MISCELLANEOUS PROBLEMS.

ART. 40. 1. What is the sum of 3,,, and?

2. What is the difference between 7 and ?

3. Multiply by 31.

4. Divide by 31.

5. What is the sum, difference, product, and quotient of 31 and 2 ?

6. What will be the cost of 15 pounds of butter at 163 cents a pound? Ans. $2.581. 7. At $41 per yard, how many yards may be bought for $114 ? Ans. 24. 8. At 284 cents per bushel, how many bushels of oats may be bought for 163 cents? Ans. bushels. 9. How many pounds in four bags, the first containing 360%, the second 580%, the third 2963, and the fourth 375,%? Ans. 161413 lbs.

10. In 5 hogsheads of sugar containing, respectively, 9451 1054, 9634, 90127, and 899, how many pounds?

11. A man has 4 lots; the first containing 3201 acres, the second 225, the third 160, and the fourth 278; how many acres in all ? Ans. 986 A.

12. A man owes the following sums: to A $32.561, to B $44.95%, to C $32.727, to D $53.31%, to E 192.05,73. How much does he owe in all ?

13. A farm is divided into 5 fields, containing, respectively, as follows: 203, 56, 36, 9, and 102 in all ?

14. A man purchased of a yard of $3.62 per yard; what did it cost him?

acres. How many Ans. 2263 A. velvet at the rate of

Ans. $3.17.

15. A man owned

14

of a boat, and sold of of his share for $2400. At that rate, what was the whole worth of it?

Ans. $19200.

16. James has of an orange. He gives Horace of this amount, and then divides the remainder equally between three boys. What part does each of the three boys receive ?

Ans..

of a

Ans. $12.

17. If of a barrel of flour costs $5, how much will 2 bags of flour cost, one containing of a barrel, and the other barrel ? 18. Bought of of 5 yards of broadcloth at the rate of $3.50 per yard. Required the cost of it. Ans. $8.02.

19. What will be the cost of 7 yards of muslin at 12 cents per yard, and 12 yards of gingham at 183 cents per yard ? Ans. $3.281.

20. I purchased 7 loads of coal, each containing 153 bushels, at 12 cents per bushel. Required the cost. Ans. $13.781. 21. A owns of a vessel, and sells of his share to B for $45000. What part of the vessel has he left, and what is it worth at that rate? Ans. left, worth $15,000.

22. A owns of a ship. He sells of his share to B for a certain sum, and of what he then owns to C for $5,000. What was the value of the whole ship at C's rate of purchase? Ans, $72000.

23. A owns of an acre of land, and B of an acre. How much does A own more than B? How many times more? How much do they both own?

Ans. to the last, f.

24. I have $1000 and wish to lay out $346% of it in sugar at 81 cents per pound, and the remainder in coffee at 113 cents per pound. How many pounds of coffee do I buy?

Ans. 5561 lbs.

25. A merchant directed his agent to lay out of $2354 in wheat at 87 cents per bushel; of it in rye at 56 cents per bushel; and the remainder in oats at 31 cents per bushel How many bushels of each did he purchase?

Ans. to last, 564 bus. of oats.

26. What will 8 pounds of sugar cost at 183 cents per pound?

27. A has 6 acres in one lot and 7 in another; B has 5 times as much as A. How many has he? Ans. 8337 A. 28. What will of yards of cloth cost at of dollars per yard ?

33

29. A merchant owns of a mercantile establishment worth $64,000. He sells of his share to B, and the remainder to 19 C. How much does he receive from B and C respectively, and what part has he remaining? Ans. From B, $33600.

30. A merchant has 33

From C, $11200.
Has left,

yards of cloth, from which he

wishes to cut an equal number of coats, pants, and vests. What number of each can he cut if they contain 33, 21, and 1 yards respectively?

31. A merchant owns

were destroyed by fire, and

Ans. 4.

of a stock of goods, of which

of the remainder damaged by

water. What part of the whole remained uninjured? How much did he lose, provided the uninjured goods are sold at cost for $5400, and the damaged at half cost?

Ans.

uninjured.

Loses, $60,000.

DECIMAL FRACTIONS.

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ART. 41. A decimal fraction is a fraction whose denominator is some power of ten, thus, 1, 1 are decimal fractions.

In writing a decimal fraction the denominator is omitted, the numerator being written in such a manner as to indicate the denominator. This is done by continuing the decimal scale used in writing whole numbers below or to the right of the order of units.

The first order at the right of units is tenths, the second hundredths, the third thousandths, etc.

A point (.), called the decimal point or separatrix, is placed between the order of units and the order of tenths. The orders at the left of the decimal point express a whole number; the orders at the right a decimal fraction, or simply a decimal.

The names of the orders at the right and left of the decimal point, and the relation of decimals to whole numbers, are shown in the following

TABLE.

Co Millionths.

3 3

WHOLE NUMBER.

DECIMALS.

The orders at the right of the decimal point are called decimal places. Thus in .0223 there are four decimal places.

The denominator of a decimal fraction is 1 with as many ciphers annexed as there are decimal places in the numerator. Thus the denominator of .00035 is 100000.

Since the value of decimal orders decreases in a tenfold ratio from left to right, every cipher placed between decimal figures and the decimal point, thus removing them one place to the right, diminishes their value tenfold. Thus .025 is one-tenth of .25.

Ciphers placed at the right of decimal figures do not change their value. Thus .250 .25 and .8700-.87.

A whole number and a decimal written together constitute a mixed number, or a mixed decimal, as 25.037.

Note. When the denominator of a decimal fraction is written, it is usually considered a common fraction; the term decimal being only applied when the denominator is understood. The above definition of a decimal fraction is, however, strictly correct.

NUMERATION OF DECIMALS.

ART. 42. In reading a decimal expressed in figures, two things are necessary: 1st. To ascertain what the figures express as a whole number. 2d. To ascertain the order of the right hand figure. In a whole number, the right hand figure is always units. In a decimal, it is found by commencing at the decimal point and naming each order toward the right. Ex. 1. Express in words .002015607.

Explanation.-Commence at the right hand and separate the figures into periods as in whole numbers, thus: 2.015.607. Next commence at the decimal point and name the orders to the last decimal figure, which is billionths. Then read the decimal as a whole number, adding the name of the last decimal figure, thus: two millions, fifteen thousand, six hundred and seven billionths. Hence the following general

RULE.

Read the figures as in whole numbers and add the name of the last decimal order.

Examples.

Express in words the following decimals:

2. .01012305

3. .000027

4. .500006

5. 207.0084

Suggestion.-Read the whole number as units, and then

the decimal.

6. 7080.00607008

7. .002005505

8. .006

9. 600.06

10. 1000.001

11. 25000000.000250

12. 206.000000206