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MISCELLANEOUS PROBLEMS. 1. What cost 16. yards of cloth at $5.1 a yard?

2. At 22} cents a pound, how many pounds of coffee can be bought for $47.85?

3. What cost 454 acres of land at $62} an acre?

4. At 34 cents a foot, how many feet of boards can be bought for $36.53?

5. What will a steer which weighs 11124 pounds cost at 43 cents a pound?

6. If 40 barrels of apples cost $273j, what will 1 barrel cost?

7. At 28.1 cents a dozen, what will 650 eggs cost?

8. At $1330 a ton, how many tons of hay can be bought for $275 ?

9. If g of a cord of wood cost $6%, what will 10 cords cost?

10. How many pounds of butter, at 32 cents a pound, must be given for 371 pounds of sugar, at 6 cents a pound ?

11. A sold his house for $3500, and thus lost } of the cost; what was the cost ?

12. A farm was sold for $8400, which was at a gain of į of the cost; what was the cost ?

13. A horse which cost $160 was sold for $120; what part of the cost was lost?

14. A lot which cost $400 was sold for $480; what part of the cost was gained ?

15. The circumference of the hind wheel of a carriage is 10. feet, and of the fore wheel 7 feet; how many revolutions will each wheel make in going a mile (5280 feet)?

16. A and B can do a piece of work in 12 days, and B alone can do it in 20 days; how long will it take A to do it?

17. A cistern can be filled by one pipe in 15 hours, and by another in 20 hours; in what time can the two pipes fill it, flowing together?

18. B owned i of a farm, and sold of his share for $6240; what was the farm worth?

19. C's house and barn cost $8425; what was the cost of each if the barn cost as much as the house?

20. A miller sold of all his wheat, and the next day bought 200 bushels; he then found that he had ; as much as at first; how much had he at first ?

21. If a pole 12 feet long cast a shadow 98 feet long, how long must a pole be to cast a shadow 21 feet long at the same hour of the day?

22. By what number must 254 be multiplied so that of the product may be 52į?

23. A fortune was left under the following conditions: A was to receive į of it, B of the remainder, and C of what then remained. It was found that A received $10,000 more than C;. what was the fortune ?

24. A miller bought wheat at 65 cents a bushel, and sold it at 75.4 cents a bushel, gaining $117 by the transaction ; how many bushels did he buy and sell ?

25. My salary is $133} per month, and my monthly expenses amount to $150; I have previously saved $300; if I take each month from my savings enough to make up the deficiency, how long will they last?

26. A merchant invested of his capital in groceries, 1 of the remainder in dry goods, 1 of what then remained in hardware, 1 of what then remained in notions, and the balance in glassware; what was his capital, if he invested $700 more in groceries than in glassware?

27. A Western farmer, being asked how many sheep he had, said his sheep were in four fields : in the first field there were 108, which was of the number in the second; the number in the second was of the number in the third ; and the number in the third was of the number in the fourth; how many sheep had he?

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1. If a square inch is divided into ten equal parts, what is one of these parts called ? What are 2 of these parts called ? 3 parts? 7 parts? 9 parts ?

2. If one-tenth of an inch is divided into ten equal parts, what is one of these parts called ? What are 2 of these parts called ? 12 parts? 65 parts?

3. If one-hundredth of an inch is divided into ten equal parts, what is one of these parts called? What are 8 of these parts called ? 15 parts? 125 parts?

4. What is t'o of to? 1 of 10?

87. These expressions, one-tenth (o), one-hundredth 600), eight-thousandths (807), one ten-thousandth Goooo), etc., are called Decimal Fractions.

Decimal fractions are thus seen to be only a special kind of common fractions.

88. A Decimal Fraction is usually expressed by placing a point (.), called the decimal point, before the numerator, and omitting the denominator. Thus, .3,

1000 1.005, Ito = .04,

Toko = .0006,

.000348, etc.

127 100000

..00127,

34 8 1000000

89. In the common system of notation the value of figures decreases from left to right in a tenfold ratio. If this law be continued below units, the first place at the right of units will express tenths, the second place hundredths, the third place thousandths, etc.

From this it appears that decimals are not only closely connected with common fractions, but are also a continuation of the common system of notation. This is more clearly shown in the following

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90. A Pure Decimal is one which consists of decimal fig. ures only; as, .4, .25, etc.

A Mixed Decimal is one which consists of an integer and a decimal; as, 4.25.

A Complex Decimal is one which has a common fraction at the right of the decimal; as, .3 .

NUMERATION OF DECIMALS.

91. In reading a decimal, first read the integral part, if any; then the decimal part regarded as an integer; and, third, the name of the right-hand decimal place. To prevent ambiguity, pause after reading each part.

Thus, 5.408 is read five—and four hundred and eightthousandths.

400.004 is read four hundred and four-thousandths; and .404 is read four hundred and fourthousandths.

Read the following decimals: 1. .5.

8. .06. 15. 300.003.
2. .8.

9. .008. 16. .303.
3. .12. 10. .4267. 17. 600.005.
4. .64.

11. .0261. 18. .605.
5. .96. 12. .0028. 19. 42.06.
6. .437. 13. .0009. 20. 125.125.
79. .525. 14. 1.0001. 21. 1.205.

22. .000325.
23. 100.001.
24. .000035.
25. 1.2345.
26. .463
27. .085).
28. .03

29. Read the following, and notice the relative position of tens and tenths, hundreds and hundredths, etc.:

10.1; 100,01; 100.001; 10000.0001; 1000000.000001.

30. Read the following, and notice the effect of moving the decimal point one, two, three, or more places to the left :

516; 51.6; 5.16; .516; .0516; .00516.

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