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Multiply by each figure in the multiplier separately, beginning with units, taking care to set the first figure in each product directly under its own multiplier. Then add as 11. addition.

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Method 1. Change the multiplier and multiplicand; and then, if right, the product from this multiplication will be equal to the first.

Method 2. Cast the nines out of each factor separately, set down the remainders and multiply them together ; cast the nines out of this product, and note the remainder; then cast the nines out of the product, and if right, the two last remainders will be equal.

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6 Note. This last method is not absolutely certain; yet the probability is so great, that in general it may be relied on. . 3. Multiply 5221 by 145 Ans.

757045 4. 23430 230

5388900 5. 3800920


306924290000 6. 89536925


65809639875 7. 78965987


465346561391 8. What will 75 bushels of wheat come to at 1,15 cents

Ans. 86 dolls. 25 cents. 9. Bought 3950 lbs. of coffee, at 29 cts. per Ib. what must I pay?

Ans. 1145 dolls. 50 cents. 10. There are 12 pence in one shilling. How many are there in 40 ?

Ans. 480 pence.

Case 3. When the multiplier is the exact product of any two factors in the multiplication table.

RULE. Multiply the given sum by one of these; and that product multiplied by the other, will give the number required.

per bushel ?

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Case 4. When there are ciphers at the right of one or both the factors.

RULE. Omit them in the operation, but annex them to the product

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Ans. 4800 2. 3600 by 400

1440000" 3. 44000 550000

24200000000 4. 663000 60000

39780000000 Note. When the multiplier is 10, the product will be found by add. ing one cipher to the multiplicand; if 100, add two ciphers; if 1000 add three ; &c.

EXAMPLE. 1. Multiply 200 by

Ans. 2000 2.


46200 3.


879000 Application. 1. A gentleman owes 25 laborers 15 dollars each ; low much does the whole come to ?

Ans. 375 dolls. 2. A saddler owes his journeyman for 43 days' work, ai 125 cents per day; how much does he owe him in all ?

Ans. 53 dolls. 75 cts. 3. A merchant buys 440 yards of muslin at 32 cents per yard; how much does the whole cost ? Ans. 140 dolls. 80 c.

4. A farmer selis 60 bushels of wheat at 125 cents per bushel ; 40 bushels of rye at 85 cents ; 34 of corn at 50 cents ; how much is he to receive for cach, and how much does the whole amount to?

Ans. 75,00 cents for the wheat, 34,00 cents for the rye 17,00 cents for the corn ; and the whole amounts to 126,00 cents, or 126 dollars.

5. A dollar is equal to 10 dimes, and a dime is equal to 10 cents ; how many dimes and cents are there in 100 dol. lars?

Ans. 1000 dimes, and 10,000 cents. 6. How many panes of glass are there in a house that has 32 windows, 20 of which have 24 lights cach, and the rest have 18 each ?

Ans. 696 panes.

7. What sum is equal to 7525 multiplied by 125 ?

Ans. 940625. 8. A has 250 dollars, B has three times as many, and C has four times as many as B; how many dollars have B and C each, and how many have they altogether?

Ans. B has 750 dolls. C. 3000 dolls. altogether $4000.


OF DIVISION. Division is either simple or compound.

Simple division is finding how often one number is contained in another of the same name, or denomination.

The number given to be divided, is called the dividend.
The number given to divide by, is called the divisor.
The result, or answer, is called the quotient.

Case 1.
When the divisor does not exceed 12.

RULE. Find how often the divisor is contained in the first figure or figures in the dividend, under which set the result, if any remain, conceive it as so many tens added to the next figure, and then proceed in the same manner.

Division is proved by multiplying the quotient by the divisor, and adding the remainder, if any: the amount will equal the dividend.

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Case 2. When the divisor exceeds 12.

RULE. Begin with as many of the first figures in the dividend as will contain the divisor. Try low often the divisor is contained therein, and set the result in the quotient.--Subtract the product of the divisor multiplied by the quotient figure from the dividual above, to this remainder annex the next figure in the dividend for a new dividual, and su proceed till all the figures in the dividend are brought down.

Note. A dividual is when one or more figures of the dividend, (in the operation of long division) are divided separately from the rest.

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Case 3. When the divisor is the exact amount of any two factors in the table.

RULE. Divide the given sum by any one of these, and the quo. rient hv the other.

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