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In Common Fractions we learned that a number may be divided into any number of equal parts and any number of these may be taken.
Thus, of 60 means that 60 is divided into 4 equal parts and 3 of these parts are taken.
In Decimal Fractions we learned that a number may be divided into 10, 100, 1000, etc., equal parts, and that any number of these parts may be taken.
Thus, .9 of 60 means that 60 is divided into 10 equal parts and that 9 of these equal parts are taken.
We now come to a subject that divides a number into 100 equal parts only. We call this subject Percentage.
In common fractions we compute by halves, thirds, fourths, sixths, etc.; in decimal fractions we compute by tenths, hundredths, thousandths, etc. ; but in percentage we compute by hundredths only.
Another name for hundredths is per cent, usually written“ %
We may now write any number of hundredths in three different ways, thus: 180, .08, 8% ; Moo, .25, 25%.
Percentage is simply an application of decimal fractions. 1. Write the following numbers as per cents :
.05 .03 .15.20 .25 .40.06 .75 2. Write the following as decimals: 5% 20% 7% 15% 25% 16% 18% 24% 50% 75%.
3. Show by equivalent decimals that naughts added to the right of a decimal do not affect its value. 4. Write as decimals, and as per cents :
2 25 5. What is the difference between .05 of $100 and 5% of $100 ?
6. 5% = o of a number; 10% = 1o of a number. 7. 25% of $100 may be found in two ways: (a) 25 % = 1; of $100 = $25. (6) 25%=.25; .25 x $100 = $25. Learn the following :
1. Find 28% of 7500 bushels of oats. 7500 bu. .28
Since percentage is simply so many hundredths of 60000
anything, 28% of 7500 bushels equals .28 of 7500 15000
bushels or 2100 bushels. 2100.99 bu.
5. 6% of $57.40 10. 5% of $200.60 15. 80% of $905 6. 5% of $90.80 11. 7% of $500.50 16. 98% of $ 7008
17. Mr. Jordon bought a horse for $175 and sold it for 90% of the cost. For how much did he sell the horse ?
18. Raymond has $165 in the savings bank and Bertha has 80 % as much. How much more money has Raymond in the bank than Bertha ?
19. The distance between two cities is 1080 miles. After 45% of the distance is traveled, how much of the distance remains to be traveled ?
20. Mr. Watson earned $1580 in a year, and his son Henry 65% as much. Find the amount Henry earned.
21. The salary of a school teacher last year was $40, and this year her salary was increased 25% of last year's salary. Find her present salary.
22. Paul lives 560 rods from the schoolhouse and David 72% as far. Find the number of rods David lives from the schoolhouse.
23. Mr. Adams borrows $365 for one year, and pays 6 % for the use of the money for the time.
How much money will pay the debt when due?
24. Mr. Brown has loaned $1200 to one party and $1600 to another party. How much does Mr. Brown get each year for the use of the money if each party pays him 5% of the amount borrowed ?
25. Find 5% of 20; of 40; of 50; of 60; of 80.
26. A newsboy sells $18 worth of papers and gets 40% for selling. Find his profit.
27. Mary has $24 in the savings bank, and deposits 25% as much as she has in the bank. Find the amount deposited.
28. A boy borrows $200 to go to school, and pays the lender 5% for the use of the money for one year.
How much does he pay for its use ? 29. A boy bought a pony and a cart. The
pony cost $80, and the cart 60 % as much as the pony. Find the total cost.
30. A man had 400 sheep. On Monday he sold 25% of them. On Tuesday he sold 25% of the remainder. How many sheep had he then ?
31. In a spelling test of 30 words, James missed 20%. How many words did he spell correctly?
32. 1 = Tid = ?%. Compare , and .20; 4 and 20%.
33. A man bought a house for $2800. He paid 78% of the amount cash, and gave his note for the balance. For how much did he give his note ?
34. A merchant sold in one year $25,375 worth of goods. His profits were 20% of the sales. Find his profits.
OPERATIONS WITH UNITED STATES MONEY
10 mills = I cent
10 dollars = I eagle
1. From the above table tell why United States money is called a decimal system of money.
2. How many cents equal a dollar ? What part of a dollar is 1 cent ?
3. A cent is what part of a dime? A dime is what part of a dollar ? Cents are written as hundredths of a dollar. 4. Read as hundredths of a dollar : $0.01 $0.02 $0.03
$ 0.03 $5.07
$5.07 $9.09 $8.07.
NOTE. 1 cent may be written either $0.01 or $.01 ; 25 cents may be written either $0.25 or $.25, etc. The naught preceding the decimal point does not affect the result, and is sometimes written to show more prominently that cents and not dollars are represented.
5. How many mills equal $1? What part of a dollar is 1 mill? Mills are written as thousandths of a dollar. Thus 1 mill is written $ 0.001. $0.005 may be read one half cent. Why?
Mills are not coined, but are used for convenience in computations. In final results any part of a cent is usually regarded by the seller as a whole cent. Thus, for a bill amounting to $0.565, we pay $0.57.
6. How does moving a number one place to the right affect its value? one place to the left?