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When there are ciphers at the right hand of either the multipli cand or multiplier, or at both of them.

RULE.

Place the significant figures under one another, then multiply by them only; add the several products together and annex as many ciphers to the total product as there are in both the said factors.

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When the multiplier is any number between 12 and 20.

RULE.

Multiply by the unit figure only; and, as you multiply, add to the product of each single figure that of the multiplicand, which stands next on the right hand of the one you multiplied, and to the last figure in the multiplicand add what you have to carry.

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When the multiplier is the product of any two numbers in the multiplication table.

RULE.

Multiply the given sum by one of those numbers, and the product thence arising by the other; the last product will be the answer re

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Multiply 36745 by 16 89436 by 18 456789 by 21 987654 by 24

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Multiply 56787 by 96 89123 by 132 23456 by 108 45678 by 144

Ans.

APPLICATION.

1. A dollar is equal to 100 cents; therefore, how many cents are contained in 50 dollars?

2. Four quarters of a cent make a whole many quarters are there in 50 cents?

Ans. 5000 cents. one; therefore, how Ans. 200 quarters. therefore, how many Ans. 400 shillings.

3. A pound sterling is equal to 20 shillings; shillings are equal to 20 pounds sterling? 4. Twelve pence make one shilling; therefore, how many pence are contained in 400 shillings? Ans. 4800 pence.

5. Four farthings make one penny; therefore, how many farthings are contained in 72 pence? Ans. 288 farthings. 6. Suppose 40 men were concerned in the payment of a debt, and each man paid 50 dollars. How much was the debt?

Ans. 2000 dollars. 7. How many square feet are in a floor that is 46 feet long and 35 feet wide? Ans. 1610 square feet. 8. If a man travel 36 miles in a day, how far will he go in 12 days? Ans. 432 miles. 9. A merchant bought 342 bales of linen; each bale contained 56 pieces, and each piece 25 yards. How many pieces and yards were there in all? Ans. 19,152 pieces and 478,800 yards. 10. How many corn hills are in a field which contains 125 rows, with 80 hills in each row? Ans. 10,000. 11. If an orchard contain 126 rows, with 109 trees in each row, and 1007 apples on each tree, how many trees and apples are in the said orchard? Ans. 13784 trees and 13830138 apples.

12. A certain island contains 52 counties, each county 42 townships, each township 56 houses, and each house 12 persons. How many townships, houses, and persons are there on the said island? Ans. 2184 townships, 122,304 houses, and 1,467,648 persons,

SIMPLE DIVISION.

Simple Division is a short way of performing many subtractions, without respect to the denomination. It shows how often one number is contained in another, and what remains.

There are four principal members in division; namely:

1. The dividend, or number given to be divided.

2. The divisor, or number given to divide by.

3. The quotient, or answer to the question, which shows how many times the divisor is contained in the dividend.

4. The remainder, (if any) which must be less than the divisor, and of the same name with the dividend. The divisor, dividend, and quotient, are certain members; but the remainder is uncertain, beCause many questions in division have no remainders.

PROOF.

RULE 1.-Multiply the quotient and divisor together, and add the remainder to the product, which will make a sum equal to the dividend, if the operation is right.

RULE 2.-Add all the subtrahends and remainder together, according to the order in which they stand in the work; that sum will be equal to the dividend, if the operation is right.

RULE 3.-1. Cast the nines out of the divisor, and set the excess on the left hand of a cross, as in multiplication."

2. Do the same by the quotient, and set the excess on the right hand of the said cross.

3. Multiply these two figures together, add the product to the remainder, cast the nines out of that sum, and set the excess in the top of the said cross.

4. Cast the nines out of the dividend, and set the excess at the bottom of the said cross; if the operation be right, the top and bottom figures will agree.

SHORT DIVISION.

Short Division is when the divisor does not exceed 12.

RULE.

Seek how often the divisor is contained in the first left hand fig ure or figures of the dividend, under which set the result; and for each 1 that remains add 10 to the next right hand figure; try how often the divisor is contained in that sum, set down the result, and proceed on till all the dividend figures are used.

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Divisor 8)567890120 Divisor 9)36126018 Divisor 10)123456789

Quotient

Proof

11)98765431 12)984100836 3)100000000 4)561236412

6)725442012 5)345401045

7)119455217 8)9000124808

LONG DIVISION.

Long Division is when the divisor exceeds 12.

RULE.

1. For the first dividual, take as many of the left hand figures of the dividend as are just necessary to contain the divisor.

2. Try how often the divisor is contained in the said dividual, and set the result of this trial on the right hand of the dividend, for the first quotient figure.

3. Multiply the divisor by the quotient figure, now found-set the product under the aforesaid dividual and subtract it therefrom.

4. Bring down the next figure of the dividend, and join it on the right hand of the remainder to form a second dividual.

5. Try how often the divisor will go in the second dividual, and set the result in the quotient for the second figure thereof; then, multiply and subtract, as before directed.

6. But, if the second dividual be not sufficient to contain the divisor, set a cipher in the quotient; then, affix the next figure of the dividend (not yet brought down) to the said dividual, and so on, till a competent number of the dividend figures has been annexed to the remainder to form a complete dividual.

7. Try how often the divisor will go in this complete dividual, and proceed on, as before directed, till all the dividend figures are used. 8. The dividual is a partial dividend or, so many of the dividend

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