parcels of 4 each, and 3 remaining, and the 10135 parcels of 4 each are again made into 844 parcels containing 12 parcels of 4 each, or 48 and 7 parcels over, containing 4 each or 28: the 844 parcels of 48 each are again divided into 42 parcels containing 20 parcels of 48 each, and 4 parcels of 48 each over. Therefore there are 42 parcels of 960 each, 28 parcels of 48 each, 7 of 4 each, and 3 single ones, i.e., the result 42 is the quotient of 40543 divided by 960, and (4 x 12 x 4) + (7 × 4) + 3 or 223 oyer. EXAMPLES. XI. Divide (by factors): 1. 53648973 by 36. 9. 9156787 by 756. 10. 537689797 by 1296. If the divisor terminates with cyphers: Cut off the cyphers from the divisor, and as many figures from the right of the dividend as there are cyphers in the divisor; place the remainder to the left of the figures cut off from the dividend. Thus, 42762 divided by 7800. 78,00)427,62(5 390 37 Ans. 5 and 3762 remainder. PROOF. Cutting off the two cyphers we divided 7800 by 100, and 42762 is divided by 100 by cutting off the 62; the quotient will therefore not be altered, since both divisor and dividend have been divided by the same number. The re mainder 37 is the result of 42 thousands and 7 hundreds, being divided by 7 thousands and 8 hundreds, and therefore is 3 thousands 7 hundreds, to which, if we add the 62 cut off, we shall have 3 thousands, 7 hundreds, and sixty-two, i.e., 3762. EXAMPLES. XII. Divide : 1. 8213 by 20. 2. 726004 by 200. 3. 868642 by 720. 4. 769824 by 86400. 10. 7562000001 by 825000. PAPER No. 2. 1. Find the sum of 321, 8021, 73250. 2. Find the difference between 213624 and 990217. 4. Express in figures, one trillion, one million and five. 5. Multiply 8217 by 3. 6. Multiply 72184 by 321. 7. Divide 427 by 4. 8. Divide 836217 by 800. 9. Divide 7283 by 36, by factors, and write a proof showing the correctness of the remainder. 10. How many times is 28345 contained in 94486? REDUCTION. QUANTITIES expressed by numbers are of many names, as 2 pounds, 3 ounces, 4 miles. Names are distinguished as higher and lower. MONEY. The names of English money are four pound, shilling, penny, farthing. £ marks pounds, s. shillings, d. pence, q. farthings. Thus: £2 13s. 3d. 3q. (or ), stands for 2 pounds, 13 shillings, 3 pence and 3 farthings. 1 farthing is written d, 2 farthings or a halfpenny d, three farthings ad. A groat = 4d., a crown = 5s., a noble = 6s. 8d., an angel = 10s., a mark=13s. 4d., a sovereign=20s., a guinea=21s., a moidore = 27s. Used for gold, silver, jewels, and costly articles. In gold, mixed with alloy, 22 carats or 18 carats fine, means 22 or 18 parts of pure gold in 24: the former is the old and the latter the new standard. This weight is used in almost all commercial transactions. = 5280 ft. 1760 yds. = 1 ml.: 220 yds. =1 fur. Among mechanics the inch is divided into eighths, by officers of the revenue and by scientific persons it is divided into tenths, hundredths, etc. Formerly it was divided into 12 lines. A chain (100 links)=66 ft.; 1 ac. (10 sq. chains) = 100000 sq. links. 1728 cubic inches (cub. in.) = 1 cubic foot (cub. ft.) 27 cub. ft. =1 cubic yard (cub. yd.) A cubic foot of water weighs 1000 ozs. = 624 lbs. |