D. 1. 167 is 3 of what number? Solution. If 167 is of some number, of that number must be 4 of 167, which is 55}, and for the number must be 5 times 553.5 times 55 are 275, and 5 times are 1, or 31, which added to 275 are 2784. Therefore, 167=of 2784. 2. 229 s of what number? 3. 621 % of what number? 4. 81 s of what number? 5. 254 of what number? 6. 281 of what number? 7. 329 of what number? 8. 117 of what number? 9. 37 of what number? 10. 71 # of what number? 11. 311 ã of what number? 12. 87 ☆ of what number? 13. 358 : 23 times what number? 14. 418 : 14 times what number? 15. 615 =2} times what number? 16. 93 1 times what number? 17. 834 = 41 times what number? E. 1. How many are 9 times 268 ? Solution. 9 X 268=9 X 200 +9 X 60+9X8=1800 + 540 + 72 = 2412. 2. How many are 7 X 327? 5 X 861 ? 9 x 468 ? 3. How many are 4 X 813? 2 x 917? 6 X 321 ? 4. How many are 8 x 612? 3 X 999 ? 5 x 875 ? 5. How many are 6 X 348 ? 8 X 527 ? 9 X 813 ? 6. How many are 8 X 465 ? 2 X 981 ? 7 x 387 ? 7. How many are 8 X 837 ? 4 X 958? 6 X 372 ? 8. How many are 3 x 119 ? 4 X 549 ? 4 x 591 ? 9. How many are 4 X 217 ? 6 X 459 ? 9 X 645 ? 10. How many are 4 X 279? 4 X 729 ? 4 X 927 ? 11. How many are 9 x 578? 9 X 758? 9 X 875 ? = 349. F. 1. 1396 how many times 4? Solution. 1396 = 4 = 1200 + 4 + 160 = 4 + 36 • 4 = 300 + 40 + 9 Another Solution. 4 is contained in 1200, 300 times, in 160, 40 times, and in 36, 9 times. Therefore, 1396 = 349 times 4. Another Solution. 4 is contained in 1300, 400 times with a remainder of 1 hundred, or 10 tens, which added to 9 tens make 19 tens. 4 is contained in 19 tens, 4 tens times with a remainder of 3 tens, or 30 units, which added to 6 units are 36 units. 4 is contained in 36, 9 times. Therefore, 1396 = 349 times 4. Note. The only object of the above forms of solution is to explain the nature of the process; when that is well understood, the explanation should be dropped, and results only named. Thus, in performing the above division, the pupil need only say, 664 is contained in 1396, 3 hundreds 4 tens and 9 units times, or 349 times.” After a little practice in this way, the final result may be named at once. Thus, « 1396 = 349 times 4." 2. 1404 - how many times 9 ? 4? 3? 6? 8? 7 ? 5? 2? 3. 2826 how many times 3 ? 6? 9? 8? 7 ? 10 ? 2 ? 5? 4. 2873= how many times 5 ? 8? 9? 3? 7? 4? 6? 10 ? 5. 1328=how many times 6 ? 9? 3? 10 ? 7? 4? 8? 5? 6. 3418= how many times 8? 9? 3? 7? 5? 2? 6? 4? 10 ? 7. 4176 = how many times 4? 6? 8? 2? 3? 5? 7? 9? 10 ? G. 1. 2 cwt. 1 qr. 23 lb. = how many pounds ? Solution. Since 1 cwt. = 4 qr., 2 cwt. must equal 2 times 4 qr., or 8 qr., to which adding 1 qr., we have 9 qr. as the value of 2 cwt. 1 qr. Since 1 qr. = 28 lb., 9 qr. must equal 9 times 28 lb., or 252 lb., to which adding 23 lb., we have 275 lb. Therefore, 2 cwt. 1 qr. 23 lb. = 275 lb. 2. 3 dwt. 16 gr. how many grains ? 3. 7 da. 19 h. how many hours ? 4. 1 cwt. 3 qr. 17 lb. how many pounds ? 5. 6s. 8d. 2qr. ow many farthings? 6. 6 lb. 4 oz. = how many drams? 7. 2 3. 2 3. 2 3. 15 gr. how many grains ? 8. 1 sq. yd. 36 sq. in. how many square inches ? 9. 9 cu. yd. 18 cu. ft. how many cubic feet ? how many 10. 275 lb. how many cwt. dr. and lb. ? Solution. Since 28 lb. 1 qr., 275 lb. must equal as many quarters as there are times 28 lb. in 275 lb., which are 9 times with a remainder of 23 lb. But since 4 qr. =1cwt., 9 qr. must equal as many cwt. as there are times 4 qr. in 9 qr., which are 2 times with a remainder of 1 qr. Therefore, 275 lb. =2 cwt. 1 qr. 23 lb. 11. 88 gr. dwt. and gr. ? 12. 213 lb. how many and cwt. ? 13. 187 hours hours and days ? 14. 322 qr. how many s. d. and qr. ? 15. 1600 drams how many lb. and oz. ? 16. 175 gr. = how many 3, 5, and gr. ? 17. 1332 sq. in. how many sq. yd. and sq. in. ? 18. 311 qt. how many bu. pk. and qt. ? 19. 255 gills how many gal. qt. pt. and gi. ? 20. 958 gr. = how many 3, 3, 5 and gr. ? qr. how many How many H. 1. Sold 7 acres of land at 48 dollars per acre, and received in payment 9 cows at 27 dollars a piece, and the rest in money. How much money did I receive ? I invested the money thus received in apples at 3 dollars per barrel. How many barrels did I buy? 2. Gave 9 lots of pasture land, each lot containing 87 acres, for 5 lots of tillage, each lot containing 64 acres. acres of land did I give ? How many did I receive ? How many more did I give than receive ? 3. A drover bought 7 oxen for 47 dollars apiece; he sold them for 413 dollars. How many dollars did he get for each ox? How many dollars did he gain on each ? How many dollars did he gain on all of them? He spent 8 dollars of the money he received for the oxen, and gave the rest of it for 9 cows, but being unfortunate he was obliged to sell the cows for 31 dollars apiece. How many dollars did he lose on each cow ? How many on all ? How many dollars did he receive for all the cows ? 4. A man gave f of 672 dollars for 4 diamond rings. What would 9 rings cost at the same rate ? 5. Joseph has 5 pieces of rope all of the same length, and Samuel has 1 piece 336 feet in length. By measuring they find that of Samuel's rope is just equal in length to 2 of Joseph's pieces. How many feet of rope are there in all of Joseph's pieces ? 6. A man bought a quantity of sugar. He sold 378 pounds of it, and then found that of what he had sold was equal to of what remained unsold. How much remained unsold ? 7. Gave 9 casks of raisins, each cask containing 96 lb., for 8 cwt. of dates. How many lb. of raisins would 7 cwt. of dates be worth at the same rate ? 8. Edmund had a little basket that held just 76 chestnuts. He lent it to Ralph and Edgar, on condition that they should give him chestnuts enough to fill it 6 times to pay for the use of it. It turned out that Ralph used the basket just 3 times as much as Edgar. How many chestnuts ought Edgar in justice to pay ? Ought Ralph ? 9. A man gave of 432 dollars for & of an acre of land. What would an acre have cost? ģ of an acre of this land is worth only % of what the same man gave for a fast horse. How much did he give for his fast horse? What he gave for the fast horse is 20 dollars less than of the money he owes. How much money does he owe? 10. Bought 7 bags of coffee, each bag containing 45 lb. and 5% bags, each bag containing 57 lb. How many pounds of coffee did I buy in all ? 11. Bought 37 pieces of cloth each piece containing 96 yards, 4 pieces each piece containing 75 yards, and 24 pieces each piece containing 91 yards. How many yards did I buy? 12. Gave 7 bags of corn at 96 cents per bag, for 8 bushels of wheat. How many cents would 7 bushels of wheat cost at the same rate ? 13. Seth put 48 bushels of wheat into bags, each bag containing 3 pecks. How many bags did it take? 14. John put 20 lb. 12 oz. of candy into 4 oz. packages. How many packages did it take ? 15. Abner put 30 lb. 12 oz. of mustard into 6 oz. canisters. How many canisters did it fill? 16. How many times must a chain 4 rods in length be laid down to measure a distance of 7 furlongs, 32 rods ? 17. If to 4 of all the money Ellery has, 24 dollars be added, the sum will be 114 dollars. How much money has he? 18. A man being asked the distance from Albany to Syracuse, replied, “It is 109 miles from Albany to Rome, and the distance to Rome is 2 miles less than of the distance to Syracuse." How far is it from Albany to Syracuse ? 19. On the Ohio river it is 183 miles from Pittsburg to Ma. rietta, and from Pittsburg to Wheeling it is 28 miles less than of this distance. How far is Wheeling from Pittsburg ? from Marietta ? 20. From Pittsburg to Marysville it is 426 miles, and 13 times this distance is 12 mile more than the distance from Pittsburg to Cincinnati. How far is it from Pittsburg to Cincinnati ? from Cincinnati to Marysville ? 21. It is 630 miles from Pittsburg to New Albany, and of this distance is 69 miles less than of the distance from Pittsburg to Louisville. How far is it from Pittsburg to Louisville ? 22. 43 of the distance from Pittsburg to New Albany is 57 miles more than f of the distance from Pittsburg to the mouth of the Wabash. How far is it from Pittsburg to the mouth of the Wabash ? 23. Add f of the distance from Pittsburg to New Albany to of the distance from Pittsburg to Marysville, and the sum will be. 19 miles more than of the distance from Pittsburg to Cairo, at the mouth of the Ohio. How far is Cairo from Pittsburg ? from Marysville ? 24. Wheeling is 94 miles from Pittsburg, and 28 miles less than of the distance of Marietta from Pittsburg: How far is Marietta from Pittsburg ? from Wheeling? 25. Cincinnati, which is 485 miles from Pittsburg, is 12 miles less than 14 times the distance of Marysville from Pittsburg. How far is Marysville from Pittsburg ? from Cincinnati ? 26. Louisville is 627 miles from Pittsburg, and if 69 miles be subtracted from 4 of this distance, the remainder will be of the distance of New Albany from Pittsburg. How far is New Albany from Pittsburg ? 27. The mouth of the Wabash river is 880 miles from Pittsburg, and is of this distance is 57 miles less than 43 of the distance from Pittsburg to New Albany. What is the distance from New Albany to Pittsburg according to this statement ? What is the distance from New Albany to the mouth of the Wabash ? 28. Cairo is 1022 miles from Pittsburg. Prove, by using results found in the 26th and 27th examples, that of this distance is 19 miles less than the sum obtained by adding of the distance from Pittsburg to New Albany, to į of the distance from Pittsburg to Marysville. 29. What do the last five examples show concerning the answers you obtained to the 19th, 20th, 21st, 22d, and 23d examples ? |