NOTE. Both multiplier and multiplicand are in general called factors, or terms. CASE I. When the multiplier is not more than twelve. 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. 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 ex ss of 9's in the teta? product, the work is supposed to be r. it. 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 365 Multiplier 4.7 2555 1460 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. CASE III. 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. EXAMPLES. 7065000×8700-61465500000 749643000×695000=521001885000000 360000×1200000=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. 7X5-85. EXAMPLES. Multiply 41364 by 35. 7 289548 Product of 7 1447740 Product of 35 2. Multiply 764131 by 48. Ans. 36678288. Ans. 19186896. Ans. 7430778. Ans. 3721896. Ans. 88594992. CASE V. To multiply by 10, 100, 1000, &c. annex to the multiplicand all the cyphers in the multiplier, and it will make the product required. EXAMPLES. 1. Multiply $65 by 10. Ans. 5650. Ans. 465700. Ans. 5224000. Ans. 264600000. EXAMPLES FOR EXERCISE. Ans. 10835863800. Ans. 515309055188. Ans. 584113330416. Ans, 533276681481. Ans. 1960310474010. 1. Multiply 1203450 by 9004. 2. Multiply 9087061 by 56708. 3. Multiply 8706544 by 67089. 4. Multiply 4321209 by 123409. 5. Multiply s456789 by 567090. 6. Multiply 8496427 by 874359. Ans. 7428927415293. 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. RULE. 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. [lars, 36 cents. 2. What cost 35 lb. cheese at 8 cents per lb. ? ,08 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 38 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. el P bushper 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 lb. ? 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 dols. 67 cents per acre? Ans. $5383, 89 cents. 14. What does 857 bls. pork come to, at 18 dols. 96 cents per bl. ? Ans. $16223, 1 cent. 15. What does 15 tons of Hay come to, at 20 dols. 78 ets. per ton? Ans. $311, 70 cents. 16. Find the amount of the following BILL OF PARCELS. Mr. James Paywell, 28 lb. of Green Tea, New-London, March 9, 1814. 41 lb. of Coffee, 54 lb. of Loaf Sugar, 13 cwt. of Malaga Raisins, 35 firkins of Butter, 27 pairs of worsted Hose, 94 bushels of Oats, 29 pairs of men's Shoes, Received payment in full, at 0, 21 |