OBS. 2. The numbers should be written one above the other, the lowest denomination at the top and the highest at the bottom, and ciphers annexed when necessary. 175. Reduce £15 10 s. 9 d. to the decimal of a £. 12 ) 9.00 The 9 pence is divided by 12, because 12 pence make 1 shilling. The quotient, 75, is annexed to the 10 shillings. This is divided by 20, because 20 shillings make £1. 176. Reduce 16 s. 9 177. Reduce 17 s. 178. Reduce 18 s. 5 EXAMPLES. d. to the decimal of a pound. d. to the decimal of a pound. 71 d. to the decimal of a pound. 179. Reduce £58 12 s. 62 d. to the decimal of a pound. 180. Reduce 2 oz. 14 dwt. 12 gr. to the decimal of a pound. 181. Reduce 2 qr. 17 lb. to the decimal of a hundred weight. 182. Reduce 1 R. 10rds. to the decimal of an acre. 183. Reduce 365 d. 5 h. 48 m. 51 sec. to the decimal of a day. 184. Reduce 3 qr. 3 n. to the decimal of a yard. 185. Reduce 20 fur. 4 yds. to the decimal of a mile. 186. Reduce 26 sq. rd. to the decimal of an acre. 187. Reduce 3 pks. 7 qts. to the decimal of a bushel. 188. Reduce 20 min. 35 sec. to the decimal of a degree. 189. Reduce 4h. 25 min. 34 sec. to the decimal of a day. 151. Shillings, pence, and farthings may also be reduced to a decimal of a pound in the following manner: Write half the number of shillings in the place of terths, and reduce the given pence and farthings to farthings, and if they amount to 24 or more, increase them by adding 1, and if there is an odd shilling, this sum is to be increased by 50, which must be written in the place of hundredths and thousandths. Thus 12 s. 9 d., reduced to the decimal of a pound, is .637. The half of 12 is 6, and 9 d., changed to farthings, gives 36, which being increased by 1, because it exceeds 24, is made 37. Thus written, the places of hundredths and thousandths give .637. 960 The reason of the above rule is obvious from the fact, that as there are 20 shillings in a pound, half of the number of shillings will express the tenths; and as 1 farthing is go of a pound, and 960, increased by of itself, is 1000, any number of farthings, increased by part of itself, will express so many thousandth parts of a pound. When the number of shillings is odd, 50 must also be added to the farthings, as 1 shilling is 188 of a pound. 24 0 OBS. When great accuracy is required, as many twenty-fourths of the farthings should be added to the farthings as there are farthings. 152. To change decimals to denominate numbers,-RULE. Multiply the decimal by that number which is required of the next lower denomination to make a unit of the higher, and point off as in decimal fractions. Proceed thus with the decimal in each product. The figures on the left of the decimal point in the several products will be the denominate numbers. ORS. If there be a decimal in the last product, it should be changed to a common fraction, which will denote a fractional part of the lowest denominate number. What is the rule for changing decimals to denominate numbers? 190. Reduce £.840625 to denominate numbers. .840625 16.812500 £. 12 9.750000 s. 3.000000 d. Multiply the decimal by 20, because 20 shillings make 1 pound. Point off from the right of the product six figures, as in the multiplication of decimals. Multiply the next decimal product by 12, because 12 pence make 1 shilling, and point off as before. Multiply the last decimal product by 4, because 4 farthings make 1 penny. The figures in the several products, at the left of the decimal point, are the denominate numbers, viz.: £16 9 s. 3 d. EXAMPLES. 191. Reduce £.78125 to denominate numbers. 192. Reduce £.61925 to denominate numbers. 193. Reduce £.15625 to denominate numbers. 194. Reduce .728125 of a pound Troy to denominate numbers. 195. Reduce .9642857 of a month to denominate numbers. 196. What is the value of .45 of a bushel? 197. What is the value of .4 of a yard? 198. What is the value of .96 of a cord? 199. What is the value of .864 of a rod? 200. What is the value of .765 of a mile ? 201. What is the value of .965 of a ton? 202. What is the value of .875 of an hour? DENOMINATE FRACTIONS. SECTION X. 153. DENOMINATE FRACTIONS may be changed from a higher denomination to a lower, and from a lower to a higher, in the same manner as whole numbers. 154. To reduce denominate fractions from a higher denomination to a lower, RULE. Multiply the fraction by the same numbers that are required to reduce a whole number of the same denomination as the fraction, to the lower denomination required, (ART. 141.) OBS. The numbers used as multipliers may first be changed to the form of an improper fraction, and factors common to the numerators and denominators may be cancelled. 1. Reduce £o to the fraction of a penny. The fraction is multiplied by 20 and 12, the same that are required in whole numbers, and the common factors are cancelled. EXAMPLES. 2. Reduce £1536 to the fraction of a farthing. T 3. Reduce £ to the fraction of a shilling. 30 4. Reduce 1400 of a lb. Troy to the fraction of a grain. What is the rule for reducing denominate fractions from a higher denomination to a lower? 3 5. Reduce 1 of a lb. Avoirdupois to the fraction of a dram. 6. Reduce 1 of a cwt. to the fraction of a lb. 1 1344 7. Reduce 582 of a ton to the fraction of a lb. 8. Reduce of an acre to the fraction of a rod. 3. 155. To change denominate fractions from a lower denomination to a higher, RULE. Divide the fraction by the same numbers that are required to change a whole number of the same denomination as the fraction, to the higher denomination required. OBS. The numbers used as divisors may be changed to improper fractions, and factors common to the numerators and denominators may be cancelled, 9. Reduce of a farthing to the fraction of a £. Dividing of a farthing by 4, 12, and 20, the same numbers that are required to change farthings to pounds, 5 is cancelled in the numerator, and as a factor of 20 in the denominators. EXAMPLES. 10. Reduce of a penny to the fraction of a £. 11. Reduce of a farthing to the fraction of a £. 12. Reduce of a grain to the fraction of a lb. Troy. 13. Reduce g of a dram to the fraction of a cwt. 14. Reduce of a nail to the fraction of a yard. 15. Reduce & of a minute to the fraction of a day. 16. Reduce of a foot to the fraction of a mile. What is the rule for changing denominate fractions from a lower denomination to a higher ? |