5. If you have 7 pecks of nuts, and put them in threequart bags, filling each bag, and then you give me what are over; how many bags will you need, and how many quarts will you give me.

FOR WRITTEN WORK.

6. If two persons start from the same point and travel in opposite directions, one at the rate of 17 miles a day, and the other at the rate of 25 miles a day, how long will it be before they are 504 miles apart?

7. If 3 horses cost $720; what will one horse cost, and what will 13 horses cost, at the same rate?

8. There are 24 hours in 1 day and 7 days in 1 week; how many weeks are there in 39,984 hours?

9. A farmer sold 4 pairs of oxen for $214 a pair, 13 cows for $43 each, and 2 horses for $118 each; after paying a debt of $251, he bought with the remainder 20 acres of land; what did the land cost per acre?

10. A clerk received $7,500 salary for 5 years services;

he spent $3,900 for board, $1,210 for clothing, and depos

ited the rest in the bank; how much did he spend each year for board? how much each year for clothing? how much did he deposit each year in the bank?

FOR ORAL WORK.

84. 1. If 3 quarts of berries cost 36 cts., what do 5 quarts cost?

SOLUTION.-If 3 quarts of berries cost 36 cts., 1 quart costs of 36 cts., or 12 cts., and 5 quarts cost 5 times 12 cts., or 60 cts.

2. If 4 yards of cloth cost $12, what do 9 yards cost?

3. Bought 9 barrels of flour at $6 a barrel, and paid for it in coal at $3 a ton; how many tons of coal did it take? (9 x 6) ÷ 3 = ?

4. In one gallon there are 4 quarts. If I buy a quart of molasses at 48 cts. a gallon, and pay a 25-cent piece, how much change should I receive? 25 - (48 ÷ 4).

5. How much will one-half a gallon of vinegar cost at 24 cts. a gallon? At 32 cts. a gallon?

6. How much does of an acre of land cost at $36 an acre? At $96 an acre? At $192?

7. 10 meters make one dekameter; how many dekameters in 84 meters? In 49 meters?

8. If you had $67, how much flour could you buy at $5 a barrel? How much at $7 a barrel?

9. Four pecks make 1 bushel.

If you buy a bushel of apples for 84 cts, what is the cost of half a peck?

10. 5 men bought a horse for $75, paying equal shares; if they sell the horse for $40, how much will each man lose? ($75 — $40) ÷ 5 = ?

FOR WRITTEN WORK.

11. A grocer sold 64 lbs. of sugar at 14 cents a lb., and 4 lbs. of tea at 96 cents a lb., for which he was paid in butter at 32 cents a 7b.; how many pounds of butter did he receive?

12. What number multiplied by 3 will give the same product as 27 multiplied by 7?

13. A grocer buys 7,381 lbs. of cheese, at 8 cents a pound, and pays for it in coffee at 22 cents a pound; how much coffee does he give for the cheese?

14. If flour costs $14 a barrel, how much can be bought for $1,358?

15. A merchant sold 4 pieces of cloth: The first two pieces contained 45 yds. each, the third contained 47 yds., and the fourth contained 53 yds.; for the whole he received $760; how much did he receive per yard?

16. There are $750 in 4 bags; the first contains $115, the second contains $236; the third contains $60 less than the first and second together; how much does the fourth contain ?

17. A grocer packs 789 lbs. of butter, which fills 17 tubs and 7 lbs. over; how much does he put in each tub?

18. A farmer bought a farm, for which he paid $18,050 ; he sold 50 acres for 60 dollars an acre, and the remainder at 50 dollars an acre; how much land did he buy?

19. A merchant bought a hogshead of molasses, containing 96 gallons, at 35 cents per gallon; but 26 gallons leaked out, and he sold the remainder at 50 cents per gallon; did he gain or lose, and how much?

20. Mr. Bailey has 7 calves, worth 4 dollars apiece, 9 sheep, worth 3 dollars apiece, and a fine horse, worth 375 dollars. He exchanges them for a yoke of oxen, worth 125 dollars, and a colt, worth 65 dollars, and takes the balance in hogs, at 8 dollars apiece; how many hogs does it take?

21. The distance from Chicago to San Francisco is 2,448 miles; how long will it take a man to walk the whole distance at the rate of 24 miles a day?

22. A man bought a farm for $3,612; he sold half of it at $56 an acre, and received $2,408 for the half he sold ; how many acres did he buy, and what did he give per acre?

RECAPITULATION AND

GENERAL PRINCIPLES.

NOTATION.

85. A Unit is one, or a single thing.

A Number is a unit, or a collection of units.

The Simple Value of a figure is the value it expresses when standing alone, or in the units place.

The Local Value is that which it has when standing in any particular place. Thus, the value taken of 2 in the first place is 2 units, in the second place it is 2 tens, in the third place it is 2 hundreds, and so on.

Every place in a number not occupied by a significant figure must be filled by a cipher.

A Rule is a brief direction for performing work.

A Scale is an order of progression on which any system of notation is founded.

A Uniform Scale is one in which the law of progression is the same throughout, as in the Arabic notation. A Varying Scale is one in which the law of progression is changed at every step, as in the notation of English money.

ADDITION.

86. Only similar numbers can be added together.

SUBTRACTION.

87. The Minuend and Subtrahend must have the same unit, or they must be capable of being reduced to the same unit.

The same number added to or subtracted from both minuend and subtrahend, does not change the value of the remainder.

88. The Multiplier is always as an abstract number. The Multiplicand and Products are like numbers. The multiplier and multiplicand are together called Factors of the product.

Multiplying either factor by any number, multiplies the product by the same number.

The product of a number multiplied by itself is called the Square of the number.

Multiplying both factors by the same number is equivalent to multiplying the product by the square of that number.

Multiplication may be proved by dividing the product by either factor; if the quotient is equal to the other factor, the work is supposed to be right.

DIVISION.

89. Multiplying the dividend by a number, multiplies the quotient by that number.

Multiplying the divisor by a number, divides the quotient by that number.

Multiplying both dividend and divisor by the same number does not change the quotient.

Dividing the dividend by a number, divides the quotient by that number.

Dividing the divisor by a number, multiplies the quotient by that number.