A. Yes, agreeably to the decimal scale it has 10, or a multiple of 10 for its denominator, and by division it can be reduced to a still higher name. CASE II. To reduce a decimal of a higher name to a lower. Q. How is this kind of reduction performed? A. We multiply the decimals by so many as make one of a lower denomination, and point off the decimals as already observed in multiplication. The figures which remain on the left of the period, when the proper number is separated for decimals will constitute, the whole number of this denomination. Q. Can the decimal part be still reduced? A. Yes, if there be lower denominations, multiply it by the number which is equal to one of the next denomination, and proceed as before. AVOIRDUPOIS WEIGHT. CASE I.-To bring a lower denomination to a higher. 1. Reduce 8 cwt. to the decimal of a ton. ILLUSTRATION. The highest denomination mentioned is a ton, which is 20 cwt. then the fraction will be expressed thus: 8 20 or, agreeably to question 8, annex two ciphers to the numerator 200 = .40 Ans. Ans. .35 66 .25 ❝.125 2. Bring 7 cwt. to the decimal of a ton? 3. Bring 5 cwt. to the decimal of a ton? 4. Bring 14 lbs. to the decimal of a cwt? 5. Bring 21 lbs. to the decimal of a cwt? Ans. .1875 6. Bring 3 quarters to the decimal of a cwt. " 7. Bring 2 qrs. 14 lbs. to the " of a cwt." 8. Bring 5 ounces to the decimal of a lb. .75 .625 .3125 CASE II. To reduce a decimal of a higher name to a lower. 1. Bring.4 of a ton to its 20 proper value? 8.0 Answer 8 cwt. value? proper 2. Reduce .35 of a ton to its proper value? Ans. 7 cwt. 3. Reduce .25 of a ton to its 66 5 " 4. Reduce .125 of a cwt. to its proper value?" 14 lbs. 5. Reduce .1875 of a cwt. to its proper value?"21" 6. Reduce .75 of a cwt. to its proper value?" 7. Reduce .625 of a cwt, to its proper value? 3 qrs. Ans. 2 qrs. 14 lbs. 8. Reduce .3125 of a lb. to its proper value? Ans. 5 oz. APOTHECARIES WEIGHT. CASE I.—Bringing a lower number to the decimal of a higher. 1. Bring 8 ounces to the decimal of a pound? 2. Reduce 2 scruples to the decimal of a pound? Ans. .00794 3. Reduce 18 grains to the decimal of an ounce? LAND MEASURE. Ans. .0.0375 = CASE I. 1. Reduce 20 perches to the decimal of an acre? 2. Reduce 32 perches to the decimal of an acre? Ans. .125 Ans. .20 3. Reduce 16 perches to the decimal of an acre? Ans. .0.10 4. Reduce 2 roods, 32 perches, to the decimal of an acre? Ans. .7 5. Reduce 3 roods, 20 perches to the decimal of an acre? Ans. .875 6. Reduce 3 roods, 35 perches to the decimal of an acre? Ans. .96875 CASE II. 1. Bring .125 decimal of an acre to its proper value? Ans. 20 perches. 2. Bring .20 of an acre to its proper value? Ans. 32p. 3. Bring .60 of an acre to its proper value? Ans. 2 roods, 16 perches. 4. Bring .96875 of an acre to its proper value? Ans. 3 roods, 35 perches. 5. Bring .45 of an acre to its proper value? 6. Bring .40 of an acre to its proper value? Ans. 1 rood, 32 perches. Ans. 1 rood, 24 perches. 2 CLOTH MEASURE. CASE I. 1. Reduce 2 quarters and 2 nails to the decimal of a yard? Ans. .625 2. Reduce 3 quarters and 3 nails to the decimal of a yard? Ans. .9375 3. Reduce 1 quarter and 1 nail to the decimal of a yard? Ans. .3125 CASE II. 1. Bring .625 of a yard to its proper value? Ans. 2 grs. 2 nails. 2. Bring .9375 of a yard to its proper value? Ans. 3 qrs. 3 nails. 3. Bring .3125 of a yard to its proper value? Ans. 1 qr. 1 nail. 4. Bring .865 of a yard to its proper value? Ans. 3 qrs. 2 nails. 5. Bring .375 of a yard to its proper value? Ans. 1 qr. 2 nails. APPLICATION. 1. What will 3.875 acres come to at $10 per acre? Ans. $38.750 2. What will 15 125 acres cost at $30.75 per acre? Ans. $465.093 3. What will 10.625 cwt. of iron cost at $5.25 pr. cwt? 4. What will 10.1875 cwt. 66 5. What will .125 cwt. 66 Ans. $55.781 cost at $5.35 per cwt? Ans. $54.503 cost at $7.10 per cwt? Ans. .887 6. What will .3125 lbs. of tea come to .87c.5m. per lb? Ans. .273 7. What will .35 of a ton come to at $96.50 per ton? 8. What will .4 of a ton cost at $95 per Ans. 33.775 ton? Ans. $38.00 9. What will .625 of a yard cost at $4.50 per yard? Ans. $2.812 10. What will .875 of a yard cost at 37c. 5m. per yard? Ans. .328 11. What will .8 of an English Ell cost at $3.25 pr. yd? Ans. $3.25 12. What will,1875 of a yard cost at $5.00 per yard? Ans. .937 13. What will .375 of a ton cost at $80 pr. ton?" $30 14. What will .859375 bushels come to at $1.3125 per bushel? Ans. $1.128 15. What will .875 lb. avoirdupois cost at 15c. per lb? Ans. .131 16. What will 3.75 gal. cost at 33c. pr. gal.?" 1.237 17. What will .125 gals. 18. What will 333.75 ft. of boards come to at 3c. .375 66 CC .047 pr. Ans. $10.012 ft? 19. What will 331 dozen buttons cost at 87c. 5m. per dozen? Ans. $29.385 LECTURE VII. ON REDUCTION. Reduction admits of MULTIPLICATION and DIVISION, and of course, the signs x and are understood, when used in reference to these rules. REDUCTION Shows, how we of names in use, Réduction, in other words, is an application of Multiplication and Division: when higher quantities are reduced to lower, as years to seconds, Multiplication is used and the operation is called Reduction descending. ILLUSTRATION. Suppose we bring 1 year to months; we know agreeably to the law of increase, that the operation is performed by multiplication; hence, we multiply by 12, to bring years to months. On the contrary, division is used in reducing lower names to higher, as when we want to reduce (lbs.) pounds to hundreds, (or cwts.) we divide the pounds by 28, to bring them to quarters, the quarters by 4, to bring them to cwts. This reduction is called reduction ascending. FEDERAL MONEY, OR UNITED STATES CURRENCY. |