Contractions in Division. When the divisor is such a number, that any two figurur in the Table, being multiplied together, will produce it, di. vide the given dividend by one of those figures ; the quo. tient thence arising by the other; and the last quotient will be the answer. Nore. The total remainder is found by multiplying the last remainder by the first divisor, and adding in the first remainder. 22587 63 first rem. + True Quotient 225844. True rem, 645 2. Divide 178464 by 16. Ans. 11154. 3. Divide 467412 by 24. Ans. 19475!3. 4. Divide 942341 by 35. Ans. 269243's. 5. Divide 79638 by 36. Ans. 2212% 6. Divide 144872 by 48. Ans. 301816. 7. Divide 937387 by 54. Ans. 173594 8. Divide 93975 by 84. Ans. 111891. 9. Divide 145260 by 108. Ans. 1345. 10. Divide 1575360 by 144. Ans. 10940. 2. To divide by 10, 100, 1000, &c. RULE.-Cut off as many figures from the right hand of the dividen as there are ciphers in the divisor, and these figures so cut off are th remainder; and the other figures of the dividend are tlie quotient: ¿XAMPLES. 1. Divide 365 by 10. Ans. 36 and 5 remains 2. Divide 5762 by 100. Ans. 57 3. Divide 763753 by 1000: Ans. 763 62 rem. 753 rem. SUPPLEMENT TO MULTIPLICATION. To multiply by a mixt number; that is, a whole number juined with a fraction, as 81, 51, 64, &c. HULE.--Multiply by the whole number, and take 4, 3, 4, &c. of The saltiplicand, and add it to the product. EXAMPLES. Multiply 48 by 21. 2/37 48 27 12=1 96 24=} 8691 answer. 3. Multiply 211 by 501 4. Multiply 2464 by 81. 5. Multiply 345 by 193 6. Multiply 6497 by 54. 132 Ans. Ans. 106551. Ans. 20533; Ans. 65981 Ans. 33413 un ? Questions so exercise Multiplication and Division. 1. What wiii 9 tuns of hay come to, at 14 dollars a Ans. $136. 2. If it take 320 rods to make a mile, and every rod contains 5} yards ; how many yards are there in a mile ? Ans. 1760. 3. Sold a ship for 11516 dollars, and I owned of her; what was my part of the money ? Ans. $8637. 4. In 276 barrels of raisins, each 31 cwt. how many hundred weight ? Ans. 966 cwt. 5. In 36 pieces of cloth, each piece containing 241 vards ; how many yards in the whole? Ans. 873 yds. 6. What is the product of 161 multiplied by itself 1 Ans, 25921. 7. If a man spend 492 dollars a year, what is that per salendar month ? Ans. $41. 8. A privateer of 65 men took a prize, which being equally divided among them, amounted to 1191. per man; what is the value of the prize ? Ans. $7735. D per yard? 9. What number multiplied by 9, will make 225? Ans. 25. 10. The quotient of a certain number is 457, and the divisor 8; what is the dividend ? Ans. 3656. 11. What cost 9 yards of cloth, at 3s. Ans. 27s. 12. What cost 45 oxen, at 8l. per head ? Ans. £360. 13. What cost 144 lb. of indigo, at 2 dols. 50 cts. or 250 cents per lb. Ans. $360. 14. Write down four thousand six hundred and seventeen, multiply it by twelve, divide the product by nine, and add 365 to the quotient, then from that sum subtract five thousand five hundred and twenty-one, and the remainder will be just 1000. Try it and see. COMPOUND ADDITION, IS the adding of several numbers together, having dif ferent denominations, but of the same generic kind, 110 pounds, shillings and pence, &c. Tuns, hundreds, quar. ters, &c. RULE.-1. Place the numbers so that those of the same denomina tion may stand directly under each other. 2. Add the first column or denomination together, as in whole num. bers; then divide the sum by as many of the same denomination av make one of the next greater; setting down the remainder under the column added, and carry the quotient to the next superior denomination, continuing the same to the last, which add, as in simple addition.* 1. STERLING MONEY, Is the money of account in Great-Britain, and is reckoned in Pounds, Shillings, Pence and Farthings. See the Pence Tables. * The reason of this rule is evident: For, addition of this money, as I in the pence is equal to 4 in the farthings; 1 in the shillings, to 12 in the pence; and 1 in the pounds, to 20 in the shillings; therefore carrying as di rected, is the arranging the money, arising from each column, properly in the scale of denominations : and this reasoning will hold good in the ad. dition of compound numbers of any denomination whatever. EXAMPLES. What is the sum total of 471. 13s. bd.-191. 2s. 91d.-141. 10s. 114d. Thus and 121. 9s. 1 d. 14 10 12 9 Answer, £. 93 16 (3.) 41 11. Find the amount of the following £. s. d. sums, viz. 421. 13s. 5d.-111. 10s.-41. 17s. 82.-131. Os. 7d.-195. 4id.-271. and 151, 6s, Ans. £. 1157 0. 12. Add 3041. 58. and 0.d.-341. 19s. 7d.—71. 18s. 5d -2472. Os. Ild.-195. 6d. Iqr. and 45l. together. Ans. £. 640 3s. 5 d. 13. Find the sum total of 141. 19s. 60.-111. 4s. 90.251. 10s.-41. Os. 60.-31. 5s. 8d.-19s. 6d. and 0s. 6d. Ans. £. 60 Os. 5d. 14. Find the amount of the following sums, viz. Forty pounds, nine shillings, £. d Sixiy-four pounds and nine pence, Ninety-five pounds, nineteen shillings, Seventeen shillings and 4;d. Ans. £. 201 fis. 1d 13. How much is the sum of Ans. £. 10 Os. 10 d. 16. Bought a quantity of goods for 125l. 10s.; paid for truckage, forty-five shillings, for freight, seventy-nine shil lings and sixpence, for duties, thirty-five shillings and ter pence, and my expenses were fifty-three shillings and nine pence; what did the goods stand me in ? Ans. £. 136 4s. ld. 17. Six men took a prize, and having divided it equally amongst them, each man shared two hundred and forty pounds, thirteen shillings and seven pence; how much money did the whole prize amount to ? Ans. £. 1444 is. 6d 2. TROY WEIGHT. oz. put. 16. oz. put. 16 11 19 23 8 11 19 4 4 16 21 6 10 16 8 8 8 19 14 7 8 17 21 6 9 14 17 4 6 8 23 7 10 7 9 7 14 17 7 11 12 7 9 13 10 |