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14. Multiply 700483 by 9152. Ans, 6950910416. 15. What is the total product of 7603 times 365132.
Sns. 2780206650. 16. What number is equal to 40003 times 4897085.
CASE I!. 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.
7065000 X 8700=61465500000 749643000 «695000=521001885000000 360000 x 1200000=43200000000
CASE IV. When the multiplier is a composite number, that is whet it is produced by multiplying any two numbers in the table together; multiplv first hy one of those figures, and flia s
product by the other, and the last product will be the total required.
1447740 Product of 3.1. 2. Multiply 761131 by 48.
Ans. 36678288. 3. Multiply 312516 by 50.
Ans. 19180896. 4. Multiply 209102 by 72.
Ans. 15076944. 5. Multiply 91738 by 81.
Ans. 7430778. 0. Multiply 34462 by 198.
Ans. 3721896. 7. Multiply 615243 by 144.
CASE V. To multiply by 10, 100, 1000, &c. annex to the muliiplicand all the ciphers in the multiplier, and it will make the product required.
EXAMPLES. 1. Multiply 365
Ans. 3650. 2. Multiply 4657 by 100.
Ans. 465700. 3. Multiply 5224 hy 1000.
Ans, 52:24000. 4. Multiply 201460 by 10000. Ans. 264600000,
EXAMPLES FOR EXERCISE. 1. Multiply 1203450 by 9004. Ans. 10635863600, 2. Multiply 9087061 by 50703. Ans. 515309055188. 3. Multiply 870654.1 by 67089. Ans. 584113330416. 4. Iultiply 4321209 by 123409. Ans. 533270081481. 5. Multiply 3156789 by 567090. Ans. 1960310471010. 6. Multiply 84196427 by 874359. Ans. 7428927415293.
98763542 x 95703512=87542:37.228385764,
Application md Use of Multiplication. In making out bills of parcels, and in finding tlie value of goods ; when the price f one yard, pound, &c. is given (in Federal Money) to find the value of the whole quantity:
Rule.-Multiply the given price and quantity together, as in whole numbers, and the separatrix will be as many figures from the nght hand in the product as in the given price.
EXAMPLES. 1. What will 35 yards of broad- $. d. cloth come to, at
13, 4 9 6 per yard ?
17 4 80 104 8 8
Ans. $122, 3 6 0z=122 dol
(lars, 36 cents. 2. What cost 35 Ib. cheese at 8 cents
Ib. ? ,08
Ans. $2, 802 dollars 80 cents. 3. What is the value of 29 pairs of men's shoes, at I dorlar 51 cents per pair ?
Ans. $43, 79 cents. 4. What cost 131 yards of Irish linen, at 38 cents per
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 Ib. ?
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 tents per firkin ?
Ans. $357. 9. What cost 12 wt. of Malaga'raisins, at 7 dollars 31 cents per cwt. ?
Ans. $87, 72 cents. 10. Dought 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 lb. ?
Ans. $75. 12. What is the value of 75 yards of satin, at 3 dollars 75 cents per yard ?
Ans. $231, 25. 13. What cost 367 acres of land, at 14 dols. 67 cents
Ans. $5383, 89 cents.
per acre ?
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 tun?
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 Morchant.
$. cts. 28 lb. of Green Tea,
at 2, 15 per
1. 41 lb. of Coffee,
at 0, 21 34 lb. of Loaf Sugar,
at 0, 19 13 cwt. of Malaga Raisins,
cwt. 35 firkins of Butter,
at 7, 14 per fir. 27 pairs of worsted Hosc, 94 bushels of Oats,
bush. 29 pairs of men's Shoes, at 1, 1:2 per pair.
Amount, $511, 78. Received payment in full,
William MERCHANT. A SHORT RULE. Note. The value of 100lbs. of any article will be just as many dollars as the article is cents a pound.
For 100 1!, at I cent per lb.=100 ceuts=1 dollar.
100 lb. of beef at 4 cents a lb. comes to 400 cents: 5 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 sub tractions.
Four principal parts are to be noticed in Division : 1. The Dividend, or number given to be divideil. 2. The Divisor, or number given to divide hy.
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.
Rule.-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 vot exceed ihe part of ihe 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 reinainder, if there be any, to the product; if the work be right, tho sun will be equal to the dividend.*
* Another method which some make use of to prove division is as fol. lors : viz. Add the remainder and all the products of the several quotient figures multiplied by the divisor togeiher, according to the order in which they stand in the work ; and this sum, when the work is right, will be equal to the dividend.
A third method of proof by excess of nines is as follows, viz. 1. Cast the ñines out of the divisor, and place the excess on the left hand. 2. Do the same with the quotient, and place it on the right hand.
3. Multiply these two figures together, and add their product to the remainder, and reject the nines, and place the excess at top. 4. Cast the nines out of the dividend, and place the excess at bottom, Note. If the sum is right, the top and bottom Ngures wilt be alike.