PERCENTAGE. 210. Per cent means hundredth or hundredths. Per cent may be expressed as a common fraction whose denominator is 100, or it may be expressed decimally; thus, 6 per cent = 281 Te or .06; 28; per cent = or .281; per cent = 100 100 or .001 Note.—Instead of the words per cent sometimes the sign (%) is used; thus 6 per cent may be written 6%. 211. The base in percentage is the number of which hundredths are taken ; thus, in the problem, find 11% of 600, the base is 600; in the problem, 16 is what per cent of 800 ? the base is 800; in the problem, 18 is 3% of what? the base is not given, but is to be found by the student. Observe that whenever the base is given in problems like the above, it follows the word of. 212. There are three cases in percentage and only three. Case I. To find some per cent (hundredths) of a number, as: find 15% of 600. Case II. To find a number when some per cent of it is given, as : 24 is 8% of what number? Case III. To find what per cent one number is of another, as: 12 is what % of 400 ? Observe that a thorough knowledge of fractions is the necessary preparation for percentage. The work in percentage is work in fractions, the denominator employed being 100. Percentage. 213. CASE I. Find 17 per cent (.17) of 8460. Note.—We may find f of a number by finding 3 times 1 fourth of it; that is, by multiplying it by 1. So we may find .17 of a number by finding 17 times 1 hundredth of the number; that is, by multiplying by .17. Operation. Explanation. 84'60 .17 One per cent (1 hundredth) of 8460 is 84.60; 17 592.20 per cent (hundredths) of 8460 is 17 times 84.60, or 846.0 1438.20. 1438.20 PROBLEMS. 1. Find 17% of 6420; of 5252; of 31.40. 9. A sold goods for B. As remuneration for his services he received a sum equal to 12% of the sales. He sold $2146 worth of goods. How much did he receive ? 10. C is a collector of money. For this service he charges a commission of 6%; that is, his pay is 6% of the amount collected. He collected for D $375. How much should he pay over to D, and how much should he retain as pay for collecting? Percentage. 214. CASE II. 673.20 is 17 per cent (.17) of what number? Operation No. 1. Explanation. 17)673.20(39.60 Since 673.20 is 17 hundredths of the 51 100 number, 1 hundredth of the number is 163 3960. 1 seventeenth of 673.20, or 39.60; and 153 100 hundredths = 100 times 39.60, or 3960. Operation No. 2. .17)673.20°(3960 51 Explanation. We may find 100 seventeenths of a number by finding 1 seventeenth of a hundred times the number. 100 times 673.20 is 67320. 1 seventeenth of 67320 is 3960. 163 102 Observe that dividing by .17 is finding 40% of the dividend, just as dividing by is finding of the dividend, and dividing by j is finding i of the dividend. NotE.—Sometimes the process may be shortened by writing the per cent as a common fraction and reducing it to its lowest terms; then using the reduced fraction instead of the one whose denominator is 100. PROBLEMS. 1. 360 is 15% of what number? 2. 360 is 25% of what number? 3. 360 is 50% of what number? 4. 360 is 75% of what number? 5. 360 is 40% of what number? (a) Find the sum of the five results Percentage. PROBLEMS. 11. A sold goods for B. As remuneration for his services A received a sum equal to 12% of the sales. He received $33.06. What was the amount of his sales? How much money does B have left of what he received for the goods after paying out of it A's commission ? 12. C is a collector of money. . For this service he charges a commission of 6% ; that is, his pay is 6% of the amount collected. His commission on a certain collection was $74.40. What was the amount collected ? How much should the man for whom he collected the money, receive ? 13. C collected a sum of money for D, deducted his commission of 6%, and paid the remainder of the sum collected to D. He paid D $350.15.* What was the sum collected ? How much money did C retain as his commission for collecting ? *$350.15 is what % of the amount collected ? * Percentage. 215. CASE III. 625 is what per cent of 900 ? Operation No. 1. Explanation. 900)625'000.69% 625 is 875 of 900. 5400 This fraction may be changed to hundredths in the usual manner, viz., 8500 8100 by performing the division indicated, “ carrying out” to hundredths only. 400 4 36 9 Operation and Explanation No. 3. 625 : 9 69 .69% = 693% 900 900 ; 9 100 Operation and Explanation No. 4. One hundredth of 900 is 9; then 625 is as many hundredths of 900 as 9 is contained times in 625. 9 is contained in 625, 694 times; so 625 is 693% (hundredths) of 900. PROBLEMS. What per cent (how many hundredths) of 800 is(1) 250 ? (2) 375 ? (3) 475 ? (4) 350 ? (5) 150 ? (a) Find the sum of the five results. |