4. How many hundredths of $100 are $5 ? $7? $18? 5. How many hundredths of $500 are $25? $35 ? $50? 6. How many hundredths of any number is of it?? 496. Percentage is a term applied to computations in which 100 is employed as a fixed measure, or standard. The term percentage is also used to denote the result found by applying that standard to any given number. 497. Per Cent. is an abbreviation of the Latin phrase per centum, which signifies by the hundred. Thus, 5 per cent. means 5 of every 100, or, the five standing for the numerator, and the words “per cent.” for the denominator 100. The phrase "per cent.," wherever it occurs, should invariably suggest to the mind a decimal to the hundredths place. Thus, 25 per cent. = fo or .25. 498. The Sign of Per Cent. is %. It is read per sent. Thus 6% is read 6 per cent. 6 per cent., 6%, 18, and .06 are equivalent expressions; the first two are used in the statement of questions, the other two in performing the operations. 7. How many hundredths of a number is 7% of it? 9%? 31%? 15%? 88%? 63%? 25%? 184%? 45% ? 8. What per cent. of a number is of it?? .08? .124? ? ? .025? .001? .04? .375? .0325? 35 499. What per cent. of a number is of it? ANALYSIS. Since the whole of any number is 18%, of the 331 same is of 188, or equal to 33%. Hence, etc. 100 100' What % of a number is of it? 1? t? 1? ? 4: j? ? ? ? J? 2? ff? 500. What fractional part of a number is 121% of it? 121 ANALYSIS.-121% is or, equal to . Hence, etc. What part of a number is 81% of it? 16%? 15%? 20%? 371%? 71%? 61%? 25%? 66%? 75%? 501. What part of a number is 1% of it? ANALYSIS.-% is equal to . Hence, etc. 100' What is 1% of a number? %? £%? 7%? $%? $%? 70%? $%? +1%? 20%? 502. Any per cent. may be expressed either as a deci mal or as a fraction, as shown in the following 503. Change to expressions having the per cent. sign. 1. .15; .085; .331; .375; .007; 11; 11; .753. 2. 21; ; .001; 18; ; ; .00125;; 24. Change to the form of decimals, 3. 51%; 91%; 20%; 31%; 1%; %; 1%; 1121%. Change to the form of fractions, 4. 24%; 1%; 61%; 371%; §%; 31%; 120%; 75%. 504. In the applications of percentage, at least three elements are considered, viz.: the Rate, the Base, and the Percentage. Any two being given, the other can be found. 505. The Rate is the number per cent. or the number of hundredths. Thus, in 5%, .05 is the rate. Hence, Rate per cent. is the decimal which denotes how many hundredths of a number are to be taken or expressed. 506. The Base is the number of which the is taken. Thus, in the expression, 5% of $15, the base is $15. per cent. 507. The Percentage is the result obtained by taking a certain per cent. of the base. Thus, in the statement, 6% of $50 is $5, the rate is .06, the base $50, and the percentage is $3. 508. The Amount is the sum of the base and the percentage. Thus, if the base is $80, and the percentage $5, the amount is $80+$5 $85. 509. The Difference is the remainder found by subtracting the percentage from the base. Thus, if the base is $80, and the percentage $5, the difference is $80-$5 = $75. 510. The base and rate being given to find the percentage. ORAL EXERCISES. 1. What is 10% of 140? ANALYSIS.-10% is %, and of 140 is 14. Hence 10% 16. A farmer had 150 sheep, and sold 20% of them. How many had he left ? 17. A mechanic who received $20 a week had his salary increased 8%. What were his daily wages then ? 18. From a hhd. of molasses 331% was drawn. How many gallons remained? 19. A grocer bought 150 dozen eggs, and found 16% of them bad or broken. How many were salable? 20. A train of cars running 25 miles an hour increases its speed 121%. How far does it then run in an hour? 511. PRINCIPLE.-The percentage of any number is the same part of that number as the given rate is of 100%. |