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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 =
Y^ or .06; 28^ per cent=j^ or .28^; £ per cent = -^
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 bane 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 J. So we may find .17 of a number by finding 17 times 1 hundredth of the number; that is, by multiplying by .17.
Operation. 84v60 .17
One per cent (1 hundredth) of 8460 is 84.60; 17 per cent (hundredths) of 8460 is 17 times 84.60, or 1438.20.
(a) Find the sum of the twenty-four results.
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?
214. Case IL
673.20 is 17 per cent (.17) of what number?
Observe that dividing by .17 is finding W of the dividend, just as dividing by i is finding | of the .dividend, and dividing by J is finding \ 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.
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 resu1ts
19 per cent of what?
20 per cent of what?
24 per cent of what?
25 per cent of what? sum of the ten results.
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?
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, 69 J times; so 625 is 69# (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.