Contractions in Division. When the divisor is such a number, that any two figures in the Table, being multiplied together, will produce it, divide the given dividend by one of those figures ; the quotient thence arising by the other; and the last quotient will be the answer. Note. The total remainder is found by multiplying the last remainder by the first divisor, and adding in the first remainder. 2258_7 63 first rem. +? True Quotient 225841. True rem. Cat 2. Divide 178464 by 16. Ans. 11154. 3. Divide 467412 by 24. Ans. 1947544 4. Divide 942341 by 35. Ans. 269243'5. 5. Divide 79638 by 36. Ans. 2212 6. Divide 144872 by 48. Ans. 3018 7. Divide 937387 by 54. Ans. 1735934 8. Divide 93975 by 84. Ans. 111894. 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 dividend as there are ciphers in the divisor, and these figures so cut off are the remainder; and the other figures of the dividend are the quotient. EXAMPLES. 1. Divide 365 by 10. Ans. 36 and 5 remains. 2. Divide 5762 Ans. 57 62 rem. 3. Divide 763753 by 1000. Ans. 763 753 rem. SUPPLEMENT TO MULTIPLICATION. To multiply by a mixt number; that is, a whole number joined with a fraction, as 81, 5., 6., &c. RULE.-Multiply by the whole number, and take 4, 3, 4, &c. of tac multiplicand, and add it to the product. EXAMPLES. Multiply 48 by 23. 2)37 48 234 23 18! 111 24=; 74 869Answer. 3. Multiply 211 by 501 4. Multiply 2464 by 84. 5. Multiply 345 by 191 6. Multiply 6497 by 54. 132 Ans. Ans. 10655. Ans. 20533 Ans. 6598 Ans. 33413.. Questions to exercise Multiplication and Division. 1. What will 9 tuns of hay come to, at 14 dollars a tun ? Ans. $136. 2. If it take 320 rods to make a mile, and every rod coutains 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. 98637. 4. In 276 barrels of raisins, each 3; cwt. how many hundred weight ? Ans. 966 cwt. 5. In 36 pieces of cloth, each piece containing 241 yards; how many yards in the whole ? Ans. 873 yds. 6. What is the product of 161 multiplied by itself? Ans. 25921. 7. If a man spend 492 dollars a year, what is that per calendar month ? Ans. $41. 8. A privateer of 65 men took a prize, which being equally divided among them, amounted to 1191. per man ; Ans. £7735. what is the value of the prize ? D 9. What number multiplied by 9, will make 2253 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. per yard ? Ans. 275. 12. What cost 45 oxen, at 81. per head? Ans. £360. 13. What cost 144 lb. of indigo, at 2 dols. 50 cts. or 250 cents per lb. Ans. $360. 14. Write down four thousand six hundred and seventeen, multiply it by twelve, divide the product by nine, and add 365 to the quotient, then from that sum subtract five thousand five hundred and twenty-one, and the remainder will be just 1000. Try it and see. COMPOUND ADDITION, IS the adding of several numbers together, having dif ferent denominations, but of the same generic kind, as pounds, shillings and pence, &c. Tuns, hundreds, quar ters, &c. RULE.-1. Place the numbers so that those of the same denomina. tion may stand directly under each other. 2. Add the first column or denomination together, as in whole numbers; then divide the sum by as many of the same denomination as make one of the next greater ; setting down the remainder under the column added, and carry the quotient to the next superior denomination, continuing the same to the last, which add, as in simple addition.* 1. STERLING MONEY, Is the money of account in Great-Britain, and is reckoned in Pounds, Shillings, Pence and Farthings. See the Pence Tables. * The reason of this rule is evident: For, addition of this money, as 1 in the pence is equal to 4 in the farthing$; 1 in the shillings, to 12 in the pence; and 1 in the pounds, to 20 in the shillings; therefore carrying as directed, is the arranging the money, arising from each column, properly in the scale of denominations : and this reasoning will hold good in the addition of compound numbers of any denomination whatever. EXAMPLES. S. d. What is the sum total of 471. 13s. 13 6 6d.-191. 2s. 9ad.-141. 10s. ilad. 2 9 and 12. 9s. lid. Thus 14 10 111 12 9 13 Answer, ఓ. 93 16 4} (3.) (4.) d. ( లుంటే edaram Emmano -ఆ-688 ---- S. 11. Find the amount of the following ఓ. d. sums, viz. 42l. 13s. 5d.-111. 10s. 4. 17s. Bd.-131. 0s. 7d.-19s. 4Id. 271. and 151. 6s. Ans. ఓ. 11570! 12. Add 3041. 5s. and Old.-341. 19s. 7d.—71. 18s. 5d -2471. Os. 11d.-19s. 6d. Igr. and 45l. together. Ans. £. 640 3s. 5 d. 13. Find the sum total of 141. 19s. 60.-111. 4s. 9d. 251. 10s.- 41. Os. 6d.31. 5s. 8d.-19s. 6d..and Os. 6d. Ans. £. 60 Os. 5d. 14. Find the amount of the following sums, viz. Forty pounds, nine shillings, £. Ans. £. 201 6s. lld 1 15. How much is the sum of Thirty-seven shillings and sixpence, Thirty-nine shillings and 4 d. Forty-four shillings and nine pence, 'Twenty-nine shillings and three peuce, Fifty shillings, Ans. £. 10 Os. 10 d. 16. Bought a quantity of goods for 1251. 10s.; paid for truckage, forty-five shillings, for freight, seventy-nine shillings and sixpence, for duties, thirty-five shillings and ten pence, and my expenses were fifty-three shillings and nine pence; what did the goods stand me in? Ans. £. 136 4s. Id. 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; hoiv much money did the whole prize amount to? Ans. £. 1444 ls. 6d 2. TROY WEIGHT. lb. oz. pwt. gr. lb. oz. pot. gr. 16 11 19 23 8 11 '19 21 4 4 16 21 6 10 16 8 8 8 19 14 7 8 17 21 6 9 14 17 4 6 8 23 4 7 10 7 9 7 14 17 0 7 11 12 7 9 13 10 |