Compound Addition. A silversmith purchased 12 ingots of silver, each averaging 3lbs. 6oz. 16 pwt. and 20grs, what was the weight of all ? Ans. 42lbs. 10oz. 2pwt. A farmer sold 276 bags of wheat, each containing 2 bush. 1 pc., at $1,25 per bushel. How many bushels did he sell; and what did it come to? Ans. 621 bush. cost $776,25. A grocer sold 8 chests of tea, the average weight of each was 2 Crot. 2 qrs. 8 ibs. at 90 cents the Ib. What quantity of tea did he sell, and how much did he receive? Ans. 20 Ct. 2qrs. 8fbs. Received $2073,60. A teacher had 3 apartments in his building. In one were 12 linguists, at 12 dollars per quarter; in another 27, at 8 dollars; in the third, 31, at 6 dollars 50 cents, per quarter. How many pupils had he, and what was his quarterly income? Ans. 70 pupils, and Rec. $561,50. How much wine in 12 casks, each containing 63 gal. 2 qts. 1 pt.; and what would it come to, at $1, 87% the gallon? Ans. 763 gals. 2 qts. Amount $1431, 56.21. In 9 parcels of wood, each containing 4 cords, 76 feet, at $4, 25 the cord. How much wood, and what would it amount to?-Ans. 41 cds. 44 ft. Amount $175, 71. In 7 fields, each containing 97 acres, 3 roods, and 30 rods; how much land? Ans. 685 acrs. 2 rds. 10 rds. Compound Multiplication. To multiply Numbers, whether whole or decimal, so that the several Products will incline to the right-hand. RULE.-Place the multiplier under the multiplicand, so that either tens, hundreds, or thousands in the multiplier may stand under the unit's place of the multiplicand. Begin with the figure in the multiplier, which stands under the units of the multiplicand, and place the first figure of the product directly under it: if figures stand at the left of the figure already multiplied, its product will be removed one place to the left, and the product of the several right-hand figures will stand respectively under the figure which is multiplied. At all times, the right-hand figure of a product is placed under the figure multiplied, whatever may be the position of the multiplier, in relation to the multiplicand. Multiply 8253 by 826. 826 Multiplier. Compound Addition. Compound Multiplication. A person is possessed of 2 dozen of silver spoons, each weighing 3 oz. 16 pwt. 12 grs.; 13 dozen weighing 2oz. 18 pwt. and 9grs.; and 2 silvertankards, weighing 22 oz. 10 pot. and 8 grs. What is the weight of the whole? Ans. 15 lb. 9 oz. 7 pwt. 10 grs. A person sold in market, 57 chickens, at 20 cts. each; 49 turkeys, at 92 cts. ; 72 geese, at 37 cts.; and 25 partriges, at 30 cts. each. How many in the whole, and what did they amount to? Ans. 203 fowls; amt. $90,98. If 8 boys have each 12 cats, and each cat 4 kittens; what is the whole number of their stock? Ans. 480. Suppose a farmer's stock consisted of 8 horses, that devoured each 2 tons of hay; 12 oxen, 2 tons, each; 20 cows, 1 tons, each. What is the number of his stock, and how much hay would they consume in one winter? Ans. 40 stock; hay 74 tons. If a man drive to market 50 fat oxen, valued at 75 dollars, each; 40 cows, at 25 dollars each; 58 calves, at 5 dollars each; and 60 sheep, at $1,25 each; what is the whole number of the drove, and how 7638 Multiply 261986 by 7638. 1571916 1833902 785958 2095888 2001049068 Product. Multiply 23,476 by 7,35. 7,35 164,332 7,0428 1,17380 172,54860 Product. In multiplying decimals from left to right, the first figure of each product is placed one remove to the right successively, and then the separatrixes are kept in a straight line. Multiply $26,3754 by 22,6532. 22,6532 52,7508 527,508 15,82524 1,318770 791262 527508 much would they amount to? Pro.$597,48721128 Ans. 208 stock, amount $5144. If a school, consisting of 45 boys, had each 3 Latin books, 3 Greek, 3 French, and 6 English; what number of books in the whole? Ans. 675. 1. What is Compound Increase? 2. What is meant by generic kind; and why not mingle cwts., dollars, and acres? 3. What are Compound Addition and Multiplication? 4. What are the denominations of Federal money, and their relative values? 5. How is Federal money added and multiplied? 6. How is the amount, or sum total, pointed off in Federal money? how in Multiplication? and how in case of deficiency of places of figures in the product? 7. How are cents expressed when under ten? 8. Why carry by tens in Federal money? 9. Why carry by different numbers in the various tables of weights and measures? and why by different numbers usually in the same table? 10. What are the rules for Compound Addition and Multiplication? 11. When the multiplier is a composite number, what is the rule? 12. When the multiplier is not a composite number, how get the answer? 13. What constitutes an exact Julian year? 14. How is the value of a Cwt. found, when the price of one b. is given either in pence or farthings? 15. How is the value of 60s. found, when the price of one b is 1s. 3d. or 5s.? 16. How does the pedlers' rule furnish the true value, by the nett hundred ? 17. How may numbers be multiplied, so, that the several products shall incline to the right? 18. How multiply numbers, so that the several products shall alternately incline to the left or right; or in any prescribed form? 19. To which of the rules do the appropriate terms belong, and what is their import severally, viz. Amount, Product, Sum Total, Factors, or Terms, Sum, Multiplicand, Multiplier, and Total Product? and where are their several positions? DECREASE OF NUMBERS. THE Decrease of Numbers is the opposite of Increase. It has been already remarked, that in every operation of figures, numbers were necessarily increased, or diminished. The increase, to which we have already been attending, embraced the rules of Addition and Multiplication. Decrease, which diminishes a quantity, is composed also of two rules, viz. Subtraction and Division. When taken collectively, they retain the general term of Decrease; but when referred to individually, they assume their old appropriate names of Subtraction and Division. The nature and operations of each, and the similarity of the principles on which they are founded, will now demand an attentive investigation. SUBTRACTION. Simple Subtraction teaches to find the excess, or difference, between any two given numbers of the same denomination. The greater of the two numbers is called the Minuend. DIVISION. Simple Division teaches to find how many times one whole number is contained in another; and also what remains, if one number does not exactly measure the other. It is a concise SUBTRACTION. from minuo, which signifies to diminish, or to be lessened. The less number is called the Subtrahend, from subtraho, to draw out, or take from. The result of the operation is called, difference: (not remainder, for this term belongs exclusively to Division.) RULE I. 1. Place the less number under the greater, with units under units, tens under tens, &c., and draw a line under them. 2. Begin at the right-hand, and take the lower figure from the one above it, and set down the difference. 3. If the figure in the lower line is greater than the one above it, add ten to the upper figure; from which number so increased, take the lower, and set down the difference, carrying one to the next lower number; and thus proceed as before, until the whole is finished. PROOF. Add the difference to the subtrahend, or less sum, and if the amount equal the greater, or minuend, the work is supposed to be right: or, if the difference is subtracted from the minuend, and it leaves a difference equal to the subtrahend, it is right. DIVISION. way of performing several Subtractions. There are four appropriate terms used 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, or kind, with the dividend. RULE I. 1. Place the divisor at the left-hand of the dividend. 2. Consider how many times the divisor is contained in so many of the left-hand figures of the dividend, as are necessary to contain the divisor; and place the number sought, at the right-hand of the dividend, for the first figure in the quotient. 3. Multiply the divisor by this quotient figure, and place the product under the left-hand figures of the dividend already used. 4. Subtract this product from the dividend, and call the difference the first remainder. 5. To the right-hand of this remainder bring down the next figure in the dividend. 6. Consider how many times the divisor is contained in this number, place the figure at the right-hand in the quotients; E 2 |