the value of 2344 yds. of cloth, at £1 2s. 2d. per yard. Ans. £2598 9s. 9d. 35. A man wishes to put up 462 barrels of corn, each barrel to contain 2 bush. 3 pks. 2 qts.;

will he require?

how many bushels of corn Ans. 1299 bush. 1 pk. 4 qts.

COMPOUND DIVISION.

COMPOUND DIVISION is the method of dividing sums or quantities consisting of several denominations.

I. To divide by a number that does not exceed 12. RULE 1.-Set down the sum or quantity to be divided, with the divisor on the left: draw a line under.

2. Divide the largest denomination by the divisor, placing the quotient under it.

3.-If you have a remainder, reduce it to the next lower denomination: add the next lower denomination to it divide this amount by the divisor: set the quotient under, and so on through all the denominations.

PROOF. By multiplication. (See Ex. 1.)

What is Compound Division? What is the rule for working-1st? 2d? 3d? Proof?