COMMERCIAL ARITHMETIC.

PERCENTAGE.

1. Percentage is a method of computation having 100 for its unit or base.

The sign of Percentage is the symbol, %, called per cent., which is an abbreviation of the Latin per centum, and signifies by the hundred. Thus, 8% means 8 of every hundred. It may refer to any denomination, and may denote 8 cents of every hundred cents, 8 dollars of every hundred dollars, 8 bushels of every hundred bushels, etc.

2. The elements of percentage are the Base, the Rate, and the Percentage.

3. The Base is the number of which the percentage is taken.

4. The Rate is the number denoting how many hundredths of the base are to be taken.

5. The Percentage is the result obtained by taking a certain number of hundredths of the base.

6. The Amount is the sum of the base and the percentage.

7. The Difference is the remainder obtained by subtracting the percentage from the base.

In the statement 8% of $400 is $32, the base is $400; the rate, 8%, or .08; and the percentage, $32. The amount is $400 + $32 $432; and the difference, $400 – $32 = $368.

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8. One per cent. of any number is one hundredth of it; four per cent. is four hundredths, and, in general, any per cent. of a number may be expressed as so many decimal or fractional parts of that number; thus :

1. How many hundredths of a number is 9% of it? 11% 16% 25%? 18%? 50%? 64%? 80% ? 90%? 61%? 81% ?

2. What part of a number is 25% of it? 10%? 20%? 50%? 75%? 15%? 121%? 16%? 3. What per cent. of a number is

J? ? ? j ? j ?

334%? 63% ?

of it?? ?

4. What per cent. of a number is .03 of it? .05? .11? .46 ? .1875? .065 ? .0625? .75334 ?

.225 ?

.666 ?

WRITTEN

EXERCISES.

1. Express 8% as a decimal and as a common fraction.

OPERATION.

8%= .08 180 = 28

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SOLUTION.-Since 8% signifies 8 on the hundred, it may be expressed decimally, .08; or, as a common fraction, 1805

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Express in the same manner :

2.2%; 6%; 20%; 12%; 40%; 15%; 55%; 98%.
3. 142%; f18%; 61%; 81%; 371%; 40%; 223%.
4. 1121%; 116%; 1183%; 1%; 1%; 3%; 1%.
5. 3%; §%; 3%; 1%; £%; §%; £%; £%•

Change to expressions with per cent. sign:

6. .04; .27; .45; .375; .66; .05; .5; .0625. 7. ; ; ; ; ; ; ; 1; 1; 1;

CASE I.

9. The base and rate being given, to find the percentage, or amount, or difference.

12. What are my expenses, if I earn $800 a year and expend 30% of it? 60%? 25%? 15%? 27% ?

13. What is the amount of 40 increased by 5% of itself? 80%? 121%? 66%? 40% ?

14. How much is $16 increased by 25% ? $60? $250 ? $900? $1000? $24000?