1. How much cloth at 7 cts. a yard, will $1.75 buy? ANAL-AS 1 yarä costs 7 cts., there will be as many yards as 7 cts. are contained times in 175 cts. 175÷7=25.

Here, the divisor and dividend are the same denomination, cents; and the quotient, how many yards, is an abstract number.

2. Divide 65 dollars equally among 8 persons.

SOLUTION. In this case it is required to divide $65 into 8 equal parts, that is, to find one-eighth of it. One-eighth of $65 is $8, with a remainder $1100 cts. One-eighth of 100 cts. is 12 cts., with a remainder of 4 cts. which equals

Mills.

8)65000

8125

$8.12 5

OPERATION.

$ cts. m. 8)65.00 0

8.12 5

40 mills. One-eighth of 40 mills is 5 mills; hence, one-eighth of $65 is $8.12 5

The operation may be performed by reducing the dollars to mills, then dividing by 8, and after this, reducing the quotient to dollars.

3. A farmer received $29.61 cents, for 23 bhels of wheat: how much was that per bushel?

a mill of being exact, which is

9 Rem

sufficiently accurate for business purposes.

The signis annexed to denote a remainder.

Rule for Division.-1. To find how many times one sum of money is contained in another, reduce both sums to the same denomination, and divide as in Simple Numbers

2. To divide a sum of money into any number of equal parts, reduce the sum to mills; divide as in Simple Numbers; the quotient will be mills, which reduce to dollars.

PROOF-As in Division of Simple Numbers.

4. How many yards of calico, at 8 cents a yard, can be bought for $2.80? Ans. 35 yards. 5. How many yards of ribbon, at 25 cents a yard, can be purchased for $3? Ans. 12 yards. 6. At $8.05 a barrel, how many barrels of flour will $161 purchase? Ans. 20 barrels. 7. At 7 cents 5 mills each, how many oranges can be bought for $1.20 ?

8. At $1.12 5 per bushel, how can be purchased for $234?

an acre?

Ans. 16 oranges.

many bushels of wheat Ans. 208 bush.

9. If 4 acres of land cost $92.25, how much is that Ans. $23.06 2+ 10. Make an equal division of $57 and 50 cents among 8 persons. Ans. $7.18 7+ 11. A man received $25 and 76 cts. for 16 days' work: how much was that a day?

Ans. $1.61 12. I bought 755 bushels of apples for $328, 42 cts., 5 mills what did they cost a bushel? Ans. $0.43 5 13. My salary is $800 a year: how much is that a day, 313 working days in the year? Ans. $2.55 5+ equally among 133 Ans. $75.18 7+ of 154 acres, for two

14. Divide ten thousand dollars men what is each man's share?

15. A man purchased a farm thousand seven hundred and five dollars and one cent:

what did it cost per acre?

16. I sold 15 kegs of butter, of 25

$60 how much was that a pound?

:

Ans. $17.56 5

pounds each, for Ans. 16 cts.

17. I bought 8 barrels of sugar, of 235 pounds each, for $122.20: what did 1 pound cost?

REVIEW.-75. What is the object of division?

Ans. $0.06 5

How is the number

-f times one sum of money is contained in another found, Rule 1? How sum of money divided into equal parts, Rule 2?

ART. 76.-PROMISCUOUS

EXAMPLES.

1. I owe A $47.50; B $38.45; C $15.47; D $19.43 what sum do I owe? Ans. $120.85 2. A owes $35.25; B $23.75; C as much as A and B, and $1 more: what is the amount? Ans. $119.

3. A paid me $18.38; B $81.62; C, twice as much as A and B: how much did I receive? Ans. $300. 4. I went to market with $5; I spent for butter 75 cts., 35 cts., for vegetables 50 cts., for flour $1.50: how much money was left?

for

eggs

Ans. $1.90 5. A lady had $20; she bought a dress for $8.10, shoes for $1.65, eight yards of calico at 75 cts. a yard, and a shawl for $4 what sum was left? Ans. 25 cts. 6. I get $50 a month, and spend $30.50 of it: how much will I have left in 6 months? Ans. $117. 7. A farmer sold his marketing for $21.75 he paid for sugar $3.85, for tea $1.25, for coffee $2.50, for spices $1.50: how much had he left? Ans. $12.65

:

8. I owe A $37.06, B $200.85, C $400, D $236.75, and E $124.34; my property is worth $889.25, how much do I owe more than I am worth? Ans. $109.75

9. Bought 143 pounds of coffee at 13 cts. a pound: after paying $12.60, what was due? Ans. $5.99 10. A owed me $400: he paid me 435 bushels of corn, at 45 cts. a bushel: what sum is due? Ans. $204.25

11. If B spend 65 cts. a day, how much will he save n 365 days, his income being $400 ? Ans. $162.75

12. Bought 21 barrels of apples, of 3 bushels each, t. 35 ets. a bushel: what did they cost? Ans, $22.05 13. What cost four pieces of calico, each containing 19 tards, at 23 cts. a yard? Ans. $17.48

14. If 25 men perform a piece of work, for $2000, and pend, while doing it, $163.75, what will be each man's share of the profits? Ans. $73.45

15. If 16 men receive $515 for 43 days' work, how much does each man earn a day?

Ans. 75 cts.

16. C earned $90 in 40 days, working 10 hours a day: how much did he earn an hour? Ans. 22 cts. 5 m,

3d Bk.

6

17. A merchant, failing, has goods worth $1000, and $500 in cash, to be equally divided among 22 creditors: how much will each receive? Ans. $68.18+

MERCHANTS' BILLS.

A Bill or Account, is a written statement of articles bought or sold, their prices, and entire cost.

18. Bought 9 pounds Coffee, at $0.16 per lb.

4 pounds Tea,
45 pounds Sugar,
17 pounds Cheese,

What is the amount of my bill?

19. Bought 8 yards Silk,

18 yards Muslin,

1.25 do.

25 yards Linen,

12 yards Calico,

6 yards Gingham,..

What is the whole amount?

20.

MR. WILLIAM RAY,

5 Eclectic Third Readers,

12 dozen Olney,

6000 Quills,

5 Quires Paper,

3 Copies of Hutton,

Rec'd Payment,

21.

MR. JOHN JONES,

27 Spelling Books,

25 Eclectic Readers,

Cincinnati, Feb. 20th, 1860.

Bought of W. B. SMITH & Co. at $0.35 each.

8 Ainsworth's Dictionaries,

27 Greek Readers,

18 Bibles,

75 Testaments,

Rec'd Payment,

For Fractional Exercises in U. S. Money, see page 169.

REDUCTION OF COMPOUND NUMBERS.

ART. 77. Reduction is the process of changing the denomination of a number, without altering its value.

Ex-Since 3 feet make 1 yard, yards may be changed to feet by multiplying by 3; and, feet to yards, by dividing by 3: 5 yards=5X3=15 feet: and 15 feet 15÷÷3-5 yards. Hence, as shown in United States money,

Reduction Descending consists in changing a number from a higher to a lower denomination: Reduction Ascending, in changing a number from a lower to a higher denomination.

REM.-The Tables teach the names of the different units, and the number of units of one order or denomination which make a unit of the next higher order: they are analogous to the Table of Orders in Simple Numbers.

ART. 78. DRY MEASURE

Is used in measuring grain, vegetables, fruit, coal, &c.

The standard unit of dry measure is the Bushel; a circular measure

of 18 inches diameter, 8 inches deep, and contains 2150

cubic inches.

Those who resort to TABLES OF UNIT VALUES, to avoid each

successive step of an operation, lose a valuable exercise.

NOTES.-1. There are two other denominations of Dry Measure, the quarter and chaldron. The quarter contains 8 bushels, of 70 pounds each, used in England in selling wheat.

The chaldron, in England, and in some of the U. S., contains 36 bu.; in other States 32 bu., and is used for measuring coal.

2. When Grain and Seeds are bought and sold by weight, 60 pounds of Wheat, 60 of Clover seed, 56 of Rye, Corn, or Flax seed, 32 of Oats, 42 of Timothy seed, and 48 of Barley, make 1 bushel.

For information in detail in regard to foreign and domestic weights and measures, see "Ray's Higher Arithmetic."

REVIEW.-77. What is Reduction? Give an example. In what does reduction descending consist? In what does reduction ascending consist? REM. What do the Tables teach?