Dividing any number by a fraction by inverting the divisor and multiplying. 1. 1+1= how many? 2. 1+ how many? 2 = 3. 1+ how many? = 4. 1+2 = how many? 5. 1 how many? 1÷ = 6. 1÷1 - how many? = Observe that each fraction is contained in 1 as many times as the numerator of the fraction is contained in the denominator. Since = ? is contained in 1, † or 4 times, is contained in 3, 3 x 12, or 12 times. A short method of dividing any number by a fraction is to multiply the given number by the number of times the fraction is contained in 1. Since 1÷3, then 1÷ Divide the denominator of must equal of 3 or 3. by the numerator. Show that 1÷2=1×3. Observe, then, that the number of times any fraction is contained in 1 equals the fraction inverted; thus, is contained in 1, times. 48 11. Divide 8 by 2. 8 × 4 2 is contained in 1, times. In 8 it is contained 8 x times. 8x = 12. State the two methods of dividing fractions. Show that improper fractions and whole and mixed numbers are divided on the same principles as proper fractions. Change both numbers to fractions; then invert the divisor and multiply. NOTES. 1. When possible, cancellation should be used. 2. In solving problems that contain fractions, sometimes the method of changing to like fractional units is the shorter. 40. When common laborers earn $1.75 in a day of 91 hours, how much do they earn per hour? 41. The product of two numbers is 217. One of the numbers is 44, what is the other? 42. The material for a dress, containing 11 yards of cloth, cost $182. What was the cost per yard? 43. I invested $44 in books at $3 per volume. How many volumes did I buy? 44. Duffy ran 100 yards in 9 seconds. What was his rate per second? 45. Dan Patch paced a mile in 1161 seconds. How many yards did he cover in a second? 46. At $ apiece, how many tablets can be bought for $3. 47. By the Pennsylvania Railroad the distance from Pittsburg to Cleveland is 150 miles. A "fast" train runs the distance in 3 hours. What is the rate of the train per hour? 48. When cement is worth $3 per barrel, how many barrels can be bought for $1023? 49. At $1 each, how many baseballs can be purchased for $221? 50. There are 4121 grains of silver in a silver dollar. How many dollars can be made from 9900 grains? 51. A franc is worth 193 cents. How many francs are equal to 38% cents? 52. How many barrels, each holding 24 bushels, can be filled from 8991 bushels of apples? 53. Into how many pieces, each 11 yards long, can a piece of ribbon 12 yards long be cut? 54. How many cans, each holding 21 gallons, can be filled from a barrel of oil containing 50 gallons? Find, by a short method, the cost of the following articles: Since at $1 a of 14. At 61 per gal., how many gallons of oil can be bought 16. At 121 per yd., how many yards of ribbon can be bought for 25? for 50%? for $1.50? for $3? for $5? 17. At 81 per lb., how many pounds of raisins can be bought for $1? for $5? for $2.50? 18. At 25 cents each, how many fishing lines can be bought for $.50? for $1? $1.50 ? 19. At 371 a gallon, how many gallons of molasses can be bought for $2? for $4? 20. At 331 per pair, how many pairs of stockings can be bought for $1? for $3? for $5? for $15? 21. At 25 per meal, how many persons can be fed for $2? for $5? for $9? for $20? 22. At 163 per gallon, how many gallons of gasoline can be bought for $.50? for $2? for $6? for $9? 23. 25 cents is contained how often in $1? how often in $5? 24. At 25 cents a pound, how many pounds of butter can be bought for $5? 25. At 62 cents a yard, how many yards of serge can be bought for $1.25 ? 26. At 33 cents a pound, how many pounds of butter can be bought for $4? for $6? for $10? |