NOTE. Both multiplier and multiplicand are in general called factors, or terins. 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.* 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 supposed to be right. 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 365 2. Multiply 4657 by 100. EXAMPLES FOR EXERCISE. Ans. 465700. Ans. 5224000. Ans. 264600000. Ans. 10835863800. Ans. 515309055188. Ans. 584113330416. Ans. 533276081481. Ans. 1960310474010. Ans. 7428927415293. 1. Multiply 1203450 by 9004. Application and Use of Multiplication. In making out bills of parcels, and in finding the valueof 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 and quantity together, as in whole numbers, and the separatrix will be as many figuresfrom the right hand in the product as in the given price. 2. What cost 35 lb. cheese at 8 cents per lb. ? ,08 Ans. $2, 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. 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 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? 14. What does 857 bls. pork cents per bl. ? 15. What does 15 tons of Hay cts. per ton ? Ans, $5383, 89 cents. come to, at 18 dols. 98 Ans. $16223, 1 cent. come to, at 20 dols. 78 Ans. $311, 70 cents. 16. Find the amount of the following BILL OF PARCELS. 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. 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 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 products of the several quotient figures multiplied by the divisor together ac cording 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 nines 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 figures will be alike. |