FRACTIONS Multiplication 1. What is of 6 yards? What are of 6 yards? 2. of == 3. Since of #? of 4. In the diagram find of; also of ; also of . The results found in Exercises 2-16 are called the products of the fractions. 2×3 The product of any two fractions, as and, is found from the products of the numerators and denominators, as in 3×4° The common factors of the terms are then removed, as in the work shown. It is convenient to draw a line through the numbers in both numerator and denominator which are divided by the same number, as above. The quotients are the numbers left for multiplication. This process is called canceling. 17. Mr. Smith owned of a quarry and sold of his share to Mr. White; what part of the quarry did Mr. White buy? 18. If the quarry was worth $60,000, what was Mr. White's share worth? 100 MULTIPLICATION of a pound of butter at 204 a 1. What is the cost of pound? What is the cost of 2 lb.? For lb. the cost is of 20¢. For 2 lb., it is 21 times 204. We find 24 times 20 by adding 2 times 20 and 1⁄2 of 20. The words times and of have been used here with the same meaning. When the multiplier is a proper fraction the symbol × has the same meaning as "of." Thus, × 30 means of 30. 2. What is the meaning of× 16? × 36? 3. Draw a line on the blackboard another 2 times as long. ×? of a foot long. Draw 4. Draw a line 8 inches long and divide it into half-inch spaces. Show that of 8 in. = 8 times in. The factors in a product are interchangeable in the case of fractions just as in the case of integers. 7. A gasoline stove uses of a quart of gasoline per hour; how many quarts does it use in g of an hour? 2/5 in. 1 in 1/4 in. A1 in. = PLAN. of qt. = 5x4 qt. — qt. X 6 9. What is the width of the rectangle B? Its height? Its area? X = ? 10. Draw a diagram like this and shade it to show that: part of a mile is paved? Express the product and cancel the 4. A cook has of a sack of flour and uses baking; what part of a sack does she use? product and cancel the common factors. 5. A garden-bed is 15 yd., or 2 yd. long and 1 as wide; how many yards wide is it? SUGGESTION. of 21 in. may be expressed by What is the result? 12 16 3×4×3×7 in. 7. The length of the Amazon is 3 times that of the Mississippi, and the length of the Yangtse (China) is of that The Yangtse = times the Mississippi? of the Amazon. Find by canceling: 8. of 11. 1. Indicate the cost of one drum at $5.10 per dozen. Indicate the cost of 20 drums. After having indicated the processes, as value should be found by canceling. 20 x $5.10 the 2. Indicate the cost of 1 bracelet at $11.65 per dozen. Indicate the cost of 16 bracelets. Find the value by canceling. As above, indicate and find the cost of: 3. 675 dolls at $26.40 per gross. 4. 15 doz. candles at $1.75 per gross. 5. 20 doz. steel pens at 66¢ per gross. 6. 168 scarf pins at $9.75 per hundred. 7. 18 handkerchiefs at $2.70 per dozen. 8. 600 drawing pads at $17.40 per gross. 9. 32 nickel watches at $14.70 per dozen. 10. 21 bottles of ammonia at 88¢ per dozen. II. 78 toy steam engines at $65.56 per hundred. 12. 1 chest (88 lb.) Japan tea at 421¢ per pound. 13. 1 sack (76 lb.) Java coffee at 2234 per pound. 14. 1 sack (125 lb.) Rio coffee at 153¢ per pound. 15. 86 neckties at $28.08 per gross. (1 gross = 12 dozen.) 16. In New York on the longest day daylight lasts about 17 hours and on the shortest day 10 hours; what fraction of the entire day is daylight in each case? What part is darkness? 17. On paper ruled in squares draw a rectangle 3 squares wide and 8 squares long. Shade a portion of it black to represent the darkness of the longest day. 18. Draw another rectangle of the same size and shade a portion of it black to represent the amount of darkness on the shortest day. PROBLEMS-EXPRESSAGE 103 Parcels weighing several pounds are usually sent by express. The charge varies with the distance and is stated at a rate per 100 pounds. When the rate per 100 pounds is $2.50 the charges for smaller weights are: 35 lb. 40 lb. 50 lb. $1.25 | $1.25 Weight....... 15 lb. 20 lb. 25 lb. 30 lb. Parcels weighing 50 lb. and over are charged at the rate of 214 per pound. Weights between those named in the table are charged for at the rate for the next higher weight. 1. The express rate from Chicago to New York or to Boston is $2.50; what does it cost to send a 12-lb. parcel by express from Chicago to New York? A 57-lb. parcel? A 65-lb. parcel? A 98-lb. parcel? 2. What is the express charge from Chicago to Boston for parcels weighing 4 lb.? 16 lb. ? 32 lb.? 74 lb. ? 110 lb. ? 3. Which is cheaper and how much: To send a 2-lb. parcel of merchandise from Chicago to Boston by mail or by express? (See page 86.) 4. A teacher in Chicago ordered prepaid from Boston a set of books weighing 65 lb.; what was the express charge paid by the publishing house? The books cost $45.50; what did the money-order cost the teacher? 5. Miles, who lives in Boston, received for Christmas by express from Chicago a sled weighing 7 lb.; what express charge did the sender pay? 6. A person in Boston ordered a sled weighing 5 lb. sent from Chicago. The price was $2.60; he paid the expressage and sent the money by postal money-order; what was the whole cost? |