Various useful exercises may be based upon these synopses. After the pupil has become familiar with their mode of construction, he may be required to write out, from memory, an outline synopsis of each section that he has studied, so as to show whether or not he has comprehended the relations of the various parts of the subject which he has passed over. Or the whole or a part of a Synopsis, embracing one or more topics, may be placed upon the blackboard, and the pupil required to give briefly but accurately the sub-divisions, definitions, principles, etc., involved in each. By this means, if further tested by questions, a thorough and wellclassified knowledge of the whole subject will be permanently impressed upon his mind. Editions of this book are bound with and without answers. Those with answers will be sent, unless otherwise ordered. 4. How many hundredths of $100 are $5? $7? $18? 5. How many hundredths of $500 are $25? $35? $50? 496. Percentage is a term applied to computations in which 100 is employed as a fixed measure, or standard. 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 156, the 5 standing for the numerator, and the words "per cent." for the denominator 100. Thus, 25 per cent. = or .25. 498. The Sign of Per Cent. is %. It is read per cent. Thus 6% is read 6 per cent. What per cent. of a number is of it?? .08? .12?? 35? .025? .001? .043? .375? .0325? 499. What per cent. of a number is of it? 100 ANALYSIS. Since the whole of any number is 188, of the 331 same is of 100, or equal to 33%. Hence, etc. What % of a number is of it? 1? f? j? #? ? 500. What fractional part of a number is 12% of it? 121 ANALYSIS.-121% is 100' 25 or, equal to . Hence, etc. What part of a number is 81% of it? 163%? 15%? 20%? 371%? 71%? 61%? 25%? 66? 75%? 501. What part of a number is 1% of it? ANALYSIS.-% is } 100' equal to . Hence, etc. What is % of a number? %? $%? 70%? $%? $%? 70%? $%? 11%? ? 502. Any per cent. may be expressed either as a decimal 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. 5 16 2. 21;;.004; 18; ; ; .00125; ; 2. Change to the form of decimals, 3. 51%; 91%; 20%; 31%; %; %; 13%; 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. 50%. The Percentage is the result obtained by taking a certain per cent. of the base. Thus, in the statement, 6% of $50 is $3, 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. = |