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oxen, and 6 colts; in pasture No. 2, 3 horses, 4 colts, 6 cows, 20 calves, and 12 head of young cattle; in pasture No. 3, 320 sheep, 16 calves, two colts, and 5 head of young cattle. How much live-stock had he of each kind, and how many head had he altogether?

8. What is the interval of time between an event which happened 125 years ago, and one that will happen 267 years hence?

9. In 1861, John was 24 years old: in what he live, will he be 19 years older?

year, should

10. A merchant has real estate worth 45615 dollars, furniture worth 2862 dollars, merchandise in store worth 25659 dollars, cash in bank 9645 dollars, and cash on hand 456 dollars what is the amount of his fortune?

:

11. Of a debt, George paid 475 dollars, and Samuel paid the remainder, which was 625 dollars: what was the debt?

12. A lot of ground cost 750 dollars; a house was erected thereon, whose cost was, for carpenters' work, 2000 dollars, masons' work, 765 dollars, painters' work, 265 dollars, and for other work, 327 dollars: what was the cost of house and lot?

13. There are 60 seconds in a minute, 3600 in an hour, 86400 in a day, 604800 in a week, 2419200 in a month, and 31557600 in a common year: how many seconds in the periods of time named above?

14. Suppose a merchant to buy the following parcels of cloth: 3912 yards, 1856, 2011, 4540, 937, 6338, 3603, 1586, 2044, 2951, 4228, 1345, 1011, 6138, 960, 607, 5150, 43886, 617, 7513, 4079, 743, 612, 2519, 1238, and 2445 yards: how many yards does he buy in all?

15. What is the sum of two millions bushels of corn, five hundred and thirty-one thousand bushels, one hundred and twenty bushels, fourteen thousand bushels, thirty thousand and twenty-four bushels, five hundred and sixty bushels, and seven hundred and two bushels ?

16. The mail route from Albany to New York is 144 miles, from New York to Philadelphia 90 miles, from Philadelphia

to Baltimore 98 miles, and from Baltimore to Washington City 38 miles what is the distance from Albany to Washington?

17. A man, dying, leaves to his only daughter nine hundred and ninety-nine dollars, and to each of three sons two hundred dollars more than he left the daughter: what was each son's portion, and what the amount of the whole estate?

18. The number of acres of the public lands sold in 1834 was 4658218; in 1835, 12564478; in 1836, 25167833. The number of acres sold in 1840 was 2236889; in 1841, 1164796; in 1842, 1129217. How many acres were sold-in the first three, and how many in the last three years?

19. What was the population of the British provinces in North America in 1834, the population of Lower Canada being stated at 549005; of Upper Canada, 336461; of New Brunswick, 152156; of Nova Scotia and Cape Breton, 142548; of Prince Edward's Island, 32292; of Newfoundland, 75000?

20. By the census of 1850, the number of deaf and dumb in the United States was 9803; of blind, 9794; of insane, 15610; of idiots, 15787: what was the aggregate ?

21. A vessel took for her cargo, from New York to London, cotton, wheat, flour, corn, and tobacco; the cotton was valued at 16562 dollars, the wheat 5690 dollars, the flour 25645 dollars, the corn 10684 dollars, and the tobacco 35760 dollars: what was the value of the cargo ?

22. By the census of 1850, the population of the District of Columbia was 51687; of the Territory of Minnesota, 6077; of New Mexico, 61547; of Oregon, 13294; of Utah, 11380 what was the population of the Territories, including the District of Columbia ?

23. By the census of 1850, the population of Maine was 583169; of New Hampshire, 317976; of Vermont, 314120; of Massachusetts, 994514; of Rhode Island, 147545; and of Connecticut, 370792: what was the population of the six New England States?

24. A person, who was born in 1801, died at the age of 46 years his son died 15 years afterward: in what year did the son die?

SUBTRACTION.

30. John has 5 apples, and Charles 2: how many more apples has John than Charles ?

ANALYSIS.-As many more as, added to what Charles has, will make his number equal to John's: 3 added to 2, gives 5: Therefore, John has 3 apples more than Charles.

31. The DIFFERENCE between two numbers, is that number which added to the less, will give the greater.

32. SUBTRACTION is the operation of finding the difference between two numbers.

33. The MINUEND is the greater of the two numbers.

34. The SUBTRAHEND is the less of the two numbers.

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35. The REMAINDER or Difference, is the result of the operation.

If the numbers are equal, the remainder is 0, whichever be taken as the minuend.

Of the Signs.

36. The sign, is called minus, which signifies, less. When placed between two numbers, it denotes that the one before it is the minuend, and the one after it, the subtrahend; thus,

532,

denotes that 5 is the minuend, 3 the subtrahend, and 2 the remainder.

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37. The principles which control the operations of Subtraction are,

1. That the difference, added to the less number, gives the greater.

2. That the minuend and subtrahend must have the same unit.

38. 1. James has 27 apples, and gives 14 to John: how many has he left?

ANALYSIS. The 27 is made up of 7 units and 2 tens; and the 14, of 4 units and 1 ten. Subtract 4 units from 7 units, and 3 units will remain; subtract 1 ten from 2 tens, and 1 ten will remain: hence, the remainder is 13.

OPERATION.

27 Minuend.

14 Subtrahend.

13 Remainder.

2. A farmer had 378 sheep, and sold 256: how many had he left?

378

256

ANALYSIS.-We first write the number 378, and OPERATION. then 256 under it, so that units of the same order shall fall in the same column. We then take 6 units from the 8 units, 5 tens from 7 tens, and 2 hundreds from 3 hundreds, leaving for the remainder, 122.

3. What is the difference between 843 and 562?

ANALYSIS.-Begin at the units' column, and subtract 2 from 3. At the next place we meet a difficulty, for we can not subtract a greater number from a less.

If we take 1 from the 8 hundreds (equal to 10 tens), and add it to the 4 tens, the minuend will become 7 hundreds, 14 tens, and 3 units. We then say, 6 tens from 14 tens leaves 8 tens; and 5 hundreds from 7 hundreds leaves 2 hundreds: hence, the remainder is 281.

122

OPERATION

843

562

7 14 5 6

2

The same result is obtained by adding, mentally, 10 to the 4 tens, and then adding 1 to 5, the next figure of the subtrahend at the left; for, adding 1 to the 5 is the same as diminishing the 8 by 1. This process of adding 10 to a figure of the minuend, and 1 to the next figure of the subtrahend, at the left, is called, borrowing.

32

8

1

10 843

562

1

281

31. What is the difference between two numbers ?-32. What is Subtraction?-33. What is the minuend ?-34. What is the subtra hend?-35. What is the remainder ?-36. What is the sign of Subtraction ?-37. What are the principles which control the operations of Subtraction?

Hence, for Subtraction, we have the following

Rule.

I. Write the less number under the greater, so that units of the same order shall fall in the same column.

II. Begin at the right hand, and subtract each figure of the subtrahend from the one directly over it, when the upper figure is the greater.

III. When the upper figure is the less, add 10 to it, before subtracting, and then add 1 to the next figure of the subtrahend.

Proof.

Add the remainder to the subtrahend. right, the sum will be equal to the minuend.

Spelling-Reading.

If the work is

39. What is the difference between 725 and 341?

By the common method, which is spelling, we say, 1 from 5 leaves 4; 4 from 12 leaves 8; 1 to carry to 3 are 4; 4 from 7 leaves 3.

Reading the words which express the final result, we should make the operations mentally, and say, 4, 8, 3.

OPERATION.

725

341

384

Let the pupils be practiced separately in the reading, and also in concert in classes.

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38. Give the rule for Subtraction.

39. Explain what is meant by spelling and reading

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