22. Express 33 of a cwt. in terms of a pound. 350 23. Reduce .145 cwt. to ounces. OPERATION. .145 × 100=14.5 lb.; 14.5 × 16 = 232 oz. Ans. 24. In .0003 weeks how many minutes? 25. In 6.35 miles how many feet? 26. In .1756 kilometers how many meters? 27. What part of a quart is .0015 of a hogshead? 28. How many mills in $15.69? 29. How many kilograms in 3.675 tonneaux? 30. How many square rods in .94375 of an acre? 247. To reduce from a lower to a higher denomination. 1. Let it be required to reduce 15130 pennyweights to pounds. OPERATION. 210) 15130 pwt. 12) 756.. 10 pwt. 63 lb. Ans. 63 lb. 0 oz. 10 pwt. Since in 20 pennyweights there is 1 ounce, in 15130 pennyweights there are as many ounces as 20 pennyweights are contained times in 15130 pennyweights, which are 756 times, and a remainder of 10 pennyweights. Since in 12 ounces there is 1 pound, in 756 ounces there are as many pounds as 12 ounces are contained times in 756 ounces, or 63 times. RULE. Divide the given number by the number of its denomination required to make one of the next higher, and reserve the remainder, if any. Proceed in like manner with the quotient, and so continue till the whole is reduced to the required denomination. The number of the required denomination, with the several remainders, if any, will be the answer. REVIEW QUESTIONS. What is a Denominate Number? (243) A Simple Denominate Number? (243) A Compound Denominate Number? (243) A Measure? (197) A Weight? (200) Explain the operation. Repeat the Rule. 11. 31556930 seconds to days. | 14. 2429 quarts to bushels. 12. 12244 pints to hogsheads. 13. 1129171 inches to miles. 15. 127916 drams to cwt. 16. 648000 seconds to degrees. 17. Reduce 33 pints to the fraction of a gallon. OPERATION. 34 = 24; 24 ÷ 2 = 42 qt.; 424 gal. Ans. = Since in 1 quart there are 2 pints, in 33=34 pints there are as many quarts as 2 pints are contained times in 24 pints, which are 12 times. Since, in 1 gallon there are 4 quarts, in 12 quarts there are as many gallons as 4 quarts are contained times in 12, which is & of a time. 18. Reduce 70 square rods to a fraction of an acre. 19. In 1 quarters how many yards? REVIEW QUESTIONS. Repeat the Table of Troy Weight. (203) The Table of Avoirdupois Weight. (204) Of Linear Measure. (205) Of Surface Measure. (210) What is a Surface (206) The area of a figure? (207) A Square? (209) A Rectangle? (210) 20. In 13920 minutes how many days? 21. What part of a pound is of a pennyweight? 22. Express of a pound in terms of a hundred-weight. 23. Reduce 232 ounces to a decimal of a hundred-weight. 232 ÷ 16 OPERATION. 14.5 lb.; 14.5 100.145 cwt. Ans 24. In 3.024 minutes how many weeks? 25. In 33528 feet how many miles? 26. In 175.6 meters how many kilometers? 29. How many tonneaux in 3675 kilograms? CASE III. rods. 248. To reduce a fraction of a given denomination to integers of lower denominations. 1. Let it be required to reduce of a pound Troy to equivalent integers. Since 1 pennyweight equals 24 grains, of a pennyweight equals of 24 grains, or 8 grains. Therefore, & of a pound Troy is equal to 10 oz. 13 pwt. 8 gr. RULE. Multiply the fraction by the number required of the next lower denomination to make one of its denomination, and reduce the result, if possible, to a whole or mixed number. Proceed in like manner with the fractional parts, if any, and so continue till reduced as required. Explain the operat n. Repeat the Rule. Examples. 2. Reduce of a furlong to equivalent integers.* 5. Find the value of 6. Find the value of of a degree. of a hundred-weight. 7. Reduce .282 of a ton to equivalent integers. It is often most convenient to multiply the decimal art, without re-writing it, as in the second operation. lb. 14.000 8. Reduce .875 of a hogshead to equivalent integers. 9. Reduce .4765625 of a mile to equivalent integers. 10. What is the value of .09375 of an acre? 11. Reduce 5.141 tons to equivalent integers. 12. What is the value of .761 of a day? CASE IV. 249. To reduce integers of lower denominations to a fraction of a higher denomination. 1. Let it be required to reduce 10 oz. 13 pwt. 8 gr. to an equivalent fraction of a pound. Explain the operation of example 1. *For answers, see corresponding examples in Case IV. weights equal 1 ounce, 40 pennyweights equal of 40, or of an ounce. Since 12 ounces equal.1 pound, 32 ounces equal of 32, or § of a pound. RULE. Reduce the number of the lowest denomination to a fraction of the denomination next higher, and write it as a fractional part of the number of that higher denomination Reduce the number thus formed, in like manner as before, and so continue till all the numbers are reduced as required. Examples. 2. Reduce 35 rd. 3 yd. 2 in. to an equivalent fraction of a furlong. 3. Reduce 2 qt. 1 pt. 1 gi. to an equivalent fraction of a hogshead. 4. Reduce 3 d. 4 h. to an equivalent fraction of a week. 5. Reduce 21' 25" to an equivalent fraction of a degree. 6. Reduce 2 qr. 20 lb. 13 oz. 53 dr. to an equivalent fraction of a hundred-weight. 7. Reduce 5 cwt. 2 qr. 14 lb. to an equivalent decimal of a The second operation, which is an abridged form of the first, is gen erally preferred, on account of its conciseness. 8. Reduce 55 gal. O qt. 1 pt. to an equivalent decimal of a hogshead. 9. Reduce 3 fur. 32 rd. 8 ft. 3 in. to an equivalent decimal of a mile. What is the Rule? Explain the operation. |