(6.) New ORLEANS, Aug. 12th, 1845. F. C. Emerson, Esq. To W. H. Arnold of Co. Dr. For 35 hhds. Molasses, at $12.60 2100 lbs. Sugar, .053 “ 14000 lbs. Cotton, .071 1350 lbs. Coffee, .06 “ 31200 lbs. Rice, .08 150 boxes Oranges, 4.121 CREDIT. By 500 Clocks, at $5.00 " Note to balance account, What was the amount of charges, and what the amount of the note ? 66 SECTION IX. PERCENTAGE. Art. 222. The terms Percentage and Per Cent. signify a certain allowance on a hundred; that is, a certain part of a hundred, or simply hundredths. Thus the expressions 2 per cent., 4 per cent., 6 per cent., &c., of any number or sum of money, signify 2 hundredths (1ốo,) 4 hundredths (187) 6 hundredths (16.) &c. of that number or sum. For example, 1 per cent. of $100, is Too of that sum, which is 1 dollar ; 2 per cent. of $100, is too of that sum, which is 2 dollars ; 4 per cent. of $100, is 1 o o of that sum, which is 4 dollars ; 6 per cent. of $100, is 107 of that sum, which is 6 dollars, &c. Hence, universally, QUEST.—200. What do the terms percentage and per cent. signify? What is meant by 2 per cent., 4 per cent., &c. of any sum? What then does any given percentage of any number or sum of money imply? Obs. From what are the terms percentage and per cent. derived ? Any given percentage of any number, or sum of money, implies so many units for every 100 units ; so many dollars for every 100 dollars; so many cents for every 100 cents ; so many pounds for every 100 pounds, fc. Obs. The terms Percentage and Per Cent. are derived from the Latin per and centum, signifying by the hundred. MENTAL EXERCISES. Ex. 1. A boy finding a purse containing 8 dollars, the owner gave him 6 per cent. of the money: how much did the boy receive ? Suggestion. 6 per cent. is 6 cents for every 100 cents. (Art. 222.) If then he received 6 cents for 1 dollar, (100 cents,) for 8 dollars he must have received 8 times 6 cents, or 48 cents. Ans. 48 cents. 2. What is 6 per cent. of 10 dollars ? Ans. 60 cents. 3. The printer's boy collected 12 dollars on some bills, for which his employer gave him 4 per cent. for his services : how much did he receive ? 4. What is 4 per cent. of 8 dollars ? 6 dollars ? 10 dollars ? 7 dollars ? 12 dollars ? 15 dollars ? 5. A man borrowed 12 dollars for a year, and agreed to give 6 per cent. for the use of it: how much did he pay ? 6. What is 6 per cent. of 10 dollars ? 4 dollars ? 6 dollars? 8 dollars ? 11 dollars ? 15 dollars ? 7. A market-man sold 20 dollars worth of butter for one of his neighbors, who paid him 5 per cent. for his trouble : how much did he receive? 8. What is 5 per cent. of 12 dollars ? 10 dollars ? 7 dollars ? 15 dollars ? 20 dollars ? 9. A farmer bought a cow for 12 dollars, and sold it again so that he gained 10 per cent. by his bargain : how much did he gain ? 10. What is 10 per cent. of 12 dollars ? 20 dollars ? 14 dollars ? 18 dollars ? 13 dollars ? 15 dollars? 11. What is 11 per cent. of 1 dollar ? 4 dollars ? 10 dollars ? 7 dollars ? 6 dollars ? 9 dollars ? 12 dollars ? 12. A boy having 100 canary birds, lost 7 per cent. of them by disease : how many did he lose ? 13. What is 7 per cent. of 200 dollars ? 300 dollars ? 500? 900 ? 700 ? Suggestion. Since 7 per cent. is 7 dollars on 100 dollars, for 200 dollars it is twice as much, or 14 dollars, &c. 14. A merchant invested 500 dollars in a certain adventure, and gained 6 per cent. on the sum invested: how much did he gain ? 15. What is 3 per cent. of 100 dollars ? 300 ? 500 ? 600 ? 900 ? 16. What is 5 per cont. of 200 dollars ? 400 ? 300 ? 700 ? 1000 ? 800 ? 1100 ? 17. What is 8 per cent. of 200 dollars ? 500 ? 600 ? 300 ? 700 ? 400 ? 1200 ? 18. What is 6 per cent. of 300 dollars ? 500 ? 400? 700 ? 1100 ? 900 ? 1200 ? 19. What is 7 per cent. of 400 dollars ? 300 ? 500 ? 900 ? 600 ? 1000 ? 20. What is 10 per cent. of 500 dollars ? 300 ? 700 ? 1200 ? 1500 ? 2000? 21. What is 8 per cent. of 200 dollars ? 400 ? 800 ? 900 ? 1000 ? 22. What is 9 per cent. of 300 dollars ? 600 ? 500 ? 800 ? 700 ? 23. What is 12 per cent. of 8 dollars ? 7 dollars ? 6 dollars ? 24. What is 20 per cent. of 4 dollars ? 5 dollars ? 6 dollars ? 25. What is 15 per cent. of 3 dollars ? 4 dollars ? 6 dollars ? 26. What is 18 per cent. of 3 dollars ? 5 dollars ? 4 dollars ? 27. What is 25 per cent. of 4 dollars ? 5 dollars ? 8 dollars ? 28. What is 30 per cent. of 3 dollars ? 5 dollars ? 9 dollars ? 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. PERCENTAGE TABLE. 1 per cent. 2 per cent. 3 per cent. 4 per cent. 6 per cent. 7 per cent. 10 per cent. 12 per cent., &c. 25 per cent. 50 per cent. 75 per cent. 99 per cent. 100 per cent. 103 per cent. 125 per cent., &c. 3 per cent., that is, 1 of 1 per cent., * per cent., that is, of 1 per cent., i per cent., that is, į of 1 per cent., 31 per cent. 8} per cent. .01 .02 .03 .04 .06 .07 .10 .12 .25 .50 .75 .99 1.00 1.03 1.25 .005 .0025 .0075 .035 .082 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 mill. (Art. 206. Obs. 2.) 5 per 1. Write 1 per cent., 2 per cent., 3 per cent., 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 ? و 2. Write 13 per cent. ; 15; 30; 50; 75; 49; 73; 85. 3. Write ; per cent. ; £; } ; . ; ; ; } ; } ; , 1. 4. Write 3 per cent. ; 5 ; 16ý; 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 ? Suggestion. Since 3 per cent. is the constable 100 must have received to of $400, or 3 dollars for every 100 dollars he collected. Now ido of $400 is too, which is equal to $4; and 3 hundredths is 3 times $4, or $12. Operation. Since 18=.03, we have only to mul$400 tiply the given number of dollars by .03 .03 and it will give the answer in cents, which must be reduced to dollars by $12.00 Ans. pointing off 2 decimals. (Art. 209.) 3 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 is frequently supposed. For in the latter case he would receive only Tô3, instead of lồo 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 t 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 ? |