inator of the fraction, and add in the numerator for a new div. idend; then multiply the divisor by the same denominator, for a new divisor, divide, and the quotient will be the answer, and the remainder, if any, will be a numerator as before.

Q. How do you divide by a simple fraction, only, as 1, 3, §, , &c.

A. Multiply the dividend by the denominator of the fraction, and divide the product by the numerator, and the quotient will be the answer.

5. What is the quotient of 273 divided by 34?

Ans. 84.

can be filled Ans. 142 bags.

6. What is the quotient of 1273 divided by 63? Ans. 201. 7. How many bags containing 3 bushels each from a bin of corn containing 497 bushels? 8. How many barrels of cider, each holding 31 gallons, can be filled from a cistern containing 567 gallons? Ans. 18. 9. A man purchased a section of land containing 25000 acres, and laid it out in squares of 25 acres each; how many squares were there? Ans. 980

10. How many boxes are required to hold 400 lbs. of raisins, if each box contain 21 lbs? Ans. 1844, or 4.

PROMISCUOUS AND PRACTICAL QUESTIONS.

1. What must I give for 46 yards of broadcloth at 3 dollars a yard? Ans. 161 dollars. 2. What will 136 barrels of flour amount to at 84 dollars a barrel? Ans. 1122 dollars. land at 143 dollars per

3. A farmer bought 237 acres of acre; what was the whole cost?

4. What must be given for 126 dollars per yard?

Ans. 3495 dollar yards of broadclo Ans. 1138 d

5. A merchant bought 6 bales of cloth, each bale containing 14 pieces, and each piece 364 yards; how many yards in all? Ans. 3153 yards.

6. If a ship and cargo be worth 25000 dollars, what is that man's share who owns of her? Ans. 15625 dollars.

7. How many barrels, each containing 31 gallons, can be filled from 5 casks of cider, each cask holding 1284 gallons? Ans. 20 bbls. and 12 gallons.

8. If 5 yards make a rod, how many rods are there in 4575 yards? Ans. 831 rods, 4 yards. 9. How many pounds of butter in 45 kegs, each keg containing 34 pounds? Ans. 1552 lbs. 10. How many barrels containing 24 bushels each, can be filled from an apple-heap containing 154 bushels?

Ans. 56 barrels.

11. What must I give for 16 cwt. of cheese, at 7 dollars the cwt? Ans. 115 dollars. 12. How many dollars will buy a farm containing 246 acres, at 15 dollars an acre? Ans. 37014 dollars. 13. If I give of a dollar for 1 yard of ribbon, how much must I give for 12 pieces, each containing 27 yards? Ans. 123 or dollars.

14. A merchant bought 4 parcels of coffee; the first contained 9 bags, each weighing 944 lbs.; the second contained 11 bags, weighing 1044 lbs. each; the third, 12 bags, weighing 75 lbs. each; and the fourth, 8 bags, weighing 874 lbs. each; how many pounds in all ? Ans. 3602 lbs. 15. If a horse can trot 15 miles in an hour, how far will he go in 24 hours? Ans. 385 miles. 16. A person has 3 barrels of cider, each containing 32 gallons; if he wishes to put it into kegs containing only 3 gallons each, how many kegs must he get?

Ans. 27 or 27 kegs, 3 gallons. 17. If 365 days make one year, how many days from the birth of Christ, to Christmas 1830 ? Ans. 668407.

FEDERAL MONEY.

Q. What is understood by the term, Federal Money?
A. It is the coin and money of account of the United States.
Q. What are the denominations of this coin?

A. Eagles, dollars, dimes, cents and mills.

In what proportion do these denominations increase from r to the higher?

a tenfold proportion, like simple numbers.

Q. What do you mean by saying they increase in a tenfold proportion?

A. I mean that 10 mills make 1 cent, marked C.

10 cents 66 1 dime,

66 d.

10 dimes 66

1 dollar,

66 E.

Q. What is the money unit, from the other denominations?

and how is it distinguished

A. The dollar is the money unit, and is separated from the smaller denominations by a point or comma, [,] called a sep. aratrix: thus, $4,65, means 4 dollars and 65 cents.

Q. How are the figures which denote the smaller denominations valued ?

A. According to the place they stand in from the dollars' place; that is, the first figure at the right hand of the separa. trix, is dimes, the second is cents, and the third is mills;

Thus,

1 2 3 dcm $25,3 7 5

123
dcm

123

dcm

$ 75,0 4 6

$ 97,0 0 6

Q. When there are more than three figures at the right hand, what value do they possess?

A. The fourth figure is 10ths of mills; the 5th, 100ths of mills, and so on.

Q. Is it necessary to separate the dimes, cents, and mills, from each other, by a separatrix ?

A. It is not. The dimes and cents may be read all cents: as, 9d. 5c. are the same as 95 cents; also, the dimes, cents, and mills, may be read all mills: as, 7d. 6c. 5m. are the same as 765 mills, or 76 cents, 5 mills.

Q. When the cents are less than ten, how must you write them?

A. I must place a cipher in the first place or place of dimes: thus, ,05 cents, or $19,09 cents?

Q. How would you write down mills, if there were neither dimes nor cents?

A. By placing two ciphers at the left hand of mills in the places of dimes and cents: thus, $4,006.

Q. What do you mean by annexing or prefixing figures? A. To annex figures is to place them at the right hand: to prefix them is to place them at the left hand.

Q. How do you bring eagles to dollars, or dollars to dimes, cents, or mills?

A. To bring eagles to dollars, annex one cipher; to bring dollars to dimes, annex one cipher; to bring dollars to cents, annex two ciphers; and to bring dollars to mills, annex thr

F

ciphers: as, 9 eagles $90. $75=750 dimes. $75=7500 cents. $75 75000 mills.

:

Q. What reason can you give for annexing ciphers in order to bring eagles to dollars, or dollars to dimes, cents, and mills? A. Every cipher annexed to eagles or dollars, or to any sum, multiplics them by 10. Now as these denominations increase in a tenfold proportion, so multiplying any one denomination by 10 will bring it to the next lower therefore, as 10 dimes make a dollar, 100 cents make a dollar, 1000 mills make a dollar, annex one cipher to dollars, or multiply them by 10, to bring them to dimes; annex two ciphers, or multiply them by 100, to bring them to cents; annex three ciphers, or multiply them by 1000, to bring them to mills.

Q. How will you bring dimes, cents, and mills, to dollars? A. As dollars are brought to dimes, cents, and mills, by multiplying by 10, 100, 1000, these smaller denominations must be divided by the same numbers to bring them back again to dollars: therefore to bring dimes to dollars, divide them by 10, or cut off one right hand figure; to bring cents to dollars, divide them by 100, or cut off two right hand figures; and to bring mills to dollars, cut off three right hand figures; then those figures at the left hand of the cut off will be dollars; and those at the right hand will be dimes, cents, and mills.

EXAMPLES FOR MENTAL EXERCISE, SERIES 1.

1. How many cents is 2. How many cents are 3. How many cents is 4. How many cents is 5. How many cents is

8 ?

6. John sold his top for

of a dollar?

of a dollar? of a dollar? of a dollar?

10

of a dollar?

Ans. 12.

10

of a dollar, and his sled for of a dollar; how many cents did he get for both?

7. What must I give for two bushels of corn, at f of a dollar per bushel?

8. James had 9 dimes in his parse, and his father gave him 8 cents more; how many cents had he then? How many cents are 9 dimes, 8 dimes, and 7 dimes, added together?

9. What is the amount of 5 dimes, 5 cents, and 5 mills, added together?

10. What is the amount of 6 dollars, 6 dimes, 6 cents, and C mills?

1. What is the amount of 7 cagles, 7 dollars, 7 dimes, 7 and 7 mills?

ow many mills in 75 cents, and 6 mills?

13. How many mills in of a dollar? In ?
14. How many cents in 750 mills? In 875 mills?

15. How many dollars in 500 eagles? In 750 eagles? 16. If I buy a horse for 6 eagles, and a cow for 20 dollars, how many dollars do I give for both? How many dollars, added to 7 eagles, will make 100 dollars?

17. John had 7 dimes in his pocket, and his father gave him cents enough to make him up a dollar; how many cents did his father give him?

18. One man paid me 5 half dollars, and another paid me 10 quarters of a dollar; how many dollars had I then?

19. What is the amount of 7 dimes and 80 cents, added together?

SECOND SERIES OF MENTAL EXAMPLES.

1. Henry went to market and bought 3 pounds of butter at 12 cents a pound, and 24 pounds of meat at 10 cents a pound, and gave the man a dollar bill to take his pay from; how much change did Henry receive back?

2. A lady bought goods in a dry goods store to the amount of 3 dollars and, and gave a 10 dollar bill to pay for them; how much did she receive back in change?

3. A man sold a horse for 7 eagles, and bought 3 cows at 20 dollars a head; how many dollars had he left?

4. Thomas sold his sled for g of a dollar, and bought a knife for 37 cents; how many cents had he left?

5. How many dollars in 10 eagles? How many dimes? How many cents? How many mills?

6. How many cents are there in 100000 mills? How many dimes? How many dollars? How many eagles? How many half eagles?

7. There are in a bag 100 silver dollars, 20 gold eagles, and 1000 ten cent pieces; how many dollars in all?

8. A man sold 2 bushels of corn at § of a dollar the bushel, and 3 bushels of oats at of a dollar a bushel; how much did the whole amount to? If he spend of the money, what will be left?

9. If 35 dollars be taken from 14 half eagles, how many dollars will be left?

10. When flour is 6 dollars a barrel, what must you give for 2 barrels ? How much for 4 barrels ?

11. A man sold 4 barrels of flour at 64 dollars a barrel, and took his pay in ninepenny pieces; how many pieces paid for the flour?

12. How many cents are equal to 180 of a dollar?