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When there are cyphers on the right hand of either or both of the factors, neglect those cyphers; then place the significant figures under one another, and multiply by them only, and to the right hand of the product, place as many cyphers as were omitted in both the factors.
Multiply 41364 by 35.
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.
2. Multiply 764131 by 48.
289548 Product of ~
1447740 Product of 55
To multiply by 10, 100, 1000, &c. annex to the multiplicand all the cyphers in the multiplier, and it will make the product required.
1. Multiply $65
Ans. $650. Ans. 465700. Ans. 5224000. Ans. 264600000.
EXAMPLES FOR EXERCISE.
1. Multiply 1205450 by 9004.
5. Multiply 3456789 by 567090. Ans. 1960310474010. 6. Multiply 8496427 by 874559. Ans. 7428927415295. 98765542×98763542-8754237228585764.
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.
Multiply the given price andquantity 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-28. d. c. m. cloth come to, at
53, 4 9 6 per yard?
104 8 8
Ans. 122, 360
=122 dol [lars 36 cents.
2. What cost $5 lb. cheese at 8 cents per
Ans. 82, 80=2 dollars 80 cents.
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 58 cents per yard? Ans. $49, 78 cents. 5. What cost 140 reams of paper, at 2 dollars 35 cents per ream? Ans. $329.
6. What cost 144 lb of hyson tea, at 3 dollars 51 cents per lb. ? Ans. $505, 44 cents. 7. What cost 94 bushels of oats, at 35 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 pe head; what do they come to ? Ans. $1924. 11. What is the amount of 500 lbs of hog's-lard, at 13 cents per lb. ? Ans. $75. 12. What is the value of 75 yards of satin, at S dollars 75 cents per yard? Ans. $281, 25 cents. 13. What cost 367 acres of land, at 14 dols. 67 cents per aere? Ans. $5383, 89 cents. 14. What does 857 bls. pork come to, at 18 dols. 93 per bl.? Ans. 816225, 1 cent. 15. What does 15 tons of Hay come to, at 20 dols. 78 cts. per ton? Ans. BS11, 70 cents. 16. Find the amount of the following BILL OF PARCELS.
New-London, March 9, 1814. Bought of William Merchant. 8. cte.
at 2, 15 per lb.
at 0, 21
at 0, 19
at 7, 31 per cut.
Mr. James Paywell,
28 lb. of Green Tea,
Amount, $510, 78
A SHORT RULE.
NOTE. The value of 100 lbs. of any article will be just as many dollars as the article is cents a pound.
For 100 lb. at 1 cent per lb.=100 cents=1 dollar. 100 lb. of beef at 4 cents a lb. comes to 400 cents=4 dollars, &c.
DIVISION OF WHOLE NUMBERS. SIMPLE DIVISION teaches to find how many times one whole number is contained in another; and also what remains; and is a concise way of performing several subtractions.
Four principal parts are to be noticed in Division: 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, which is always less than the divisor, and of the same name with the Dividend.
First, seek how many times the divisor is contained in as many of the left hand figures of the dividend as are just necessary, (that is, find the greatest figure that the divisor can be multiplied by, so as to produce a product that shall not exceed the part of the dividend used) when found, place the figure in the quotient; multiply the divisor by this quotient figure; place the product under that part of the dividend used; then subtract it therefrom, and bring down the next figure of the dividend to the right hand of the remainder; after which, you must seek, multiply and subtract, till you have brought down every figure of the dividend.
PROOF. Multiply the divisor and quotient together and add the remainder if there be any to the product; if the work be right, the sum will be equal to the dividend.*
Another method which some make use of to prove division is as follows: viz. Add the remainder and all the pro
her, according to the order in which they stand in the 1)6k; and this sum, hen the work right will equal to the dividend.
A third method of proof by excess of nines is as follows, viz. 1. Cast the nines out of the divisor and place the excess n the left hand.
2. Do the same with the quotient and place it on the right urand.
it, 3. Multiply these two figures together, and add their proquact to the remainder, and reject the nines and place the extieess at top.
14. Cast the nines out of the dividend and place the excess the bottom.
ing NOTE. If the sum is right the top and bottom figures will