Cancellation Cancellation consists in rejecting the same factor from a divisor and a dividend. 4. If a barrel of gasoline will drive an engine 9 hours a day for 14 days, how many barrels will be required to run it 8 hours a day for 84 days? indicated product below the line (as a divisor). Cancel 14 and 84, writing 6 above the latter. Cancel 6 and 9 by dividing each by 3, writing 2 above the former and 3 below the latter. Write 16 (2 × 8) as the numerator of an improper fraction and 3 as its denominator. Change to a mixed number. Write bbl. in a parenthesis. Sight Problems 1. A's farm is twice as large as B's. B's contains 80 acres. How many acres are there (a) in A's farm ? (b) In both farms? 2. How many square rods are there in a rectangular field 20 rods long and 12 rods wide? 3. John has saved 7 cents. His sister has saved three times as much. How many cents have both saved? 4. After filling 3 five-gallon cans with oil from a barrel there are 30 gallons left in the latter. How many gallons were in it at first? 5. One pipe discharges 40 gallons in 2 minutes, the other discharges 36 gallons in 3 minutes. How many gallons per minute do both together discharge? 6. How many times does a clock tick in 5 minutes if it ticks 60 times a minute? 7. At the rate of 31 miles per hour, how far will a train go from 1 P.M. to 10 P.M.? 8. A man bought a wagon for $100 and spent $20 on repairs. What was his profit, if he sold it for $150? 9. A train that was due at 9.15 A. M. did not arrive until 10 A.M. How many minutes late was it? 10. How much change should a girl receive if she buys 63 cents' worth of groceries and gives the storekeeper a $1 bill? 11. I bought 2 pounds of coffee and gave the storekeeper 75 cents. If he gave me 15 cents in change, what was the price of the coffee per pound? 12. A 160-acre farm is divided into 4 fields of the same size. One field yielded 120 tons of hay. What was the yield per acre? Written Problems 1. X's farm is three times as large as Y's. Y's contains 97 acres. How many acres are there (a) in X's farm? (b) In both farms? 2. How many square rods are there in a rectangular field 27 rods long and 24 rods wide? 3. A farmer paid $13 for a calf and four times as much for a cow. What did he pay for both? 4. After filling 3 forty-five gallon barrels of oil from a tank the latter still contains 95 gallons. How many gallons did it contain at first? How 5. One pipe discharges 169 gallons in 13 minutes. Another discharges 196 gallons in 14 minutes. many gallons per minute do both together discharge? 6. How many times does a clock strike in a week if it strikes 156 times a day? 7. At the rate of 28 miles per hour, how far will a go from 2 P.M. to 3 A.M.? train 8. A man bought a carriage for $275. ing $47 for repairs he sold it for $350. profit? After spend What was his 9. How many minutes late was a train that was due at 9.15 A.M. and did not arrive until 10.26 A.M.? 10. How much change should a man receive if he buys 6 yards of cloth at $1.35 per yard, and gives 3 two-dollar bills in payment? 11. I bought 14 pounds of coffee and received $6.50 change out of a 10-dollar bill. What did the coffee cost per pound? 1. Into how many parts is A divided? B? C? D? E? 2. If A were placed upon B, how many parts of B would be covered (a) by the shaded part of A? (b) By the white part of A? 3. If A were placed upon C, how many parts of C would be covered (a) by the white part of A? (b) By the shaded part of A? 4. If A were placed upon E, how many parts of E would be covered (a) by the white part of A? (b) By the shaded part of A? 5. If B were placed upon C, how many parts of C would be covered (a) by the shaded part of B? (b) By the white part of B? 6. If D were placed upon E, how many parts of E would be covered (a) by the shaded part of D? (b) By the white part of D? 7. What fraction is shaded (a) in A? (b) In B? (c) In C? (d) In D? (e) In E? 8. What fraction is white (a) in A? (b) in B? (c) In C? (d) In D? (e) In E? When is changed to , it is reduced to lower terms; when it is changed to, it is reduced to lowest terms; when it is changed to or to , it is expressed in higher terms. |