CASE III. When there are cyphers on the right hand of either or bath 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. 7065000×870061465500000 749643000×695000=521001885000000 360000×1200000432000000000 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 wil be the total required. CASE V. To multiply by 10, 100, 1000, &c. annex to the mul plicand all the cyphers in the multiplier, and it will make the product required. EXAMPLES. 1. Multiply 365 by 10. Ans. 3650 Ans. 465700 Ans. 5224000 Ans. 264600000 EXAMPLES FOR EXERCISE. 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 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 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. 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. 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. 8399. per el ? 6. What cost 144 lb. of hyson tea, at 3 dollars 51 cents lb. ? Ans. $505, 44 cents. 7. What cost 94 bushels of eats, at 33 cents per bushAns. 831, 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 $67 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. 93 Ans. $16225, 1 cent. 15. What does 15 tons of Hay come to, at 20 dols. 78 cts. per ton ? Ans. $311, 70 cents. cents per bl. ? 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 divi sion is as follows: viz. Add the remainder and all the products of the several quotient figures multiplied by the divisor together, 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 nines out of the divisor and place the excoUS 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 sines and place the excess at top. 4. Cast the nines out of the dividend and place the excess at bottom.. NOTE. Nthe sum is right, fie top and bottom figures will be alike |