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NOTE. Both multiplier and multiplicand are in general called factors, or terms.

CASE I.
When the multiplier is not more than twelve.

RULE. Multiply each figure in the multiplicand by the multiplier ; carry one for every ten, (as in addition of whole numbers) and you will have the product or answer,

PROOF.*
Multiply the multiplier by the multiplicand.

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EXAMPLES.

What number is equal to 3 times 365 ?

Thus, 365 Multiplicand.

3 Multiplier.

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CASE II.
When the multiplier consists of several figures.

RULE. The multiplier being placed under the multiplicand units under units, tens under tens, &c. multiply by each significant figure in the multiplier separately, placing the first figure in each product exactly under its multiplier ;

Multiplication may also be proved by casting out the 9's in the two factors, and setting down the remainders ; then multiplying the two remainders together ; if the excess of 9's in their product is equal to the excess of 9's in the total product, the work is gup posed to be right.

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then add the several products together in the same order as
they stand, and their sum will be the total product.

EXAMPLES.
What number is equal to 47 times 365 ?

Multiplicand 3 6 5
Multiplier 4 7

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14. Multiply 760483 by 9152. Ans. 6959940416. 15. What is the total product of 7608 times 365432.

Ans. 2780206656 16. What number is equal to 40003 times 4897685

Ans. 195922093055

1

CASE III. When there are ciphers on the right hand of either or both of the factors, neglect those ciphers; then place the significant figures under one another, and multiply by them only, and to the right hand of the product, place as many ciphers as were omitted in both the factors.

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7065000 X 8700=61465500000 749643000 x 695000=521001885000000 360000X1200000=432000000000

CASE IV. When the multiplier is a composite number, that is, when it is produced by multiplying any two numbers in the table together; multiply first by one of those figures and that product by the other; and the last product will be the total required.

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CASE V. To multiply by 10, 100, 1000, &c. annex to the multiplicand all the ciphers in the multiplier, and it will make the product required.

EXAMPLES.

1. Multiply 365 by 10.

Ans. 3650. 2. Multiply 4657 by 100.

Ans. 465700. 3. Multiply 5224 by 1000. Ans. 5224000. 4. Multiply 26460 by 10000. Ans. 264600000.

EXAMPLES FOR EXERCISE. 1. Multiply 1203450 by 9004. Ans. 10835863800. 2. Multiply 9087061 by 56708. Ans. 515309055188. 3. Multiply 8706544 by 67089. Ans. 584113330416. 4. Multiply 4321209 by 123409. Ans. 533276081481, 5. Multiply 3456789 by 567090. Ans. 1960310474010. 6. Multiply 8496427 by 874359. Ans. 7423927415293.

98763542 98763542=8754237228385764.

Application and Use of Multiplication. In making out bills of parcels, and in finding the value of goods; when the price of one yard, pound, &c. is given (in Federal Money) to find the value of the whole quantity.

RÜLE. Multiply the given price and quantity together, as in whole numbers, and the separatrix will be as many figures from the right hand in the product as in the given price.

1. What will 35 yards of broad- $. d. c. m. cloth come to, at

$ 3, 4 9 6 per yard?

3 5

EXAMPLES.

17 4 8 0 104 8 8

Ans. $122, 3 6 0 =122 dol

[lars, 36 cents. 2. What cost 35 lb. cheese at 8 cents per lb. ?

,08

Ans. $2, 80.2 dollars 80 cents.

per ream ?

per lb. ?

3. What is the value of 29 pairs of men's shoes, at 1 dollar 51 cents per pair ?

Ans. $43,79 cents. 4. What cost 131 yards of Irish linen, at 38 cents per yard?

Ans. $19, 78 cents. 5. What cost 140 reams of paper, at 2 dollars 35 cent;

Ans. $329. 6. What cost 144 lb. of hyson tea, at 3 dollars 51 cents

Ans. $505, 44 cents. 7. What cost 94 bushels of oats, at 33 cents per bushel ?

Ans. $31, 2 cents. 8. What do 50 firkins of butter come to, at 7 dollars 14 cents per firkin ?

Ans. $357. 9. What cost 12 cwt. of Malaga raisins, at 7 dollars 31 cents per cwt. ?

Ans. $87,72 cents. 10. Bought 37 horses for shipping, at 52 dollars per head: what do they come to?

Ans. $1924. 11. What is the amount of 500 lbs. of hog’s-lard, at 15 cents

per
Ib. ?

Ans. $75. 12. What is the value of 75 yards of satin, at 3 dollars 75 cents per yard ?

Ans. $281,25 cents. 13. What cost 367 acres of land, at 14 dolş. 67 ce per acre ?

Ans. $5383, 89 cents. 14. What does 857 bls. pork come to, at 18 dols. 93 cents per bl. ?

Ans. $16223, 1 cent. 15. What does 15 tuns of hay come to, at 20 dols. 78 cts. per ton ?

Ans. $311, 70 cents. 16. Find the amount of the following

BILL OF PARCELS.

New-London, March 9, 1814. Mr. James Paywell,

Bought of William Merchant

$. cts. 28 lb. of Green Tea,

at 2, 15 per lb. 41 lb. of Coffee,

21 34 lb. of Loaf Sugar,

at 0,19 13 cwt. of Malaga Raisins, at 7, 31 per cwt. 35 firkins of Butter,

at 7, 14 per fir. 27 pairs of worsted Hose, at 1, 04 per pair. 94 bushels of Oats,

at 0, 33 per bush. 29 pairs of men's Shoes, at 1, 12 per pair.

Amount, $511,78. Received payment in full,

WILLIAM MERCHAN

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