121-39. 6. 253-158. c. 46-5-275. d. 193-147. b. 424 c. 16,6 16 9. Subtract: a. 311 61 16 183 53 9/ 10. What is the area of a parallelogram whose base is 15.23 ft. long, and whose altitude is 19.64 ft.? 11. Multiply 1373.78 by 29, 36, 58, and 47. 12. Write in words 10056932812647829032. 13. What is the area of a rectangle 16 mi. by 32 mi.? 14. Change to decimals: a. 2 b. 35 15 c. 12 d. 15. In a town the tax rate for schools was .92 mills per dollar. What was the amount of the tax on a total valuation of $9,875,632.58? 16. The distance of the sun from the earth is 93,000,000 miles. Find its ratio to the moon's distance, 240,000 miles. ADDITION OF MIXED NUMBERS 1. Add 21, 33, 45, 83, 103, 75. 2 + 3 + + + 8 + 10 + 7 = 34, the sum of the integers. Another way is to reduce all the mixed numbers to improper fractions with a common denominator. 60 = 6 22-116 35-210 32-256 61-183 24 88 +88 +126+210 +256 + 183 = 213=3824 24 24 24 2. Add 14, 25, 41, 53, 63, 71. 3. Add 18, 24, 33, 41, 51, 81. 4. Add $33, $51, $83, $91, $101. 5. A boy was sent by his father to collect three bills. His father gave him $23 in change; and he collected from one man $21, from another $65, and from another $103. How much money in all did he then have to hand to his father? 6. Prove the answer in 5 by reducing the money to decimal amounts, and adding. FRACTION PROBLEMS 1. I bought cloth at $13 a yard, and sold it at $21 a yard. What did I gain on a yard? 2. From a barrel of vinegar containing 31 gallons, 12ğ gallons were drawn. How many gallons were left? 3. I purchased 10 tons of coal at one time, and 245 tons at another; after using 161⁄2 tons, how much remained? 4. A boy having $4, gave $ for oranges, and $4 for a flag. How much money had he left? 3 5. A man spent $15 for provisions, and $12 for clothing. How much money had he left from $501⁄2? 6. A merchant bought two pieces of velvet, one containing 54% yards, and the other 5611 yards. He sold 4313 yards at one time, and 34 yards at another. How many yards had he left? 7. A grocer bought two tubs of butter, one tub containing 27 pounds, the other 32 pounds. After he sold 401 pounds, how many pounds had he left? 8. It is 95 feet from one house-lot on a city street to the opposite, and the sidewalks on the street are 121 feet wide. How wide is the street between the sidewalks? 9. The Capitol at Washington is 324 feet wide and 752 feet long. What is the difference between its length and its width? 10. From a piece of cloth containing 343 yards, there were sold 123 yards. How many yards were left? 11. There was a total eclipse of the sun on May 28th, 1900. The path of the eclipse crossed Alabama. The region in temporary darkness was 537 miles wide. If the eastern boundary of Alabama is 331 miles long, how many miles of the boundary were not in the path of the eclipse? MULTIPLICATION OF FRACTIONS Multiplying the numerator has what effect on the fraction? Dividing the denominator has what effect? Why? If the numerator of the fraction 18 be divided by 5, how will the fraction be affected? If the numerator be multiplied by 4, how will the fraction be affected? What difference will be made in the value of the fraction if the denominator is multiplied by 2? If the denominator is divided by 2? 1. Multiply by 4. This means repeat four times. }+&+&+ &=12. 3×4=12. 17' 17 17 17 First we cancel the factors common to denominator and multiplier. Then we multiply. we reduce to a mixed number. The resulting fraction a. 13 × 8. b. 5 x 4. To multiply a whole number by a fraction is the same as to multiply a fraction by a whole number. We may take three fourths of eight things or eight three-fourths of something, with the same result. 10. Discuss in this way: a. 9 × or × 9. b. 27 bu. × or bu. × 27. Would it make any dif c. 16 lb. × 1 or § lb. × 16. ference in the total amount of tea used, if we put of 16 lb. in one package or lb. in each of 16 packages? d. 10 yd. xor yd. x 10. e. 60 min. x or 1 min. x 60. 11. Multiply 15 minutes by . This means, take four fifths of fifteen minutes. 15 ÷ 5 = 3. One fifth of fifteen minutes is three minutes. 3 min. × 4 = 12 min. Three minutes multiplied by four is twelve minutes. 12. Discuss multiplying: b. 30 days by §. c. 365 days by . a. 200 qt. by b. 30 days by 5. 3 10' |