18. 180= 1 times what number? 19. 180= 4 times what number? 20. 640= 24 times what number? 21. 350= 5 times what number? 22. 210= 44 times what number? G. 1. 9 × 20+ 60, ÷ 40, × 5, × 7+90, ÷ 5,÷ 3, ÷ 4, X 8, × 7, + 40 = how many times 8? 10, 2. 309060+ 50+40,9330,÷4, x7+ 80, X 70-20= how many times 6? 3. 8109-30, x 6, +9 x 40, 90, 30, X 50 = how many times 30? 80, 9×9+ 4. 5 × 70 + 50 + 80, ÷ 6, ÷ 4, × 7 + 3 × 30 + 310,÷6, ÷ 30, × 10, X 6 = how many times 90 ? 5. 10 X 7 X 7+70,8 20, x 5+ 70, 40, X 5, × 9, ÷ 6, ÷ 3, × 9 = how many times 9 ? 6. 10 × 3 × 3 × 3 + 30, ÷ 60, × 6, × 6, ÷ 2, × 7 +70,÷70, × 5, × 5, 40= how many times 70? 8. 7 of 720 + 3% of 250, ÷ & of 280, × of 210 + § of 100 how many times 80 ? 9. 4 of 280 × 5% of 150 — 8 × 60, ÷ of 210, × † of 180+40= how many times 60? H. 1. I bought of Mr. Grover 3 lb. of cloves at 50 cents per lb., 4 lb. of cinnamon at 40 cents per lb., and 7 lb. of citron at 40 cents per pound. What was the amount of my purchase? Gave in payment 5 bushels of potatoes at 90 cents per bushel, and paid the rest in butter at 20 cents per lb. How many lb. of butter did I give ? 2. Rode 8 hours at the rate of 20 miles per hour, 9 hours at the rate of 10 miles per hour, and 4 hours at the rate of 30 miles per hour. How many miles did I ride? On my return I rode 180 miles at the rate of 30 miles per hour, 50 miles at the rate of 10 miles per hour, and the remaining distance at the rate of 20 miles per hour. How many hours was I returning? 3. A farmer gave a trader 40 lb. of cheese at 9 cents per lb. for cloth at 60 cents per yard, 30 ib. of cheese at 8 cents per lb. for rice at 6 cents per lb., and 4 dozen eggs, at 20 cents per dozen, for sugar at 8 cents per lb. How many yards of cloth did the farmer receive? How many lb. of rice? How many lb. of sugar? 4. During the first week in February, Mr. Hamilton earned 60 cents per day; during the second he earned 90 cents per day, during the third he earned 70 cents per day, and during the fourth he earned 80 cents per day. How much did he earn in the month, there being 6 working days in a week? 5. A farmer exchanged 7 acres of land worth 60 dollars per acre, for land worth 50 dollars per acre. How many acres did he receive? 6. Gave 8 bushels of corn at 60 cents per bushel, for potatoes at 50 cents per bushel. How many bushels of potatoes did I receive? 7. Gave 9 yoke of oxen worth 70 dollars per yoke, and a calf worth 10 dollars, for ploughs at 8 dollars apiece. How many ploughs did I receive? Sold sixty of the ploughs at 9 dollars apiece and the rest at 8 dollars apiece. What did I receive for them all? How much did I gain by the transaction? 8. If a bushel of potatoes weighs 40 lb., and a bushel of wheat weighs 60 lb., how much more will 8 bushels of wheat weigh than 9 bushels of potatoes? 9. A shoemaker gave 9 pairs of shoes worth 80 cents per pair, for 6 gallons of molasses at 30 cents per gallon, and sugar at 9 cents per pound. How many lb. of sugar did he receive? 10. A bushel of clover-seed weighs 60 lb., and 63 bushels of clover-seed weigh as much as 8 bushels of salt. How much does a bushel of salt weigh? 11. A man bought 94 gallons of brandy at 70 cents per gallon. He took out 14 gallons for his own use, and then sold the rest for what the whole of it cost him. For what did he sell it per gallon? 12. Worked 6 days at 80 cents per day, and received in payment 6 yards of cloth. I sold 4 yards of the cloth at cost. How much did I get for it? 13. George is 20 years of age and his father is 3 times as old. How old is his father? 4 times George's age added to 8. times his father's age, is equal to 7 times the age of his Uncle William. How old is his Uncle William ? 14. Mr. Crane and Mr. Snow were asked how old they were. Mr. Snow replied, "I am 20 years older than Mr. Crane, and 7 times the difference between our ages is three times my age.' How old was Mr. Snow? was Mr. Crane? 15. A lady being asked her age replied, "My father is 30 years older than my sister Sarah, and 84 times the difference between their ages is 5 times my father's age. Now, if you will tell me how old my father and sister are, I will tell you how you can find my age." What were the ages of her father and sister? A correct answer having been given the lady said, "To 3 times my father's age add 6 times my sister's age and you will obtain a sum of which will be 9 years more than 44 times my age." What was her age? 16. of the value of a piece of cloth, worth 36 dollars, is 10 dollars more than all the money Horace has. How much money has Horace? 17. The value of 50 barrels of flour at 8 dollars per barrel is 20 dollars less than 14 times the cost of an acre of land. What will be the cost of of an acre of land at the same rate? 18. A man in Albany bought a lot of flour. He sent of it to N. York, of it to Boston, and the rest of it, 180 barrels, he shipped to England. How many barrels of flour did he buy? How many did he send to N. York? to Boston ? ૐ 19. If to 9 times the number of states belonging to the United States in 1850, 80 be added, ₫ of the result will be 27 more than the number of states originally belonging to the Union. Moreover, if 7 be added to the number of original states, 6 times the sum obtained will be 30 less than & of 400. How many states were there originally in the Union? How many in 1850? SECTION XVI. A. 1. How many are 9 times 27? Solution. 9 X 27 9 × 209 × 7; but 9 X 20 = 180, and 9 X 7= = 63; 180 +63 = 243. Therefore, 9 × 27 =243. NOTE. As soon as the principle is understood, the pupil should solve the problem by naming only the results. Thus, 9 X 27 = 180 +63 = 243. 2. How many are 5 X 49? 6. How many are 3 X 54? 2 X 96? 8 X 14? 9 X 54? 7. How many are 98 times 3? Solution. 98 × 3 = 90 x 3 +8 × 3 = 270 + 24 = 294. 47 X 4? 83 X 6? 17 X 7? 96 × 6? 97 × 10? 78 × 8? 8. How many are 59 × 9? 76 × 8? 98 × 7? B. 1. What is the greatest multiple of 6 that can be taken from the tens of 216, and what remainder will it leave if subtracted from 216? Ans. The greatest multiple of 6 that can be taken from the tens of 216 is 18 tens, and if this be subtracted from 216, there will be a remainder of 36. 2. Into what parts then will you separate 216 for convenience of division by 6? Ans. 180 and 36, because 180 is the greatest multiple of 6 that can be taken from the tens of 216. 3. 216 how many times 6? 180636÷630 + 6 = 36. Or, by Solution 2nd, 6 is contained in 21 tens 3 tens times, with a remainder of 3 tens. But 3 tens 30 units, which added to the 6 units equals 36 units. 6 is contained in 36, 6 times. Therefore, 216 equals 36 times 6. NOTE. Both forms of solution should be dispensed with as soon as the pupil can readily give the results without them. 4. What is the greatest multiple of 7 that can be taken from the tens of 245, and what remainder will it leave if subtracted from 245? 5. Into what parts, then, will you separate 245 for convenience of division by 7? 6. 245= how many times 7? 7. Into what parts will you separate 261 for convenience of division by 9? 8. 261 how many times 9 ? 9. Into what parts will you separate 609 for convenience of division by 7? by 9? by 10? by 8? 10. 609 = how many times 7? 9? 10? 8? 11. Into what parts will you separate 456 for convenience of division by 8? by 5? by 10? by 7? by 6? 12. 456 = how many times 8? 5? 10? 7? 6? 13. Into what parts will you separate 532 for convenience of division by 8? by 6? by 10? by 9? by 7? 14. 532= how many times 8? 6? 10? 9? 7? 15. 117 how 16. 219: = = many times 9? 6? 2? 3? 10? 4? 5? 7? how many times 7? 3? 5? 10? 8? 6? 4? 9? 17. 324 how many times 4? 8? 9? 10? 6? 7? 5? how many times 2? 5? 7? 9? 4? 3? 10? 6? 8? = how many times 5? 9? 4? 6? 3? 7? 2? 8? 10? times 4? 10? 8? 7? 3? 6? 9? 5? times 9? 7? 4? 6? 2? 3? 8? 7? 10? times 8? 9? 10? 6? 7? 5? = 18. 168 19. 147 20. 288 21. 93 = how many how = how 23. 224 how 22. 427 = 24. 100 25. 316 26. 237 many many = many times 3? 9? 8? 4? 5? 7? 6? 10? how many times 5? 6? 4? 3? 7? 8? 2? 10? 9? how many times 10? 4? 6? 9? 7? 5? 8? = = how many times 9? 4? 8? 3? 6? 7? 10? 5? 27. 627= how many times 6? 8? 9? 10? 7? how many times 7? 8? 9? 4? 3? 5? 2? 10? 6? C. 1. What is 4 of 459 ? of 459 of 420 of 3960 +54= = Solution. |