82. Make a receipted bill for each of the following forms: 1. A pleasure boat contains 40 How many people does the ladies, 50 men, and 49 children. pleasure boat contain? 2. A merchant made $18 by selling an overcoat for $60. How much did the coat cost him? 3. There were 35 girls and 36 boys in a certain grade at school. How many boys and girls in all were there in the grade? 4. Mr. Howe had $100 and spent $40 for travelling and $35 for hotel expenses. How much money did he then have ? 5. A barrel of flour was bought for $4.25 and sold at a gain of $.75. What was the selling price? 6. From a piece of cloth containing 75 yards, 51 yards were cut. How many yards were left in the piece? 7. A farmer had 80 bushels of wheat, 40 bushels of oats, and 25 bushels of barley. How many bushels in all did he have? 8. A spool contained 1,000 yards of thread. How many yards were left on the spool after 550 yards had been cut off? 9. Mr. Jacobs bought one book for $.48, and another book for $1.00. How much did both books cost him? 10. A horse costs $100, and a wagon $40. They were sold together at a loss of $80. What was the selling price? 11. If one book cost $.48 and another $.99, how much will both books cost? 12. Sarah had 40 grapes; she gave to three children, 10, 5, and 15 grapes. How many did she have left ? 13. Edgar spent $.48 for a bat and $.49 for a cap. How much did he pay for both? 14. The minuend is 45, and the remainder 29. What is the subtrahend? 15. John bought a slate for $.12, a reader for $.38, and a drawing book for $.35. He gave in payment $1.00. How much change is due him? 16. Mrs. Morrow had two $10 bills and a $5 bill. She spent $15 for a bonnet, and $8 for a parasol. How many dollars did she then have ? 17. Hannah bought ribbon for $.18, lace for $.17, and buttons for $.10. How much change is due her on paying with $.50 ? 18. Frank gave $.60 for a book worth $.45 and a slate. How much did the slate cost him? 84. Written Problems. 1. Mrs. Edwards paid $45.35 for a cloak, $28.75 for one dress, $19.82 for another dress, and $26.95 for lace. How much did she pay for all? 2. A man bought a horse and wagon for $325. He sold the horse for $275 and thereby gained $15. What did the wagon cost him? 3. What is the entire surface of the great lakes, with respectively the following number of square miles: Superior, 31,500; Michigan, 23,150; Huron, 23,100; Erie, 7,800; Ontario, 6,900 ? 4. The population of five cities is as follows: 21,480, 39,604, 270,299, 175,618; and 199,089. What is their total population ? 5. A house and two lots were bought for $10,000. the lots was sold for $1,500 at a loss of $500. other lot with the house cost? One of What did the 6. A farmer sold four loads of hay weighing respectively, 1,905, 1,826, 2,309, and 1,998 pounds. What was their entire weight? 7. Mr. Francis bought two horses and a carriage for $650. One of the horses was sold for $300 at a gain of $75; the other for $200 at a loss of $50. What did the carriage cost Mr. Francis ? 8. Mr. Thomas started business with $5,000 capital. His profits the first year were $1,906 and the third year $929. His losses the second and fourth years were respectively $1,581 and $2,390. What was his capital at the end of the fourth year? 9. Mrs. Brown had $1,000; she paid $250 for a horse, $175 for a city lot, and $500 for furniture. How much money did she then have ? 10. A man bought a house for $5,500, and expended $4,700 in repairs and alterations, and $147 in taxes. He sold the house for $7,000. Did he gain or lose, and how much? 11. Mr. Boyd started on a journey, having $1,500. His travelling expenses were $478; hotel bills, $708; and his purchases, $279. How many dollars did he have left? 12. A farm of 500 acres valued at $37 an acre was sold with live stock at $1,250 for $35,000. What was the profit ? 13. If a farm, costing $15,700, a mill, $3,895, a house and lot, $23,750, and some live stock together cost one hundred thousand dollars, what is the value of the live stock? MULTIPLICATION. 85. 1. Frank is 9 years old. His father is 7 times as old How old is the father? as Frank. 2. Mr. Thomas bought 8 tons of coal at $5 a ton. What was the entire cost of the coal? 3. Mr. Samuels worked 12 hours a day for 6 days in the week. How many hours in all did he work? 4. If 7 men can do a piece of work in 5 days, in what time can one man do the work? 86. To multiply one number by another is to take the one number as many times as there are units in the other. 87. Multiplication is a short method of finding the sum of several equal numbers. Thus John earned $25 a week. How much money did he earn in 5 weeks? ss. The multiplicand is the number to be repeated, or multiplied. Multiplication. $125 $125 89. The multiplier is the number by which to multiply. It shows how many times the other number is to be taken, or repeated. In practice the smaller number, abstract or concrete, is frequently used as the multiplier. 90. The product is the result obtained by multiplying. 91. Numbers which, multiplied together, give the product, are called its factors or makers; thus, 6 and 5 are factors of 30. $25 Multiplicand. 5 Multiplier. $125 Product. 92. Factors that cannot be separated into smaller factors are called prime factors, as 2, 3, 5, 7, etc. 93. The sign of multiplication is ×; it is read times, or multiplied by; thus, 9 x 7 is read 9 times 7, or it may be read 9 multiplied by 7. Read thus: 7 times 2 are 14; of 14 is 7, or 2 in 14, 7: etc. 95. Construct a table similar to the preceding, for each of the other numbers to and including 12. 96. Copy, and commit to memory the following table: X 27 30 33 36 40 44 640 44 48 45 50 55 60 9 9 10 24 | 32 | 4 40 48 56 64 72 80 88 96 18 27 36 45 10 20 11 12 12 24 36 48 60 72 84 96 108 120 132 144 In each square is the product of the number at the top multiplied by the number at the left in the first column. 97. Find the cost of the following: 98. Make problems for the numbers in Art. 97. Thus, Ex. 1: How much change should Frank receive, if he gives 3 quarters of a dollar in payment for 8 pounds of sugar at 8 cents ? |