How

5. How many quarts of chesnuts, at 8 cents a quart, can John buy for 10 quarts of walnuts at 6 cents a quart? many times 8, in 6 times 10?

6. A stationer sold 9 dozen books, at 5 dollars a dozen, and took his pay in paper at 6 dollars a ream; how many reams of paper did he receive? How many times 6, in 5 times 9 ?

7. A man sold 40 acres of land at 10 dollars an acre, and took his pay in horses at 50 dollars a head; how many horses paid for the land? How many times 50, are in 10 times 40?

8. Mr. B. gave to his sons, Charles and John, 30 cents, in such a way, that Charles had twice as many as John; how many cents had each ?

9. How can you divide 48 cents between 2 boys, so that 1 of them shall have 3 times as many as the other?

10. How many times 8, in 9 times 6; how many over? 11. How many times 7, in 5 times 12; how many over? 12. How many times 6, in 8 times 7; how many over? 13. How many times 12, in 11 times 11; how many over?

MISCELLANEOUS EXAMPLES FOR MENTAL EXERCISE.

1. If I sell 2 yards of cloth at 5-eighths of a dollar a yard, how much do I get for the cloth? How much is 10-eighths of a dollar? 12-eighths? 14-eighths? 16-eighths?

2. John found 72 chesnuts, and gave his brother 1-eighth of them; how many did he give him?

3. Charles found a certain number of walnuts, and gave 9 of them to his sister, which was 1-ninth of the whole; how many nuts did he find? Of what number is 9 the 1-ninth?

4. Of what number is 9 the 1-eighth? the 1-seventh? the 1-sixth the 1-fifth? the 1-fourth? the 1-third?

5. If 1-third of a ship be worth $3000, what will 2-thirds be worth? What will the whole be worth?

6. A man sold 5-ninths of a ship; how much of it did he still own? How many 9ths make the whole ?

7. A man bought 2-8ths of a house, and afterwards bought ths more; how many more 8ths must he buy to get the whole ? 8. What will 5 yards of cloth cost at 3-8ths of a dollar the yard? At 4-8ths the yard? at 5-8ths? at 6-8ths?

9. When corn is 6-8ths of a dollar a bushel, what will 6 bushels cost? What 7? what 8? what will 10?

10. How many barrels of flour, at 6 dollars a barrel, must I give for 12 yards of cloth, at 5 dollars the yard?

11. What number will be equal to 6-7ths of 84?

12. If 3-4ths of a chest of tea be worth 24 dollars, what will the whole be worth? What will 2 chests be worth?

13. What number is that, of which 7 is the 8th part?

14. If 2-5ths of a bushel of corn cost 20 cents, what will 2 bushels cost? How many are 8-5ths of 50?

15. If I buy 3-7ths and 4-7ths jo a vessel, how much of it do I own? How many are 6-7ths of 63 ?

16. What will 9 yards of cloth cost at 3-4ths of a dollar the yard?

17. When wheat is 9 shillings a bushel, what will 1 peck be worth? 2 pecks? 3 pecks? What will 2 bushels?

18. What number, divided by 8, will produce 9 for a quotient? What will produce 12 as a quotient?

19. What number, multiplied by 8, will produce 96? 20. What number, added to 19, will make 30?

21. What number, taken from 36, will leave 24 ?

22. If I sell 8 barrels of flour for 48 dollars, and thereby lose 8 dollars, what did it cost a barrel?

23. If you buy 7 yards of cloth for 35 dollars, and wish to make 8 dollars by selling it, for what must you sell it a yard? 24. What number, added to 6, and the sum multiplied by 9, will produce 108 ?

25. What number, added to 29, and the sum divided by 9, will produce 5 for a quotient?

26. When wheat is 6-eighths of a dollar the bushel, what will 1 peck cost? What will 2 pecks? 3 pecks?

27. John lost 1-fifth of his marbles, and then had 32 left; how many did he lose, and how many had he at first?

28. A market-man sold a box of butter for 12 cents a pound, 1-fourth of which amounted to 1 dollar; how much butter was in the box?

29. A man set out on a journey, and travelled the first day 25 miles, which was 1-6th of the whole distance; how many days will he be performing the journey, and how many miles in all?

30. What number divided by 8, will produce 1-8th? 3-8ths? 6.8ths? 1-half? 3-fourths?

31. What number, multipled by 6, will produce 1? Will 'produce 2? 3? 4? 5? 6?

33. If I buy 7 barrels of flour at 6 dollars a barrel, and wish to keep one for myself, and sell the other 6 for enough to pay for the whole, what must I get a barrel for it ?

SHORT DIVISION.

Q. What is meant by Short Division?

A. It is when the divisor is not more than 12.

Q. What is the RULE for short division?

A. Find how many times the divisor is contained in the first figure or figures of the dividend; place the result underneath, and if any thing remain, call it so many tens; that is, if 1 be over, call it 10; if 2 be over, call it 20; if 3, 30, &c. and add it to the next figure of the dividend; then divide this sum as before, and thus continue until you have divided all the figures of the dividend.

Q. How do you prove short division ?

A. Multiply the quotient by the divisor, and add in the remainder, and if the product be equal to the dividend, the work is right.

EXAMPLES FOR EXERCISE ON THE SLATE.

(1)

Divisor 2)24

(2) Divisor 3)36

(5)

(6)

Divisor 8)170 Divisor 8)297 Divisor 11)240 Divisor 12)269

9. If 36 chesnuts be divided among 3 boys, how many does each boy have?

10. Three boys earned 45 cents; how many cents had each boy?

11. Four men received 140 dollars for doing a job of work; how many dollars did each man receive?

12. If 4 yards of cloth will make a suit of clothes, how many suits will 136 yards make?

13. If a man travels 225 miles in 5 days, how many miles does he travel in each day?

14. If one man can build a house in 365 days, how long will 5 men be in doing the same?

15. Henry found 225 chesnuts, Samuel found 134, and James found 175. They divided them equally among themselves, and their three little sisters; how many had each?

16. James sold 14 watermelons at 6 cents apiece, John sold 28 pears at 3 cents apiece, and Joseph sold 36 peaches at 2 cents apiece; out of all the money, they bought 4 lbs. of coffee at 15 cents a pound, and divided what was left equally between them; how many cents had each boy?

17. A company of 9 men purchased three tickets in a lottery; one ticket drew 1758 dollars, another 730 dollars, and the last came up a prize of 500 dollars; what was each man's share?

18. How many 8 gallon kegs, can be filled from 4 casks of wine, each cask containing 64 gallons?

19. Six men went on a gunning expedition; during three days they shot 67 plover, 36 snipe, 103 quails, and 76 partridges; after dividing the spoil, what was each man's part?

20. A boy was rolling a hand-cart with 36 bundles of starch in it, and the wheel coming off, prevented him from going any farther; 6 of his playmates coming along offered to carry the bundles for him; how many bundles did each of his friends carry?

21. Seven boys at school read 3 pages to the master, each page contained 42 lines; how many lines was each boy's share?

12. If 9 barrels of pork cost 153 dollars, how much is that a barrel ?

13. A field of 6 acres yielded 270 bushels of corn; how many bushels was that to the acre?

14. If a button maker can make 150 gilt buttons in a day, how many dozen can he make in 30 days?

15. If I sell 8 barrels of beef for 80 dollars, and thereby gain 16 dollars, can you tell me how much it cost a barrel? 16. If a pigeon can fly across the Atlantic, a distance of 3000 miles, in 8 days; how far must it fly each day?

17. If I give 64 dollars for 8 barrels of flour, how must I sell it a barrel, in order to gain 16 dollars by the sale?

18. A man dying left an estate worth 250000 dollars, but his debts amounted to $75000, to be paid out of it; the remainder was equally divided among his 6 children; how much was each child's share? Ans. 291664 dolls.

LONG DIVISION.

Q. What is Long Division?

A. It is when the divisor is more than 12.
Q. What is the RULE for long division?

A. First see how many of the left hand figures of the dividend are necessary to make a number as large, or larger, than the divisor, then see how many times the divisor is contained in these figures; place the result at the right hand of the dividend for the first quotient figure, multiply the divisor by this quotient figure, and place the product under those figures of the dividend which you use, then subtract it therefrom, and to the right hand of the remainder bring down the next figure of the dividend; thus continue to seek, multiply, subtract and bring down, until you have used all the figures of the dividend.

Q. If, when you have multiplied your divisor by the quotient figure, the product be larger than that part of the dividend used, what must you do?

A. My quotient figure is too large: I must therefore rub out the last process, and place a smaller figure in the quotient. Q. If, on subtracting the product from that part of the dividend used, your remainder be larger than the divisor, what must you do?

A. My quotient figure is too small. I must therefore rub out the last process, and place a larger figure in the quotient. Q. After bringing down a figure to the remainder, if the new dividend be too small to contain the divisor, what must you do? A. Place a cipher in the quotient, bring down another figure, and proceed as before.

Q. How do you prove long division?

A. Multiply the quotient by the divisor, and if there be any remainder, add it in; should the product be equal to the divi⚫dend, the work has been performed right; or divide the dividend by your quotient, and if the last quotient be equal to your first divisor, the sum is correct.