199. REDUCTION OF WHOLE NUMBERS OF LOWER DENOMI NATIONS TO THE FRACTION OF A HIGHER DENOMINATION. ILL. EX., I. Reduce 5 s. 3 d. 3 qr. to the fraction of a £. ILL. EX., II. Reduce 7 oz. 6 pwt. 16 gr. to the fraction of a lb. Hence the To reduce whole numbers of lower denominations to the fraction of a higher denomination: Reduce the number of the lowest denomination to a fraction of the next higher. Annex it to the number of that higher denomination, and change the mixed number thus obtained to an improper fraction. Reduce as before, and thus continue as far as desired. EXAMPLES. Reduce 1. 6 s. 3 d. to the fraction of a £. 2. 3 p. 6 qt. 1 pt. to the fraction of a bu. 3. 1 qt. 0 pt. 1 gi. to the fraction of a gall. 4. 1 3,2 3, 29, to the fraction of a lb. Ans. L Ans.bu. 5. 5 cwt. 1 qr. 16 lb. 10 oz. to the fraction of a T. 6. 6 fur. 2 r. 2 y. 1 ft. to the fraction of a m. 9. 1 A. is 2 R. 1 r. 24 sq. y. 6 sq. ft. 108 sq. in.? 10. 1 cu. yd. is 13 cu. ft. 864 cu. in.? 11. 1 cd. is 5 cd. ft. 4 cu. ft. 576 cu. in.? 12. 1 c. y. is 162 d. 5 h. 20 m.? 13. 1 1. y. is 146 d. 9 h. 36 m.? 14. 1 J. is 250 d. 15 h. 21 m. 36 s.? y. 15. If 1 £ is worth $4.84, what is the value of 4 s. 6 d.? SOLUTION. 4 s. 6d. £. 1 £ $4.84,... 16. 3 pk. 2 qt. of meal at $.60 a bu.? 17. 2 qt. 1 pt. of kerosene oil at $.52 a gall.? 18. 62 lb. 8 oz. soap at $7.50 per cwt.? 19. 23, 1 3, 4 gr., quinine at $4.00 per 3? £ff of 20. How long will it take a man to travel 9 miles at the rate of 3 m. 6 f. 26 r. 3 yd. 2 ft. an hour? 21. At $60.00 an acre, what cost 2 A. 3 R. 134 sq. rd.? 22. At $9.00 a ton, what cost 1 T. 5 cwt. 2 qr. 14 lb. of coal? (Long ton.) 23. At $198 a lb., what cost 10 oz. 10 pwt. 10 gr. of gold? 24. The weight of a cubic foot of water being 62 lbs., how many pounds of water will a tank contain which measures 9 ft. 6 in. by 8 ft. 8 in., and is 6 ft. 9 in. deep? 25. A cubic foot of granite weighs 163 lbs. 5 oz.; what is the weight of a block 3 ft. 2 in. by 2 ft. 4 in. and 1 ft. 3 in. thick? For Dictation Exercises, see Key. Addition of Compound Numbers is the process of fir ding a number equal in value to two or more given compound numbers. The process is similar to addition of simple numbers. ILL. EX. What is the sum of 3 £ 11 s. 6 d. 3 qr., 4 £ 7 s. 8 d. 2 qr., 7 s. 6 d. 2 qr., and 9 £ 18 s.? OPERATION. 3 11 6 3 4 7 8 2 7 6 2 Writing the numbers, pounds under pounds, £. S. d. qr. shillings under shillings, &c., we commence by adding the numbers in the farthings' column, and find the amount=7 qr. 1 d. + 3 qr. Writing 3 in the farthings' place, we add the 1 d. with the column of pence, and have for the amount, 21 d. 1s. +9 d. Writing 9 in the 9 18 Ans. 18 £ 4 s. 9d. 3 qr. pence' place, we add the 1 s. with the shillings, and have 44 s. -2 £ +4 s. Writing 4 in the shillings' place we add the 2 £ with the column of pounds, and have for an answer, 18 £ 4 s. 9 d. 3 qr. Hence the Write the RULE FOR ADDITION OF COMPOUND NUMBERS. numbers of like denominations in the same column, and commence in adding with the numbers of the lowest denomination. Divide the amount by the number it takes of that denomination to make one of the next higher, write the remainder under the column, and add the quotient with the numbers of the next higher denomination. Add the next column in the same manner, and thus continue till all the numbers are added. |