EXERCISES FOR THE SLATE. 223. We have seen that hundredths are decimal expressions, occupying the first two places of figures on the right of the decimal point. (Arts. 181, 182.) Now, since percentage and per cent. signify hundredths, it is manifest they may be expressed by decimals. OBS. 1. It will be seen from the preceding Table, that when the given per cent. is less than 10, a cipher must be prefixed to the figure expressing it, in the same manner as when the number of cents is less than 10. (Art. 206. Obs. 1.) 2. When the given per cent. is more than 100, it must plainly require a mixed number to express it. (Art. 183. Obs. 2.) 3. Parts of 1 per cent., as,, &c., require three or more places of decimals, and are written like mills and parts of a mill. (Art. 206. Obs. 2.) 1. Write 1 per cent., 2 per cent., 3 per cent., 5 per cent., 8 per cent., and 9 per cent. in decimals. QUEST.-223. How is percentage or per cent. expressed? Obs. When the given per cent. is less than 10, how is it written? When more than 100, how? How many decimal places do parts of 1 per cent. require? 2. Write 13 per cent. ; 15; 30; 50; 75; 49; 73; 85. 1 5 4 3 1 3. Write per cent. ; ; ; ; ; 10; 1; 1; 1; }. 8 4. Write 3 per cent.; 5; 161; 125; 3314; and 462 per cent. 5. A merchant handed some bills amounting to $400 to a constable, and gave him 3 per cent. for collecting them how much did the constable receive, and how much did he pay over to the merchant? 100 Suggestion. Since 3 per cent. is 130, the constable must have received 3 of $400, or 3 dollars for every 100 dollars he collected. Now of $400 is 400, which is equal to $4; and 3 hundredths is 3 times $4, or $12. Operation. $400 .03 $12.00 Ans. 3 1 00 100 1009 Since =.03, we have only to multiply the given number of dollars by .03 and it will give the answer in cents, which must be reduced to dollars by pointing off 2 decimals. (Art. 209.) Note. It is important for the learner to observe, that the amount of money collected, is made the basis upon which the percentage is computed. That is, the constable is entitled to 3 dollars, as often as he collects 100 dollars, and not as often as he pays over 100 dollars, as frequently supposed. For in the latter case he would receive only 103, instead of 100 of the sum in question. This distinction is important, especially in calculating percentage on large sums. 6. What is 2 per cent. of $350 ? Ans. $7. 225. Hence, to find the percentage of any number, or sum of money. Multiply the given number or sum by the given per cent., expressed decimally; and point off the product as in multiplication of decimal fractions. (Art. 191.) 7. What is 4 per cent. of $63? Ans. $2.52. 8. What is 3 per cent. of $145.25 ? Ans. $4.3575. 9. What is per cent. of $180.42? (Art. 224. Obs. 2.) QUEST-Note. When it is said that a man receives a certain per cent. for collecting money, upon what is the per cent. calculated? 225. How do you calculate percentage? Obs. If the per cent. contains a common fraction which cannot be expressed decimally, how proceed? 10. What is 11. What is 12. What is 13. What is per cent. of $827.63 ? 10 per cent. of $600.451 ? 14. What is 12 per cent. of $2500.63 ? 15. What is 20 per cent. of $2250.84? 16. What is 3 per cent. of $436? Suggestion. 3 per cent. is equal to .032. (Art. 223.) OBS. If the per cent. contains a common fraction which cannot be expressed decimally, first multiply by the decimal, then by the common fraction of the given per cent., and point off the sum of their products as above. 17. What is 23 per cent. of $144? Operation. $144 .02 $2.88-2 per ct. 48= per ct. $3.36 Ans. 18. What is 4 19. What is 8 20. A merchant Since per cent. cannot be exactly expressed by decimals, we first multiply by .02, then by ; (Art. 134. a. ;) and point off two decimal places. per cent. of 257 ? per cent. of 673 ? having deposited $20 in a bank, afterwards drew out 10 per cent of it: how many dollars did he draw out? 21. A merchant makes a deposit of $1864 and draws out 25 per cent. of it: how much has he left in the bank? 22. A merchant shipped 865 boxes of lemons; on the passage home 15 per cent. of them were thrown overboard: how many boxes did he lose? how many had he left? 23. How much is 63 per cent. of $1000? 24. How much is 7 per cent. of $1526.33? 25. How much is 8 per cent. of $16.325? 26. A young man worth $1500, lost 314 per cent. of it in gambling: how much did he lose? how much had he left? 27. A merchant bought a cargo of flour for $1230, and paid 4 per cent. for bringing it home: what was the whole cost of his flour? 28. What is 371⁄2 per cent. of $100? Of $2537.50? 29. What is 112 per cent. of $150 ? 30. What is 125 per cent, of $635 ? 31. What is 250 per cent. of $17.35? 32. Which is the most, 7 per cent. of $1000, or 6 cent. of $1100? per 33. What is the difference between 6 per cent. and cent. of $12000 ? 7 per 34. What is the difference between 9 per cent. of $2000, and 6 per cent. of $3000 ? 35. What is 17 per cent. of $10000 ? 36. What is 20 per cent. of $10500? 37. A man gave his two sons $10000 apiece; the elder added 15 per cent. to his the first year, and the younger spent 15 per cent. of his what was the difference of their property at the end of the first year? 38. A laboring man earning $225 a year, lays up 23 per cent. of it: how much does he spend ? 39. A man having deposited $856.25 in a savings bank, drew out 314 per cent. of it: how much had he left in the bank ? 40. A farmer owing 3560 sheep, lost 50 per cent. of them by disease: how many had he left? APPLICATIONS OF PERCENTAGE. 226. Percentage, or the method of reckoning by hundredths, is applied to various calculations in the practical concerns of life. Among the most important of these are Commission, Brokerage, the Rise and Fall of Stocks, Interest, Discount, Insurance, Profit and Loss, Duties, and Taxes. Its principles, therefore, should be thoroughly understood by every scholar. QUEST.-226. To what are the principles of percentage applied? What are some of the most important of these calculations? COMMISSION, BROKERAGE, AND STOCKS. 227. Commission is the per cent. or sum charged by agents for their services in buying and selling goods, or transacting other business. OBS. An agent who buys and sells goods, &c. for another, is called a Commission Merchant, a Factor, or Correspondent. 228. Brokerage is the per cent. or sum charged by money dealers, called Brokers, for negotiating Bills of Exchange, and other monetary operations, and is of the same nature as Commission. 229. By the term Stocks, is meant the Capital of monied institutions, as incorporated Banks, Manufactories, Railroad and Insurance Companies; also, the funds of Government, State Bonds, &c. OBS. Stocks are usually divided into portions of $100 each, called shares; and the owners of these shares are called Stockholders. 230. The original cost or valuation of a share is called its nominal, or par value; the sum for which it can be sold, is its real value, which varies at different times. OBS. 1. The rise or fall of Stocks is reckoned at a certain per cent. of its par value. The term par is a Latin word, which signifies equal, or a state of equality. 2. When stocks sell for their original cost or valuation, they are said to be at par; when they sell for more than cost, they are said to be above par, or at an advance; when they do not sell at cost, they are then said to be below par, or at a discount. 3. Persons who deal in Stocks are usually called Stock-Brokers, or Stock-Jobbers. 231. The commission or allowance made to factors and brokers, and the rise and fall of stocks, are usually reckoned at a certain percentage on the amount of money QUEST.-227. What is commission? Obs. What is an agent who buys and sells goods for another usually called? 228. What is brokerage? 229. What is meant by stocks? How are stocks usually divided? What are the owners of the shares called? 230. What is the par value of stocks? What the real value? Obs. What is the meaning of the term par? When are stocks at par? When above par? When below? 231. How are commission, brokerage, and the rise or fall of stocks reckoned? |