Write in words :

9. .7; .05; .01; .01(5; .203 ; .25 ; .324; 8#.

10. .601; .0015; .0125; .2405; .00025; .00123.

11. 2.7; 5.04; 6.008; 4.0019; 12.02301; 202.0202.

12. How many tenths can be expressed by one figure ?

How is 10 tenths written ?

13. How many hundredths can be expressed by one figure ?

By two ? How is 100 hundredths written ? How is 100 per

cent written ?

14. Since 1 tenth equals 10 hundredths, 100 thousandths,

1000 ten-thousandths, etc., it is plain that .1 = .10 = .100

= .1000 = .10000, etc. Hence,

159. PRINCIPLE. Annexing ciphers to a decimal reduces

it to a lower denomination without changing its value.

QUERY. Does omitting ciphers from the right of a decimal change

its value ?

1. Change .5, .03, .027, and .4850 to thousandths.

.5 = . 500 In the first two decimals we annex ciphers enough

.03 .030 to make the 3 places required to express thou-

.027 =.027 sandths. The third needs no changing. Why? The

.4850 .485 last is changed by omitting the cipher at the right.

This process is called reducing to a common name or de-

nomination (or denominator).

2. Change .8, .25, .030, .4600, and .07 to thousandths.

3. Reduce .75, .013, .020, and .0146 to ten-thousandths.

106 SCHOOL ARITHMETIC.

4. Keduce .09, .0240, .3275, .1, .00010 to millionths.

5. Change .30, 5, .400, .8000, and 1.7 to tenths.

6. Change .0032, .2, .470, and .835000 to ten-thousandths.

7. Reduce 5 ones to tenths, 3 ones to hundredths, 10 ones

to tenths, and 2 ones to per cent.

8. How does .1 compare in value with .01 ? How in form ?

Then what is the effect of prefixing a cipher to .1?

9. How does .01 compare in value with .001 ? Then how

is .01 affected by prefixing a cipher ? Prefix ciphers to other

decimals, and compare values.

160. PKINCIPLE. Prefixing a decimal cipher to a decimal

divides the value of the decimal by ten.

QUERIES. 1. How does prefixing a cipher affect the place of each

figure in the decimal ?

2. Does a figure in that place express as much value as it did before

being moved ?

3. What part of its former value does it express ? Then by what has

the decimal been divided ?

ADDITION AND SUBTRACTION.

161. In addition and subtraction of decimals the opera-

tions are the same as the like operations in integral numbers.

1. What is the sum of .613, .0176, .2, and .601 ?

.613 By arranging the decimal points in a vertical line,

.0176, we make units of the same order stand in the same

2 vertical column. The numbers are added precisely as

. (\~\

Ql in integers, and the decimal point is placed before

1.4316 tenths. (Is 14 tenths a fraction ? How is it written?)

2. From .3 subtract .1235.

( a ) (b) By arranging the decimal points in a verti-

.3 = .3000 ca j ii n6j we ca use units of the same order to

12o5 = .1/soO stand in the same column. We subtract as

.1765 .1765 i n integers or U. S. money.

QUERIES. Why may .3 be written as in (b) ? (See Art. 159.) Is it

necessary to annex ciphers to the minuend ? When the remainder is q,

mixed number, where |s the decimal point placed ?

FRACTIONS. 107

Find the value of the following :

3. .17 + .002 + .2509. 11. .75 - .25.

4. .005 + .301 + .29. 12. .5 - .005.

5. 19.909 + 100.01 + 199. 13. 100.01-25.001.

6. .375 + .048 + 255.0. 14. 10 .0678.

7. 4.372 + .4293 + 3.87. 15. .16 -.06814.

8. 5.0008 + 124 + .016. 16. 1000 - .1000.

9. 86.45 + .001 + .05. 17. .6504 .067.

10. 2.3 + .004 + .2 + .88. 18. .1 - .0053.

19. 94.61 + .00421 4- .0003 + .0044 + 10.

20. 84.56 + 9.245 + .8763 + 8.009 + 7.7.

21. 1 million one millionth.

22. 10. 10 ten-thousandths.

23. 94 thousandths 253 ten-millionths.

24. 25 thousandths 25 ten-thousandths.

25. 1 1 thousandth + 1 tenth + 100 hundredths.

26. The minuend is the sum of .3 and .003 ; the subtra-

hend is .02875. What is the remainder ?

27. From what number must .0105 be subtracted to leave

the remainder 1.807 ?

28. The larger of two numbers is 3822.078 ; their differ-

ence is 1934.124. What is the less number ?

29. Find the least decimal which added to 1.4142 .0022

will make the result an integer.

30. A owes $1,000 to B, and $1,347.55 to C. He has in

cash $1,955.75. If he pays C in full, how much will he lack

of having enough to pay B ?

31. Mr. Slaven bought an organ for $85.50 on a credit of

three months. He concluded to pay cash, and was allowed

a discount of $1.27. How much had he left out of a $100 bill ?

32. Bishop Brothers sold goods amounting to $190.50 on

Monday, $250 on Tuesday, $117.25 on Wednesday, $57 on

Thursday, $135.75 on Friday, and $427.37 on Saturday,

What were the total sales for the week ?

108 SCHOOL ARITHMETIC.

33. Find the sum of 345 millionths, forty and 40 millionths,

seven and 7 thousandths, thirty-eight and 87 ten-thou-

sandths.

34. In a corncrib that will hold 572.5 bushels of corn

there are 329.375 bushels. How many bushels will be re-

quired to fill it ?

35. One side of a square field is 42.375 rods long. If 12.5

rods of the fence around it are blown down, how many rods

will remain standing ?

36. A tank that will hold 1050.75 gallons contains 396.7

gallons. If 135.5 gallons be added, how much will still be

needed to fill the tank ?

37. A man bought a farm for $1,750 and a lot for $975.75.

For what amount must he sell both to gain $289.50 ?

MULTIPLICATION AND DIVISION.

162. The processes of multiplication and division of deci-

mals are the same as the like processes in integers, the locat-

ing of the decimal point being the only thing that needs

special attention.

(a) (b) (c) (d)

.1 1. .25 25

1. In (a), the figure 1 expresses 1 tenth, in (b) it ex-

presses 1 one. What has been the effect of moving the deci-

mal point one place to the right ?

2. In (d), the 2 expresses 2 ones, in (c) 2 tenths. The

5 in (d) expresses 5 tenths, in (c) 5 hundredths. What has

been the effect of moving the decimal point one place to the

left?

163. PRINCIPLE. Each removal of the decimal point one

place to the right multiplies the decimal ~by 10 ; each removal

one place to the left divides the decimal by 10.

Thus, by moving the point one place to the right, .825 becomes 3.25 ;

that is, 3 tenths have become 3 ones, the 2 hundredths have become 2

tenths, and the 5 thousandths have become 5 hundredths. Since the

FRACTIONS. 109

value of each figure has been multiplied by 10, the value of the entire

decimal has been multiplied by 10.

(fl^gf Have the pupil illustrate the second part of the principle, which

is the converse of the first.

164. To multiply or divide a decimal by 1C, 1OO,

1OOO, etc.

RULES. 1. To multiply a decimal by 10, 100, 1000, etc.,

move the decimal point as many places to the right as there are

ciphers in the multiplier, annexing ciphers when necessary.

2. To divide a decimal by 10, 100, 1000, etc., move the deci-

mal point as many places to theleft as there are ciphers in the

divisor, prefixing ciphers when necessary.

1. Multiply .275 by 100 ; also by 10000.

.275 x 100 = 27.5. .275 x 10000 = 2750.

2. Divide .275 and G2.5 each by 100.

.275 -f- 100 = .00275. 62.5 ~ 100 = .625.

Find the value of :

3. 3.25 x 10. 8. 37.5 ~ 10. 13. .37685 x 1000.

4. 69.3 x 10. 9. 6.25 -f- 10. 14. 52.16 x 1000.

5. .75 x 100. 10. .314 -r- 10. 15. 7.013 -f- 100.

6. .486 x 1000. 11. .209 4- 100. 16. 3875 -=- 1000.

7. 1.625 x 100. 12. 632 -f- 100. 17. 41.065 + 100.

165. To multiply or divide a decimal by .1, .01,

.OO1, etc.

RULES. 1. To multiply by .1, .01, .001, etc., move the deci-

mal point as many places to the left as there are decimal places

in the multiplier.

2. To divide by .1, .01, .001, etc., move the decimal point as

many places to the right as there are decimal places in the

divisor.

1. Multiply 1.093 by .1 ; also by .01.

1.093 x .1 =3 1.093 -f- 10 = .1093.

1.093 x .01 = 1.093 -f, 100 = .01093.

To multiply a number by .1 is to take one tenth of it ; that is, to

110 SCHOOL ARITHMETIC.

multiply by .1 is to divide by 10 ; to multiply by .01 is to divide by 100,

etc. By comparing the products with the multiplicands, we find that the

decimal point has been moved to the left as many places as there are

ciphers in the multiplier. (See Art. 164.)

2. Divide 32.5 by .1 ; also by .01.

32.5 -*-.! = 32.5 x 10 = 325.

32.5 -f- .01 = 32.5 x 100 - 3250.

Since there are 10 tenths in 1, one tenth is contained in any number

10 times as often as one is contained in it. But dividing a number by 1

does not alter its value. Hence to divide a number by .1 is to multiply

it by 10 ; to divide by .01 is to multiply by 100, etc.

Multiply : Divide :

3. .258 by 10. 14. 37.5 by 100.

4. 7.07 by 100. 15. 436 by 1000.

5. 3. 916 by 1000. 16. .900 by 100.

6. .846 by 10000. 17. 24.57 by 1000.

7. 7.5 by .1. 18. 5 by 1000.

8. 83.7 by .01. 19. .99 by .1.

9. 3.25 by .01. 20. .0075 by .01.

10. .3004 by .001. 21. .0003 by .001.

11. 179.5 by .001. 22. 4444 by .0001.

12. 3.428 by .0001. 23. 18 by .01.

13. .5 by .0001. 24. 100 by .1000.

25. Which is the greater, .5 x 100, or .5 -f- .01 ?

26. How much greater is .75 x 1000 than .25 ~ .001 ?

166. To multiply or divide in decimals universal

case.

PRINCIPLES. 1. TJie product of two decimals contains

as many decimal places as there are decimal places in both

factors.

2. The quotient of two decimals contains as many decimal

places as the number of decimal places in the dividend exceeds

the number in the divisor.

The number of decimal places in the dividend can be increased as you

please, by principle in Art. 159.

FRACTIONS. HI

1. Multiply .036 by .27.

.036 The multiplier .27 = 27 x .01. We therefore multiply

.27 first by 27, then the resulting product by .01. 36 thousandths

x 27 = 972 thousandths, or .972. Multiplying this product

wo by .01 moves the decimal point two places to the left (Art.

'nhH79 1^5). Hence the required product is .00972. It has as many

decimal places as both factors have.

If we multiply as in integers, we get the product 972, to which we pre-

fix two ciphers to make the required five places.

2. Divide .00972 by .27.

.27).00972(.036 The dividend being the product of divisor and

81 quotient must contain as many decimal places as

](j both of them. Since the dividend contains 5 decimal

162 places and the divisor 2, the quotient must contain 5

2, or 3 decimal places. Dividing as in integers,

we get the quotient 36, to which we prefix a cipher to make the required

three places.

167. RULES. 1. In the multiplication of decimals multiply

as in integers, and from the right of the product point off as

many decimal places as there are in both factors, prefixing

ciphers, if necessary, to make the required number of decimal

places.

2. In the division of decimals, divide as in integers (annex-

ing ciphers, if necessary, to the dividend), and point off from

the right of the quotient as many decimal places as those of the

dividend exceed those of the divisor.

If the quotient does not contain a sufficient number of decimal places,

ciphers must be prefixed to make the required number.

(a) Find the product of :

1. .28 x 4.8. 9. 10000 x .0001.

2. .6 x .7. 10. 7.5 x .0005.

3. .35 x .16. 11. 1000000 x .000001.

4. 10 x .1. 12. .001 x 10000.

5. .134 x 25. 13. .1 x .1.

6. 216 x .24. 14. .5 x .5.

7. .478 x .152. 15. .5 x .05,

8. .0017 x .09. 16. .05 x .005.

SCHOOL ARITHMETIC.

(a) Find the product of :

17. .01 x .001.

18. 150 x .1.

19. $1 x .1.

20. 7 x 1.1.

21. 2.5 x 2.5.

22. $100 x .06.

23. .017 x 3.7.

24. 101 x 1.01.

25. 1.03 x 1.09.

26. 5.005 x .005.

(b) Find the quotient of

1. .00125 -4-. 5.

2. .0075 -4-1.5.

3. 1 ~ .1.

4. .01 -4- 100.

5. 16.84-4- .02.

6. .00884-4- .34.

7. .0355 + .71.

8. 16.025 -4- .045.

9. 10000 -4- .0001.

10. .000375 -4- .0005.

11. 1000000 -4- .000001.

12. .000001 ~ 1000000.

13. $150 -4- $ .06

14. $1 -4- $ .05.

15. 159.750 + .00375.

16. 14400 -4-. 32.

17. 14400 ~- 3.2.

18. 200 -4- .002.

19. .735 ~ 500,

20. 78.13 -4- 5.

21. 78.39 -f- 3.

22. 125 ~ 25000.

27. .008 x 800.

28. 5 tenths x 50 hun-

dredths.

29. .01 x .1 x 1.

30. .05 x 5 x .50.

31. 72.5 x 10.

32. .1225 x .1.

33. 25.6 x .20.

34. .054 x 100.

35. 125 x 1.05.

23. 12 -4- .0012.

24. 5.4768-4-22.82.

25. .025 '-4- 250.

26. .0567 -4- 43.

27. 1 -4- 3.1416.

28. ten -4- .01.

29. 1 millionth -4- .01.

30. 300 hundredths ~ 15

tenths.

31. 3.1416 -T- .31416.

32. .25 -4- .0025.

33. 9 ones -4- 40 tenths.

34. 25 tenths -4- 25 hun-

dredths.

35. 25 hundredths -4- .025.

36. 27.45 -r 1.5.

37. 250 -4- .025.

38. 2750 4- .25.

39. 3.609 -4- .9.

40. 27.63^.003.

41. 4.914-4- 70.

42. .026 ^- .000013.

FRACTIONS. 113

1<>8. 1. Multiply 4.05 by 700, and divide the product by

300.

4.05 x 100 = 405. Then 405 x 7 = 3255.

3255 -T- 100 = 32.55 ; and 32.55 -*- 3 = 10.85.

Find the value of :

2. 520.53 x 50. 7. 030 -5- 500.

3. 245.0 x 400. 8. .844-5- 400.

4. .864 x 900. 9. 307.2 H- 1200.

5. .7854 x 700. 10. 2697.5 -5- 8300.

6. 150 x 25$. 11. 150 -f- 25#.

12. What is the value of .05 x .07 + .28 -5- .5 ?

13. If I give 3 pigs for $7.50, how many must I give for

$37.50?

14. A man paid $17.25 for 300 pounds of sugar. What

did it cost per pound ?

15. How many eggs in a crate containing 24.5 dozen ?

16. If 8 pounds of coffee cost $1.74, what will 5 pounds

cost?

17. At 2%<fi each, how much will 3.25 dozen lemons cost ?

18. A man paid $15 for rice, at the rate of 4 pounds for a

quarter. How many pounds did he get ?

19. A has $1.40 and B has 2.5 times as much. How much

must B give A so that each may have the same amount ?

BILLS AND ACCOUNTS.

169. Prof. Samuel Andrews bought of J. R. Weldin &

Co. the following: 6 dozen lead pencils at $.30 a dozen, 2

gross pens at $.85, 5 reams note paper at $1.50, and 20

arithmetics at $.75.

In a few days he received the following bill :

COLUMBIA, S. C., May 1, 1899.

Mr. SAMUEL ANDREWS,

Bought of J. R. WELDIN & Co.

To 6 dozen Lead Pencils @ $.30

1

80

" 2 gross Pens " .85

1

70

" 5 reams Note Paper " 1.50

7

50

" 20 Arithmetics " .75

15

00

26

00

When this bill was paid, the following was written on

it as a receipt- :

"Received payment,

J. R. WELDIN & Co.

G."

(The " G " is the initial of Mr. Greene, who receipted the bill.)

1. Mrs. R. D. White ordered the following from Davis

& Russell, New Orleans, La. :

18 yd. Scotch Gingham @ 21^.

36| yd- Calico @ 6^.

12 yd. India Silk @ 45$*.

25 yd. Cashmere @ $1.25.

Make out her bill, and receipt it.

BILLS AND ACCOUNTS,

115

17O. The following is a specimen of a receipted bill, with

a discount, and credits :

JACKSON, Miss., Oct. 1, 1899.

Mr. T. B. DEARMIT,

To GORDON, HAY & Co., Dr.

1899.

Jan. 13

May 21

Aug.

To 50 Grammars. .. $.40

" 24 Arithmetics. . .60

" 42 Histories 1.00

20

14

42

00

40

00

76

40

Less 10$

7

64

July 25

Or.

By Cash $25.00

68

76

Sept 8

" " . 25 00

50

00

18

76

Received payment,

GORDON, HAY & Co.

By WILSON.

171. A Debt is the amount which one person owes another.

A Debtor is a person or firm that owes a debt.

172. A Credit is the amount paid on a debt. A Cred-

itor is a person or firm to whom a debt is due.

In the transaction mentioned in Art. 170, who is the

debtor ? Who is the creditor ? Name the credits.

173. An Account is a record of the debts and credits be-

tween two parties a debtor and a creditor.

174. A Bill is a creditor's written statement of the quan-

tity and price of each item in his account with a debtor,

together with the discount and credits, if any, and the net

amount due.

Bills are commonly called invoices.

116 SCHOOL ARITHMETIC.

175. A Statement is a written summary of an account

between two parties, rendered at stated intervals, usually

monthly.

1 76. Make out and receipt the following bills, Supply

dates and names where needed.

1. Mr. R. P. Lougeay bought of McAllister & Co. 25 pounds

of coffee at 28 cents a pound, 75 pounds of sugar at 5| cents

a pound, and 20 pounds of prunes at 12 cents a pound.

2. Mrs. M. B. Kifer bought of Campbell & Smith 10 yards

of silk at $1.50 a yard, 36 yards of muslin at 7 cents a yard,

15 yards of flannel at $.75 a yard,jind 2 pairs of shoes at

$3.25 a pair.

3. Mrs. A. C. McLean bought of Kan ff man Bros. 3 table-

cloths @ $3.50, 1 piano cover @ $4.75, 4. pairs of lace cur-

tains @ $5.25, 2 doz. towels @ $3.60 a dozen, and 12 yards

cashmere @ $1.25 a yard.

4. Miss Nannie Mackrell bought of W. M. Laird 2 pairs

ladies' shoes @ $2.75 a pair, 6 pairs overshoes @ $.75 a

pair, 1 pair Oxford ties @ $1.25, 3 pairs misses' shoes @

$2.15, and 1 pair gum boots @ $3.25.

5. Mr. S. M. Brinton bought of Hopper Bros. & Co. 2

doz. silver knives @ $36 a dozen, 4 doz. silver teaspoons @

$16 a dozen, 2 doz. silver tablespoons @ $10.25 a set, and 1

silver spoon holder for $9.

6. Mr. Wm. Hasley bought of Fred Gray 12.5 tons of coal

@ $3.25, 40 bushels of apples @ $.75, 200 Ib. grapes @ 3

cents a pound, and 25 bushels of potatoes @ $.85.

7. On May 25, J. M. Logan bought of W. II. Keech 5

bedsteads @ $14, 1 bookcase for $35, and 18 chairs @ $15 a

dozen. On July 3, he bought 3 hammocks @ $2.25, and a

leather couch for $45. On June 15, he paid $50 in cash, and

on the 19th $37.50 more.

REVIEW WORK.

ORAL EXERCISES.

177. 1. How many tenths in 80 hundredths ?

2. How many hundredths in 7 tenths and 15 hundredths ?

3. I paid 3 tenths of a dollar for 3 cakes of soap. At the

same rate, ho\v much would I pay for a dozen cakes ?

4. A lady spent .1 of her money for a hat, and .4 for a

shawl, and the remainder for a dress which cost $15. How

much had she at first ?

5. At $.09 each, how many slates can be bought for $3.60 ?

6. If 80 is divided into 10 equal parts, what is one part

called ? Three parts ? Nine parts ? How many are 7 tenths

(.7) of 80?

7. If 18 is .3 of some number, what is the number ?

8. Thirty-five is .5 of what number ?

9. Of what number is 9 three tenths ?

10. The sum of .2 and .05 is .5 of what number ?

11. A has $1.50, and .3 of his money is .1 of B's money.

How much has B ?

12. B and C together have $40. If .3 of B's money equals

.9 of C's, how much has each ?

13. How often must .3 be added to itself to make 3 ?

14. How many times must .7 be subtracted from 3.5 to

leave a remainder of 1.4 ?

15. How many hundredths can be taken from 25 tenths ?

WRITTEN EXERCISES.

178. 1. If seven sheep are worth $31.50, how many sheep

can be bought for $184.50 ?

118 SCHOOL ARITHMETIC.

2. A man divided his farm of 227.5 acres into 14 equal

fields. How many acres in 5 of the fields ?

3. At $2.625 a yard, how many yards of cloth can be

bought for $55.125 ?

4. If a person's taxes are 5.8 mills on $1, how much will

they be on $2500 ?

5. Find the cost of 237.25 bushels of oats at .42 of a

dollar a bushel.

6. At $.08 each, how many copy books can be bought for

$24?

7. Gold weighs 19.36 times as much as an equal bulk of

water, and a cubic foot of water weighs 62.5 pounds. How

many cubic feet of gold weigh a ton, or 2,000 pounds ?

8. One pound of dry oak' wood when burnt yields .023 of

a pound of ashes. How many pounds must be burnt to pro=

duce 46 pounds of ashes ?

9. Every day a newsboy buys 70 papers at 30 cents a

dozen, and sells them at 5 cents each. How much money

does he make in 6 days if 40 papers remain unsold ?

10. If a boy saves 6 dimes a week, in how many days can

he save enough to buy a suit worth $5.40 ?

11. How often can .013 be subtracted from 26 ?

12. Find the cost of 8 bushels 3 pecks of turnips at $.125 a

peck.

13. The divisor is 27.125, the quotient 7.32, and the re-

mainder 18.0825. What is the dividend ?

14. Divide 3 ten-millionths by 10 millionths, and multiply

the quotient by 30.

15. At $1.50 a thousand, what will 1,750 envelopes cost ?

16. The distance around a circle is about 3.1416 times

the distance across it through the center. If the distance

around a circular pond is 50 feet, what is the distance across

it?

17. Two men start from the same place at the same time

and travel in the same direction, one going 3.28 miles an

REVIEW WORK. 119

hour, the other 4.07 miles an hour. How far apart will they

be in 9 hours ?

18. The circumference of the wheel of a bicycle is 11.28

feet. How many times will it turn in going 2.5 miles, there

being 5280 feet in a mile ?

19. Find the cost of 8375 feet of lumber, when lumber is

worth $18 a thousand feet.

20. In a city of 240,000 inhabitants .125 of the population

are school children. If each teacher has 50 pupils, how

many teachers are in that city ?

21. Add 155 ones, 155 tenths, 155 hundredths, 155

thousandths.

22. The divisor 5.125 is 5 times the quotient; what is the

dividend ?

23. The product of three factors is 78. GG ; two of the

factors are respectively 6.9 and 7.125; what is the third

factor ?

24. Find the least decimal fraction which added to the

sum of 87.43 and 109.578 will make the sum an integer.

25. A man paid .15 of his money for rent, .02 for wood,

.18 for clothing, and had $812.50 left. How much had he at

first?

26. Find the product of the two smallest decimals that can

be expressed by the figures 0, 0, 9, and 3.

27. Gunpowder is composed of .76 nitre, .14 charcoal, and

.10 sulphur. How much of each is required to make 2000

pounds of powder ?

28. At $0.34 a bushel, how many barrels of apples can be

had for $13.60, allowing 2.5 bushels to the barrel ?

29. How many pounds of butter could be made from 46

cows during the month of June, each cow averaging 2.5

gallons of milk daily, and each gallon making .5 of a pound

of butter ?

30. If 4 cords of wood are worth as much as 13.4 bushels

of rye, how much rye can be obtained for 15 cords of wood ?

120 SCHOOL ARITHMETIC.

31. If a Mexican dollar is worth 10.85, how many Mexican

dollars equal the value of $080 in U. S. money ?

32. If the land that produces a bale of cotton yields 30

bushels of cotton seed, w-hat is the value @ $.20 per bushel of

the cotton seed produced by the land that yields 21 bales of

cotton ?

33. In one manufacturing establishment the average weekly

wages paid to 202 operators was $12.85 ; in another, to 355

operators, $13.84; and in a third, to 128 operators, $15.11.

Find the average weekly wages in all three establishments.

34. If a railroad train runs 350 miles in 19.5 hours, but

makes three stops of 20 minutes each, and ten stops of

minutes each, what is the average rate per hour while run-

ning ?

35. A franc is 19.3 cents. Find the cost in United States

money of goods bought in Paris amounting to 1,000 francs.

36. A cubic foot of water weighs 1000 ounces. How

many pounds does a cubic foot of gold weigh, gold being 19.4

times as heavy as water ?

37. If oysters yield 1.25 gallons to the bushel, how many

bushels in the shell must I buy so that when opened they will

fill a 10-gallon can ?

38. In the year 1897, the total ordinary expenditures of the

United States government were $365,774,159, which was $5.02

to each person. What was the population in that year, to

the nearest 1000 ?

SUPPLEMENTARY EXERCISES (FOR ADVANCED CLASSES).

179. 1. Can 75 tenths be written as a decimal fraction ?

Why not ? Can it be written as a mixed number ?

2. Divide one by seven, carrying the quotient to 12 decimal

places, and carefully note the result.

3. Investigate the result of dividing one by 3, 11, 13, and

17, carrying the division as far as may be necessary.

REVIEW WOKK. lv>i

4. Aftor spending .015 of his money, and 2 tenths of the

remainder, B had 1 15.7(1 left. I Tow much did lie spend ?

5. Kind the cost, at $8 75 per thousand, of the rails for r>40

panels of 14- rail fence.

6. The multiplicand is .005, and the product, is 1. By

what must the multiplier l>c divided to give a quotient equal

to the product ?

7. I gave .44 of my money for a farm, and .75 of the re-

mainder for a store. If the 1'arm cost $250 more than the

store, how much did I pay for the store ?

8. Cork weighs 15 pounds per cubic foot, and its weight is

.24 of the weight of water. Find the weight of 10 cubic feet

of oak, if the weight of oak is .934 of the weight of water.

9. The distance of the moon from the earth is 59.97 times

the earth's radius. If this radius is 3902. S24 miles, find the

distance to the moon.

10. In 1890 the native population of the United States was

85.23$ of the whole. The foreign born was what decimal