Let the pupil recite, thus, by line: 1% of anything is 1 onehundredth of that thing, and 1 one-hundredth of 500 is 5; of 5000 is 50; Too of 50 is .5; of 5 is .05; of 4250 is 42.5. Then 10% of anything is of that thing, and 50; of 5000 is 500; of 50 is 5, etc. of 500 is Read the above, by line and by column, as miles, rods, days, etc. Thus, 10% of 500 mi. is 50 mi.; of 5000 mi. is 500 mi.; etc. See 402, 403, and 404. DEFINITIONS. 234. In the applications of percentage, at least three elements or parts are involved, viz.; the base or multiplicand, the rate or multiplier, and the percentage or product. Any two of these being given, the third is readily found. 235. The base is the number on which the percentage is computed. 236. The rate is a decimal which denotes how many hundredths of the base are to be taken. 237. Percentage has two significations: 1st. It is the process of computing by hundredths. 2d. It is such a part of the base, as is indicated by the rate. Thus, in the statement, 5% of $40 is $2, the rate is .05, the base $40, and the percentage $2. 238. The amount is the base, plus the percentage. 239. The difference is the base, minus the percentage. Thus, if the base is $80, and the percentage is $5, the amount is $80+$5 $85; and the difference is $80 - $5 = $75. 240. PRINCIPLES.-I. The BASE is either an abstract, or a denominate number. II. The RATE is always abstract. III. The PERCENTAGE, AMOUNT, and DIFFERENCE are always like the BASE. 241. The base and rate given to find the percentage. 1. What is 10% of 80? ANALYSIS.-10% of 80 is 10%, or 1 of 80, which is 8. 10. What is the amount of $60 increased by 5% of itself? By 10%? By 20%? 121%? 25%? 33% ? 11. What is the difference of 360 feet diminished by 4% of itself? By 8%? By 12%? 163%? 20%? 33%? 50%? 12. What is the amount of $200 increased by 5% of itself? 13. A farmer having 120 bu. of wheat, sold 25% of it. How many bushels did he sell? What % did he keep? 14. Bought 25 bbl. of apples, and upon opening them found 4% of them worthless. How many were good? PRINCIPLE.-Percentage is always a product, of which the base and the rate are factors. $1260 Base. 242. 1. What is 124% of $1260? The am't and difference? .125 Rate. $157.50 $1260 $157.50 $1102.50, Diff. Percentage. 121 EXPLANATION.-Since 12% of any number is equal to, or .125 100' of that number, 121% of $1260 is $1260 x .125 = $157.50; or, it is of $1260 = $157 50. 1. Base × rate = percentage. FORMULAS 2. Base + percentage amount. 3. Base-percentage = difference. (3. Formulas will take the place of rules, whenever practicable, and the pupil may be required to construct a rule in ordinary language from each formula. Thus, for the preceding: 1. The base multiplied by the rate equals the percentage. 2. The percentage added to the base equals the amount. 3. The percentage subtracted from the base equals the differ nce. What is 2. 35% of 695 lb.? Find 9. 331% of 8736 bu. 16. The bread made from a barrel of flour weighs 35% more than the flour. What is the weight of the bread? 17. A man having a yearly income of $4550 spends 20% of it the first year, 25% of it the second year, and 371% of it the third year. How much does he save in 3 years? 18. Bought a bill of goods amounting to $875.50, from which was deducted 5%. What was the percentage allowed, and the amount paid? 19. Having $10720, I invested 25% of it in land, and 124% of the remainder in fencing it. What remained? 20. Two men engaged in trade, each with $3540. One of them gained 334% of his capital, and the other gained 60%. How much more did the one gain than the other? 243. The base and percentage given, to find the rate. ORAL EXERCISES. 1. What per cent. of 84 is 7? ANALYSIS.—Since 7 is of 84, it is of 100%, or 81% of 84. What per cent 2. Of 21 lb. are 7 lb.? 3. Of 25 bbl. are 15 bbl.? 14. 15. 16. of 40 is what per cent. of 40? of a cargo is what per cent. of it? 17. 1 times a number is what per cent. of it? 18. If a miller take 4 qt. of every bushel he grinds, what per cent of it does he take? 19. If $5 is paid for the use of $20 one year, what is the rate per cent.? PRINCIPLE. The rate is the quotient of the percentage divided by the base. WRITTEN EXERCISES. 244. 1. What per cent. of 320 is 80? EXPLANATION.-Since the percentage is the product of the base and rate, the rate is the quotient found by dividing the percentage by the base; and 80÷320 = .25, the re Base. Pereentage. 320) 80.00 80 .25 Rate. quired rate. Or, since 80, the percentage, is or of the base, the rate is of 100%, which is 25%. 17. A regiment went into battle with 600 men, and came out with 320. What % were lost? 18. Of 4000 A. of land, I sell 140 A. 19. A grocer sold from a hogshead sugar, of it at one time, and What % do I retain ? containing 600 lb. of of the remainder at another time. What per cent. of the whole remained? 20. A merchant owes $15120, and his assets are $9828. What per cent. of his debts can he pay? 21. If $52.50 is paid for the use of $750, 1 yr., what is the rate %? If $56.70 is paid for the use of $1260 ? 22. A man shipped 2600 bushels of grain from Chicago, and 455 bushels were thrown overboard during a gale; what was the rate per cent. of his loss? |