13. What is the difference between nine thousand, and nine hundred? Ans. 8100.

14. America was discovered in the year 1492, by Christopher Columbus; and American Independence was declared in 1776. I wish to know the number of years between these two events. Ans. 284.

15. A vintner bought 31 pipes of brandy, containing 3746 gallons; and sold 19 pipes, containing 2294 gallons-How many pipes and gallons were left? Ans. 12 pipes, 1452 gals.

16. It is said that on the 19th day of June, 1835, a tornado passed near Gravel Hill, Warren county, New Jersey, which prostrated all the apple trees, in an orchard containing three hundred trees, except four or five. I desire to know how many there were prostrated. Ans. 295 or 296.

ADDITION AND SUBTRACTION.

1. A tradesman, happening to fail in business, called all his creditors together, and found he owed to A. 75 dollars, to B. 140 dollars, to C. 64 dollars, to D. 95 dollars, to E. 72 dollars, to F. 27 dollars, to G. 55 dollars, and to H. 92 dollars. His creditors found the value of his stock to be two hundred dollars; recoverable book debts, 112 dollars; besides money on hand, 134 dollars. I desire to know whether they were gainers or losers, and how much?

2. A man setting out on a journey of 976 miles, travels the first day 52 miles; the second, 50 miles; the third, 61 miles; the fourth, 49 miles; the fifth, 56 miles; the sixth, seventh, eighth, ninth and tenth days, each, 55 miles-How far is he from his journey's end? Ans. 433 miles.

3. A merchant, at his outsetting in trade, owed 1200 dollars he had in cash, 600 dollars; good debts, 1150 dollars: he cleared the first year, by commerce, 1000 dollars-What is the neat balance at the twelve months' end?

Ans. 1550 dollars.

4. A farmer has 5 granaries of wheat, containing 576 bushels: one contains 104 bushels; another, 79 bushels; a third, 85 bushels; a fourth, 159 bushels-How many bushels does the fifth contain ? Ans. 149.

5. Sent a servant to market to purchase vegetables: he laid out for radishes, 12 cents; for onions, 9 cents; for asparagus, 16 cents; for potatoes, 14 cents, and for lettuce, 19 centsHow much change should he return, 90 cents being the amount he took with him? Ans. 20 cents.

6. A farm of one hundred acres is divided, as follows, viz: 12 acres of wheat, 5 of rye, 17 of corn, 16 of oats, 1 of potatoes, 16 of grass, 12 of barley, 1 of flax; the orchard, garden and buildings, occupy 16 acres; the remainder is woodland-How much is there of it? Ans. 4 acres.

7. Bought of A. 1000 bushels oats; of B. twice as much: of which were sold to C. 500 bushels; to D. twice as much, and to E. as much as to them both-How much have I on hand? Ans. None.

8. A gentleman, having a farm of one hundred and ten acres, purchased one adjoining, containing one hundred and fifty-seven acres; which at his decease he bequeathed to his three sons to Thomas, seventy-five acres ; to Edmund, ninetyeight acres, and the remainder to Gilbert-How many acres fell to Gilbert's share?

Ans. 94.

MULTIPLICATION is the multiplying of any two numbers together, and compendiously performs the office of many additions. To this rule belong three principal members, viz:

1. The multiplicand, or number to be multiplied;
2. The multiplier, or number to multiply by;
3. The product, or number produced by multiplying.

RULE.

Set down the multiplicand, place the multiplier under it, and draw a line under them. Then begin with the right hand figure, and with it multiply the unit figure in the multiplicand; set down its product; proceed in this way with each figure; but if either of the products be ten or more, set down only the number expressed by its right hand figure, and add the number expressed by its left hand figure or figures to the product of the next figure; and so continue to the last, where the whole product must be set down. The multiplicand and multiplier are called factors.

Proof. Multiplication may be proved by inverting the factors. There is however a more compendious, but less accurate mode, that is, by casting out the nines from the multiplicand and multiplier, the remainders put on each side of a cross; multiply the figures on each side together, cast the nines from the product, and put the overplus at top; then cast out the nines from the product of the multiplication, and place its remainder at the bottom of the cross; if it be the same as the top, the work is supposed to be right. But the former mode is the surest.

MULTIPLICATION TABLE.

Twice 3 times 4 times 15 times 16 times

1 are 2 1 are 31 are

4 1 are 5 1 are

17 times 6 1 are 7

Explanation. Here I say 9 times 4 are 36: I put down 6 and carry 3; saying 9 times 5 are 45, and 3, that I carried, make 48: I put down 8 and carry 4; then I say 9 times 3 are 27, and 4, that I carried, make 31: I put down 1 and carry 3; I then say 9 times 7 are 63, and 3, that I carried, are 66: I put down 6 and carry 6; then I say 9 times 2 are 18, and 6, that I carried, are 24: I put down 4 and carry 2; then I say 9 times 6 are 54, and 2, that I carried, make 56: I put down 6 and carry 5; then I say 9 times 7 are 63, and 5, that I carried, make 68: I put down 8 and carry 6; I then say 9 times 9 are 81, and 6, that I carried, make 87: and here I set down the full product.

I commence with the right hand figure of the multiplicand, and say 2 and 2 are 4, and 4 are 8, and 3 are 11. I cast 9

from this, and 2 are left, which I add to the two remaining figures, which makes five. I set down this on the left hand of the cross; then I add together the figures in the multiplier, and find they amount to only 3. I put this down on the right hand of the cross. I then multiply these two figures together, saying 3 times 5 are 15. I cast 9 from this, and 6 are left: I put this down at the top of the cross. Then I add the

figures of the product, thus-I say 4 and 6 are 10; I cast 9 from this, and 1 is left. I then say 1 and 1 are 2, and 8 are 10: here I cast away 9 again, and 1 is left. I then say 1 and 4 are 5, and 1 are 6, which is the same as the top figure-the work is, therefore, presumed to be right.

When the multiplier is more than 12, and less than 20, multiply by the unit figure of the multiplier, adding to the product the back figure to that you multiplied.