II. Pupils should be taught to annex a zero and to divide by 2 to find 5 times any integer. Thus, 5 X 625 = 1o X 625, or 2) 6250. The applications should be of this type: 3125 1. How many bushels of apples can a man pick in 10 days at the rate of 36 bushels a day? What part does he pick in 5 days? How many bushels? 2. Following the plan of Exercise 1 find how many bushels of apples a man can pick in 5 days at the rate of 42 bushels a day? 3. There are 144 pieces of crayon in a box. How many are there in 10 boxes? In 5 boxes? 4. At 12c. each what will 10 grape-fruit cost? 5? 5. At a clearing sale pieces of linen containing 10 yeards each were sold at 65c a yard. What would half of a piece be sold for? 6. One package of nasturtium seeds contains 45 seeds; how many seeds are there in 5 packages? 7. Find the cost of 5 horses at $135 apiece. Find the cost of 5 articles of each kind: III. To multiply a number by 25 annex two zeros and divide by 4, thus 25 × 625 (100 X 65, or 4) 62500 15625 The applications should be of this type: 1. What is the cost of 100 pounds of butter at 16 cents a pound? What is the cost of 14 as much, or of 25 pounds? 2. 25 is how many fourths? To multiply a number by 25 is to multiply by how many fourths? What is the easiest way to multiply it by 25? Multiply by 25: 3. 16. 4. 7.5. 5. 45 pounds. 7. 25 yards. 8. 179.60. Find the cost of 25 articles of each kind: 6. $16.80. 19. If a sheep consumes on the average, besides pasturage, 400 pounds of hay în a year, how many tons of hay are needed to feed a flock of 25 sheep for one year? 20. If a cow consumes on an average, besides pasturage, 4.5 tons of hay in a year, how many tons are required to feed a herd of 25 cows for one year? FIFTH YEAR. The use of the decimal notation having now been established short processes in division may be attempted. To divide a number by 5 move the decimal point one place to the left and multiply by 2. I. Thus, 6535653x2, or 65.3 X 2 = 130.6. The applications should be of this type: 1. If the board bill of 5 people amounted in one year to $910, what did each pay a year? 2. If the room rent of 5 people was $455 a year, what did each pay a year for his room? 3. A man spends % of his yearly income of $1,800 in house rent. To what does it amount? 4. The distance from New York to Buffalo is 440 miles, and the distance from New York to Rhinecliff is % of the former. What is the distance between New York and Rhinecliff? 5. When of the 84 gallons in a cask had been drawn out, how many remained? 6. In an assemblage of 485 persons there were 5 times as many adults as children; how many were children? 7. In 1900 the population of a certain village was 14,920. 40 years before it was as large; what was the population in 1860? 8. If of the 290 books drawn from a library during one month are biographies, % histories, and the rest fiction, how many of each kind are drawn? 9. Mr. Hart spent 2% of the money received for the rent of his houses in repairing them; the houses rented for $660, how much did he spend? 10. The number of square feet in the area of the windows of a room equals of the area of the floor. The floor covers 416 square feet; how many square feet in the windows? 11. George weighs as much as his father who weighs 185 pounds. What is George's weight? 12. A certain man is away from his business % of the year including Sundays; how many days is he away from it? II. To divide a number by 25 move the decimal point two places to the left and multiply by 4. The applications should be of this type: 1. If 25 turkeys weigh 450 pounds, what is the average weight of each? 2. 25 (?) fourths. To divide a number by 25 is to divide it by how many fourths? How is this done? 3. How many quarters are there in $65? 4. A retail grocer bought 25 boxes of canned lobster for $10; what was the price per box? 14. When 25 bunches of lath cost $8.75, what is the price per bunch? 15. When 25 bunches of shingles cost $90, what is the cost per bunch? 16. If 25 persons make 7,000 regular trips in a year from Brooklyn to Jersey City, how many trips does one person make? 17. If in one round trip the total number of fares for 25 persons equals $5, what is a single fare, round trip? 18. How many note books at $.25 each can be bought for $18.75? 20. An agent received $11.25 in one day for sending telegrams at $.25 each; how many did he send? III. When multipliers differ little from multiples of ten, it is usually easier to multiply indirectly. Thus, 19 X 12 =20 X 12 tions should be of this type: 12, or 240 12 228. The applica 1. Do 12 dozen eggs at 19 cents a dozen cost more or less than 12×20 cents? How much? How many are 12 X 20 or 20 X 12? What is the cost of 12 dozen eggs at 19 cents a dozen? 2. Do 9 pounds of butter at 28 cents a pound cost more or less than 9 X 30 cents? How much? How many are 9 × 30 or 30 × 9? What is the cost of 9 pounds of butter at 28 cents a pound? 3. What is the cost of a dozen pairs of lace curtains at 98 cents a pair? What is the cost of 15 yards of muslin at 11 cents a yard? Of 24 yards of gingham at 9 cents a yard? 5. What is the cost of 5 pounds of spring chicken at 18 cents a pound? of 13 pounds of pork at 11 cents a pound? 6. What is the cost of 101 boxes of soap at $2.75 a box? 7. What is the cost of three shirt waists at $.99 each? Of 4 pairs of gloves at $.98 a pair? 8. What is the cost of 5 pounds of coffee at 29 cents a pound? Of 9 pounds at 19 cents a pound? 9. How much do 11 yards of carpet cost at 79 cents per yard? 10. What is the area of a square 21 inches on a side? 11. What is the area of a triangle of base 12 inches and altitude 11 inches? 12. Hoy many miles does a train run in 18 hours at the rate of 31 miles per hour? 13. How many miles does an automobile travel in 11 hours at the rate of 21 miles per hour? 14. What is the weight of a load of apples containing 22 barrels, if each barrel of apples weighs 130 pounds? 15. How many square rods are there in a field 17 rods long and 9 rods wide? 'SIXTH YEAR. Much use should be made of the aliquot parts of 10 and 100 in the work of this grade. I. The following problems will suggest sufficiently the nature of the work: 1. What part of $10 is $21⁄2? What is the cost of 84 hats at $22 each? 2. How much does a dairyman receive a day if he sells 140 quarts of milk at 22 cents a quart? The rate of anything at 2 for 5 cents is the same as how many for 10 cents? How much is this for one article? 3. What is the cost of 2 dozen lemons at the rate of 2 for 5 cents? At a flower sale a lady bought a dozen carnations at 2 for 5 cents; what did she pay for them? 5. How many pencils can be bought for $.50 at rate of 2 for 5 cents? 6. How many souvenir postal cards at rate of 2 for 5 cents can be bought for $1? What part of 10 is 3? 7. Find the cost of 24 souvenir postal cards at rate of 3 for 10 cents. 8. What will 12 bananas cost at rate of 3 for 10 cents? 9. Find the cost of 6 pairs of hose at rate of 3 pairs for $1. 10. What part of a dollar is 122 cents? What is the cost of 1 dozen collars at 122 cents each? 11. What is the cost of 14 yards of muslin at 121⁄2 cents a yard? 12. What part of $100 is $122? What is the cost of 9 harnesses at $121⁄2 each? 13. What part of $100 is $3313? What is the cost of 6 suites of furniture at $33% a suite? 14. Find the cost of 6 dozen handkerchiefs at 333 cents apiece. 15. What part of $100 is $163? What is the cost of 18 tables at $16 each? 16. A real-estate agent bought some property for $2,400 and sold it so as to gain 333%; for how much did he sell it? 17. What is the cost of 42 dozen pencils at 333 cents per dozen? = 18. 33 thirds? To divide a number by 333 is to divide it by how many thirds? How is this done? 19. When 333 yards of cloth cost $30, what is the price per yard? 20. At 33 cents apiece, how many pieces of lace can be bought for $4? 21. 125 is what part of 1,000? How may a whole number be multiplied easily by 125? Illustrate the method. How may a whole number be multiplied easily by 1.25. Find the cost of: 22. 16 lb. of coffee at 25 cents a pound. 23. 36 cans of baking powder at 25 cents a can. 24. 84 cans of corn at 5 cents each. 25. 124 bottles of olives at 25 cents a bottle. 26. 82 dozen oranges at 50 cents a dozen. 27. 24 packages of rolled oats at 25 cents a package. 28. 60 pounds of candy at 25 cents a pound. 29. 136 arithmetics at 75 cents each. 30. 48 chairs at $1.25 each. 31. 96 caps at 75 cents each. 32. 120 pairs of mittens at 50 cents a pair. 33. 112 dozen teaspoons at $1.25 a dozen. 34. 320 pairs of skates at $1.25 a pair. 35. 444 pairs of slippers at 75 cents a pair. II. On account of the many prevailing business customs of indicating cut prices on price lists there should be plenty of drill on work like the following: = 1. 9 10 minus what? What must be taken from 10 times a number to leave 9 times the number? State a short way to multiply a number by nine. 2. Multiply by 9: 23; 54; 76; 97. 3. Find the cost of 47 packages of macaroni at 9 cents a package. 4. Find the cost of 381 packages of breakfast food at 9 cents a package. 5. 99 = 100 minus what? What must be taken from 100 times a number to leave 99 times the number? State a short way to multiply by 99. 6. Multiply by 99: 27; 14; 59; 84. 7. Find the cost of 52 shirt waists at 99 cents each. 8. Find the cost of 16 pairs of curtains at 99 cents a pair. 9. State a short way to multiply a number by 999. 10. Multiply by 999: 4; 51; 84; 26; 718. 11. State a short way to multiply by 98. 12. Multiply by 98: 7; 15; 36; 49; 72. 13. A man sold 12 horses at $98 each; how much did he receive for the horses? 14. State a short way to multiply by 199. |