SOLUTION 2d.-12.3084+2.34-48 +18==Ÿ>] ??=bu =100x138001=1 of 526=5.26. From either of these solutions we derive the following

Rule.-I. Annex ciphers to the dividend, if necessary to make the number of decimals equal to the number of deci mal places in the divisor.

II. Divide as in whole numbers, annexing ciphers to the dividend when needed to continue the division.

III. Point off as many decimals in the quotient as the number of decimal places in the dividend exceeds the num ber in the divisor.

NOTES.-1. When there are ciphers at the right of the divisor, cut them off, divide by the significant part, and then point off as many decimal places as before, plus the number of ciphers cut off.

2. Make complex decimals pure or divide them like common mixed numbers, or multiply both by the L. C. M. of the denominators, and then divide.

Ans. 2.5. | 17. 1÷.125.

13. .375 .025 ? Ans. 15. 18. .51+.015.

12. .065÷.026?

14. .008.04?

15. .012.06?

Ans. .2. 19. 155.0625.

Ans. 8.

Ans. 34.

Ans. 2480.

Ans. .2. 20. .00625÷25.

16. .004 2.5? Ans. .0016. 21. 25÷.00625.

22. (2.04÷17+47÷200 x 5000)-?

Ans. .00025.

Ans. 4000.

Ans. 1174.245.

28. (789-.789)+(.75-.075x.75 of 8)? Ans. 194.62.

24. 45x.181+3.6×.31÷(3.5—3.48)? Ans. 8.5436

25. ($347.84 $10.87)×.0025+.01 × 50? -=

Ans. 32.

26. ($1080×3.27)÷$10.90-($790÷$3.95)? Ans. 124.

of 8.75.

Ans. 307. 1.25

7. Divide 1184 by .04; also 2.4001 by 1.56

61

9. Divide £240 by of 24 of 4 of 14. Ans. £2851.

2 28

10. What number multiplied by 7g will give 6 for a product?

Ans. .

11. Divide seven millionths by twelve and a half ten-mil lionths.

Ans. 5.6.

.375, and .5, and multiply the sum by 6.24.

621

15. Multiply by 25 millionths, and divide the pro

duct by .0012)

Ans. .00125.

16. The product of two numbers is †, and one of them is of of 2; what is the other? Ans. 1.

17. Add 2.5 cwt., 1.25 cwt., 5 cwt., 4.375 cwt., 1.875 cwt., 8.5 cwt., 1.225 cwt., and 1.275 cwt. Ans. 20 cwt.

18. What number multiplied by of 1 of 5 is equal to
of 274?
Ans. 876.

· of

19. Divide the sum of six thousandths and six millionthe by their difference, to 6 decimal places. Ans. 1.002002+. 20. From the sum of,, and, take the remainder ob tained by subtracting from of 5 of 4.

21. What number must be divided by

make a quotient equal to the value of 64 of

Ans. 188.

of 2 of 1층

51

to

of 6?

Ans. 24.

10

22. John had $225 and earned of 3 times $88 more; having lost part of his money, he found that he had $1868 remaining; what amount did he lose? Ans. $978.

23. A ton of iron ore from the mines of Cornwall yields .65 of a ton of pure iron; how much iron will 578.8 tons of ore yield? Ans. 376.22 tons. 24. An oil refiner has on hand 16,745 gallons of coal oil; how many casks, each containing 42.5 gallons, can be filled with it? Ans. 394 casks.

25. How many dress patterns of 12.25 yards each, can be cut from a piece of French percale, containing 50 yards? Ans. 4+ patterns.

26. An engine pumped 41.25 barrels of 31.5 gallons each from a tank containing 1500 gallons; how many gallons remained? Ans. 200.625 gal.

27. I bought 3 loads of wood, the first containing 1.02 cords, the second 1.05 cords, he third .945 cords; what did it cost at $3.60 a cord? Ans. $10.854.

28. A dealer bought 1086 bushels of wheat; how many bins, each holding 20.25 bushels, will it fill, and how many bushel-bags can be filled from what remains?

Ans. 53 bins; 12.75 bags. 29. Two speculators bought 4320 acres of Western land.

which they divide so that one has .37 and the other .62

of it; how many acres had each?

Ans. 1620; 2700.

30. How many lengths of 6-inch stove-pipe can be inade from 87.48 pounds of Norway iron, if one length requires 3.24 pounds?

Ans. 27.

31. Mr. Newlin paid $4000 for a truck farm, giving $76.25 an acre for 27.25 acres, and $85.75 for the remainder; how many acres did he buy? Ans. 49.66+ acres.

32. A man bought 345.75 tons of hay, at $16.25 a ton, of which he sold at $17.75 a ton, and the rest at cost; how much was the gain? Ans. $172.87.

33. Mr. Hartman bought a lot of wheat and sold .15 of it to one man, and .25 of it to another, and kept 572.85 bushels; how much did he buy? Ans. 954.75 bu.

34. A man devotes .12 of his income to charity, .25 for educating his children, .45 for household expenses, and saves the remainder, which is $284.76; required his income.

Ans. $1582.

35. How many cords of wood, at $5.12 a cord, must 1 give for 91.25 bushels of wheat, at $1.40 a bushel, and 85 bushels of rye, at $1.25 a bushel? Ans. 45.66 cords.

36. The circumference of the fore wheel of a wagon is 12.75 feet, and of the hind wheel 14.25 feet; how much oftener does one turn than the other in going 5280 feet, or one mile? Ans. 43.59+ times.

87. A ship whose cargo was worth $25,000, being disabled in a storm, .45 of the whole cargo was thrown overboard; what would a merchant lose who owned .25 of the cargo ? Ans. $2843.75.

38. A grain dealer expended $6210 for grain, of it being for wheat, at $1.25 a bushel, of it for corn, at $0.75 a bushel, and the remainder for rye, at $1.12 a bushel; how many bushels of each kind did he purchase?

Ans. Wheat, 1656 bu.; Corn, 2070 bu.; Rye, 2300 bu

UNITED STATES MONEY.

211. United States Money, or the currency of the United States, is expressed in the decimal system.

212. The several denominations and their relation to each other are presented in the following table:

213. The dollar is the unit and is indicated by the symbol $; the eagle and dollar are read as a number of dollars. Thus $245 is read 245 dollars, instead of 24 eagles, 5 dollars.

214. The dime is one tenth of a dollar, and is expressed as tenths, the decimal point being placed between dimes and dollars. Thus $2.3 expresses 2 dollars and 3 dimes.

215. The cent is one tenth of a dime or one hundredth of a dollar, and is written in hundredths place. Thus $6.75 indicates 6 dollars 7 dimes and 5 cents. Dimes and cents, however, are usually read as a number of cents. Thus $6.75 is read 6 dollars and 75 cents.

216. Since dimes and cents are regarded as a number of cents, when the number of cents is less than 10, a cipher must be written in tenths place. Thus 3 dollars and 4 cents are written $3.04.

217. The mill is one tenth of a cent or one thousandth ot a dollar, and is written in thousandths place. Thus $8.375 is read 8 dollars 37 cents and 5 mills.

NOTES.-1. In checks, notes, drafts, etc., cents are usually written as tundredths of a dollar in the form of a common fraction, as $12,75.

2 When the final result of a business computation contains mills, if 5 or more they are reckoned 1 cent, and if less than 5 they are rejected. Thus $7.187 would be reckoned as $7.19 and $3.162 as $3.16.

3. We used dollars and cents in treating the fundamental rules; we now give a more formal treatment of decimal currency, involving problems that pupils were not then prepared to solve.