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A PRACTICAL

ARITHMETIC

STEVENS

LIBRARY

OF THE

UNIVERSITY OF CALIFORNIA.

GIFT OF

^ I

Class

A PRACTICAL ARITHMETIC

MAY 29 i9ii

GIFT

COPYRIGHT, 1909, BY

CHARLES SCRIBNER'S SONS

PREFACE

THE primary object of arithmetic is to enable the

student to acquire skill in computation. In addition to

the attainment of this essential end, great benefit is de-

rived from the exercise of the reasoning powers and

their consequent development. While the first of these

must ever remain the fundamental reason for the study

of arithmetic, and the second will always be held in

high esteem, there is a third major object which the

teaching of arithmetic may accomplish, one which is usu-

ally almost entirely ignored in the preparation of an

arithmetic ; namely, the incidental teaching of valuable

facts by basing the problems of the book upon the prob-

lems of real life.

In the preparation of this book, it has been the aim

of the authors to secure the maximum results in these

three functions of arithmetic teaching.

It is chiefly in the careful consideration which has been

given to the subject-matter of the problems, and to the

inferences that will unconsciously and unavoidably remain

in the mind of the pupil, that this book differs from other

arithmetics.

Skill in computation comes from learning a few methods,

followed by extensive drill or practice. Methods have

been carefully and clearly presented in this book, and

an abundance of drill problems provided.

The development of the reasoning powers comes from

work with problems requiring careful analysis before pro-

ceeding to the more mechanical solution. A large number

2191 55

VI PREFACE

of carefully graded thought problems, necessitating accu-

rate analysis, serves this end.

The special value of this book, however, depends upon

the fact that a large proportion of its problems bring out

clearly in their statement or in their solution important

facts bearing upon the practical activities of life. Since

agriculture is the one fundamental industry of America,

especial attention has been given to this subject, and a

large proportion of the thought problems are based upon

agriculture, without, however, in any way leading to

neglect of other industries.

The problems relating to agriculture are based upon

wholly reliable information, upon the most recent find-

ings of the State Experiment Stations and of the National

Department of Agriculture. The facts used in these

problems and the legitimate inferences which may be

drawn from them are trustworthy. In solving these

problems, the pupil will unconsciously absorb and retain

many valuable facts and principles relating to agricul-

tural practice, such, for example, as the value of seed

selection, purity and vitality, judicious use of fertilizers,

balancing of animal rations, crop rotation, prevention or

treatment for plant diseases, conservation of soil moisture,

preservation of soil fertility, prevention of insect injury,

economy in methods of harvesting, proper dairy methods,

the improvement of the herd by selection, poultry culture,

value of good roads, etc.

A feature of value is the outline problems to be com-

pleted by the pupils with data from their homes.

Teachers, parents and pupils are invited to write to the

authors of this book for information upon any agricultural

points involved.

THE AUTHORS.

RALEIGH, N.C., November, 1908.

CONTENTS

PAGH

NOTATION AND NUMERATION 1

The Arabic System 1

The Roman System 9

United States Money 11

ADDITION 13

Addition of United States Money .... .19

SUBTRACTION 29

Subtraction of United States Money 36

MULTIPLICATION 41

Multiplication of United States Money . . . .52

DIVISION 57

Short Division . . . . . . . . . 61

Long Division ......... 64

Division of United States Money 68

Cancellation . . .72

REVIEW PROBLEMS .74

DIVISORS AND MULTIPLES . . . ... . .86

Tests of Divisibility, Greatest Common Divisor, Least Com-

mon Multiple.

DECIMAL FRACTIONS 92

Notation and Numeration 92

Addition 95

Subtraction. .......... 97

Multiplication ......... 99

Division . . .. . . . . . . . 103

REVIEW PROBLEMS ......... 106

COMMON FRACTIONS . . . 113

Addition 120

vii

Vlii CONTENTS

PAGE

Subtraction 122

Multiplication . . . . . . . .125

Division 129

REVIEW PROBLEMS 138

ACCOUNTS AND BILLS ......... 147

DENOMINATE NUMBERS 150

Units of Length, Reduction, Metric Units of Measure,

Representation of Magnitudes, Surface Measure (English

and Metric), Surveyor's Measures, Measures of Volume

(English and Metric), Measures of Weight (English and

Metric), Measures of Time, Angle Measure, Counting,

Addition and Subtraction, Multiplication, Division.

REVIEW PROBLEMS 179

MEASUREMENTS 186

PRACTICAL MEASUREMENTS 198

Plastering, Painting, Paving, Carpeting, Papering, Masonry

and Brickwork, Wood Measure, Board Measure, Round

Logs, Temperature, Longitude and Time, Standard Time.

REVIEW PROBLEMS 216

PERCENTAGE . 227

Profit and Loss 256

Commission 260

Commercial Discount 263

Insurance . . . . 265

Taxes 268

INTEREST 275

Stocks and Bonds . 285

Bank Discount . . . . . 293

Partial Payments . . .296

RATIO .302

The Nutritive Ratio, Specific Gravity.

PROPORTION 308

Levers, Compound Proportion.

CONTENTS ix

PAGE

POWERS 318

ROOTS 321

MISCELLANEOUS REVIEW PROBLEMS 326

APPENDIX ........... 367

Surfaces of Solids, Volumes of Solids, Extraction of Cube

Root, Proof of Fundamental Processes by casting out

Nines, Arithmetical Progression, Geometrical Progression,

Tables of Measures, Weights of Produce, Interest Tables,

Cattlemen's Notation, Lumbermen's Notation.

\

PRACTICAL ARITHMETIC

NOTATION AND NUMERATION

EXERCISE l.-OBAL

1. How many ones in 2, 8, 9?

2. How many tens in 20, 30, 50?

3. How many tens and ones in 18, 36, 45, 47, 98 ?

4. How many one hundreds in 200, 400, 600, 900?

5. How many one hundreds, tens, and ones in :

876 425 743 437 982

123 896 456 847 225

378 549 874 953 629

6. How many one hundreds in this number, 1000?

7. What name is given to this number?

8. How many thousands, hundreds, tens, and ones in :

6387 4702 6512 5068 6728

7080 1400 8150 6740 4963

8824 1814 3096 2263 9184

9. How many thousands in this number, 10000?

10. How many ten-thousands, thousands, hundreds,

tens, and ones in :

50207 34291 23845 10205 23814

35842 78354 91846 35841 87961

26459 52796 87964 88249 18462

i

PRACTICAL ARITHMETIC

11. How many thousands in this number, 100000?

12. How many hundred-thousands, ten-thousands, thou-

sands, hundreds, tens, and ones in:

259132

660878

802136

271186

504001

275360

350006

116006

275253

495271

203841

134410

468796

398178

884192

1. Hundreds, tens, and ones written together form a

group or period, called Units' Period.

2. Hundred-thousands, ten-thousands, and thousands

written together form a period, called Thousands' Period.

3. The next period higher than thousands' period is

called Millions' Period ; the next higher, Billions' Period,

and the next Trillions' Period ; but rarely is there use for

these larger numbers.

4. The following diagram will aid in reading large

numbers. Read the numbers given :

NAMES OF

PERIODS :

PERIODS :

TRILL-

IONS

BILL-

IONS

"g

MILL-

IONS

THOU-

SANDS

I

UNITS

.1

al

ORDERS :

la*

!

la*

^!

Is*

III

la*

^

-2 *2

III

000

000

000

129

654

000

000

004

201

250

000

000

020

045

600

020

006

302

463

001

204

875

001

609

451

NOTATION AND NUMERATION 3

5. Numbers of more than four figures are usually

written with a comma between the periods, thus:

1,642,001 63,105,005 78,121

6. To read a number. Begin at the right and point

off into periods of three figures each ; then begin at the

left and read each period as if it stood alone, adding the

name of the period.

7. The place value of a figure. What effect does it

have upon the value of a figure to move it one place to

the left in its period? To move it one place to the right?

Moving a figure one place to the left increases its

value tenfold. Moving a figure one place to the right

decreases its value tenfold.

EXERCISE 2. ORAL

THE MEANING OF NUMBERS

There are 5 people in my neighbor's home : father,

mother, daughter, and 2 sons. In 20 such homes there

would be 100 people. In a small village of 100 homes

there are about 500 inhabitants. Ten times as many peo-

ple as this in one community would be 5000, and in 100

such towns together there would be 500,000 people.

The following numbers show the population of some

capital cities in 1900. Read the numbers and try to

realize their meaning :

1. Albany, 94,151 3. Richmond, 85,050

2. Harrisburg, 50,167 4. Trenton, 73,307

PRACTICAL ARITHMETIC

5. Dover,

6. Baltimore,

7. Augusta,

8. Boston,

9. Concord,

10. Providence,

11. Bismarck,

12. Pierre,

13. Lincoln,

14. St. Paul,

3,329 15. Jefferson City, 9,664

508,957 16. Madison, 19,164

39,441 17. Lansing, 16,485

560,892 18. Columbus, 125,560

19,632 19. Springfield, 34,157

175,597 20. Raleigh, 13,643

3,319 21. Jackson, 7,816

2,305 22. Tallahassee, 2,981

40,167 23. Phoenix, 5,544

163,065 24. Atlanta, 89,872

Read the following numbers, which express the corn

and wheat produced and the number of milk cows of cer-

tain states in 1906 :

CORN, BUSHELS

WHEAT, BUSHELS

MILK Cows

25.

North Carolina,

41,796,846

5,297,028

282,600

26.

New York,

22,685,000

9,350,180

1,826,211

27.

Georgia,

52,066,596

3,161,070

305,469

28.

Ohio,

141,645,000

43,202,100

919,100

29.

Mississippi,

40,789,207

17,610

329,664

30.

Iowa,

373,275,000

9,212,218

1,555,300

31.

Texas,

155,804,782

14,126,186

993,122

32.

Kansas,

195,075,000

81,830,611

729,274

8. Any one thing is called a Unit.

9. A unit or collection of units is called a Number.

10. Numbers representing whole units are called Whole

Numbers, Integral Numbers, or Integers.

NOTATION AND NUMERATION 5

11. Figures or Digits are symbols used to express

numbers.

12. The process of reading numbers is called Numeration.

13. Numbers may be expressed by Figures, Letters, or

Words.

EXERCISE 3. WRITTEN

Write these numbers in figures, using the comma to

separate periods :

1. Six hundred seventy -five.

2. Two hundred thirteen.

3. Four hundred ninety-six.

4. Two hundred twenty-nine.

5. Four hundred eight.

6. One thousand, three hundred fifty-two.

7. Six thousand, forty.

8. Eighty thousand, eighty.

9. Seven thousand, three hundred.

10. Thirteen thousand, four hundred fifty.

11. Ninety-nine thousand, nine.

12. Forty-four thousand, sixteen.

13. Four hundred six thousand, one hundred fifty.

14. Three thousand, fourteen.

15. Nine thousand, seventy-seven.

16. Fifty thousand, sixty-eight.

17. Eleven thousand, nine hundred seventy-three.

18. Seven hundred eighty-five thousand, two.

6 PRACTICAL ARITHMETIC

19. Ninety-two thousand, one hundred six.

20. One million, three hundred ninety-seven thousand.

21. Eight thousand, four hundred eighty- two.

22. Nineteen million, one hundred fifty-six thousand.

23. Eight million, six.

24. Five thousand, one hundred thirty-one.

25. Sixty-three million, sixty-eight thousand, seven.

14. The art of writing numbers is called Notation.

EXERCISE 4. WRITTEN

Write in figures the following numbers, which express

the wool production and the number of hogs in several

states, arranging in columns and using the comma between

the periods, as in Exercise 2.

POUNDS OF WOOL PRODUCED IN 1906

1. North Carolina, eight hundred seventy-one thou-

sand, two hundred fifty.

2. Alabama, five hundred sixty-eight thousand, seven

hundred fifty.

3. Montana, thirty-five million, eight hundred fifteen

thousand.

4. Florida, three hundred sixteen thousand, six hun-

dred two.

5. Wyoming, thirty-two million, eight hundred forty-

nine thousand, seven hundred fifty.

6. Texas, nine million, three hundred sixty thousand.

7. Missouri, four million, six hundred seven thousand,

three.

NOTATION AND NUMERATION 7

NUMBER OF HOGS IN 1907

8. New York, six hundred seventy-five thousand, five

hundred forty -five.

9. Iowa, eight million, five hundred eighty-four thou-

sand, five hundred.

10. Pennsylvania, nine hundred eighty-nine thousand,

six hundred eighty-five.

11. Kentucky, one million, two hundred thirteen thou-

sand, three hundred eighty.

12. Illinois, four million, four hundred forty-nine thou-

sand, seven hundred five.

13. Texas, two million, eight hundred sixty thousand,

eight hundred seventy-nine.

14. Ohio, two million, four hundred thirty-six thousand,

seven hundred ninety-seven.

15. Alabama, one million, two hundred fifty-one thou-

sand, two hundred fifty-one.

16. Nebraska, four million, eighty thousand.

The following are the distances between several impor-

tant cities. Write the numbers in figures and try to real-

ize what they mean.

17. By rail from Albany, N.Y., to Troy, N.Y., six

miles ; from Utica, N.Y., to Rome, N.Y., fifteen miles ;

from Syracuse, N.Y., to Rochester, N.Y., eighty-one

miles.

18. From St. Paul, Minn., to Portland, Ore., two

thousand fifty-three miles; from Cleveland, O., to Cin-

cinnati, O., two hundred sixty-three miles.

8

PRACTICAL ARITHMETIC

STREET SCENE IN ATLANTA, GA.

From a photograph.

Copyright, 1907, by Underwood & Underwood.

19. From Chattanooga, Teim., to New Orleans, La.,

iour hundred ninety-two miles ; from Nashville, Tenn., to

New Orleans, La.,

six hundred twenty-

four miles ; from

New Orleans, La.,

to Atlanta, Ga., four

hundred ninety-six

miles.

20. By water from

New York to Liver-

pool, three thousand

fifty-eight miles ;

from San Francisco

to Yokohama, four

thousand, seven hundred ninety-one miles.

21. From New York to Manila, sixteen thousand, five

hundred miles; from New York to Havana, one thou-

sand, four hundred twenty miles.

22. From New York to Strait of Magellan, six thousand

eight hundred ninety miles; from Strait of Magellan to

San Francisco, six thousand one hundred ninety-nine miles.

23. By rail from New York to Omaha, one thousand

three hundred eighty-five miles ; to San Francisco, three

thousand two hundred fifty miles.

24. The railroads of the United States aggregate one

hundred ninety-three thousand miles, bearing thirty-eight

thousand locomotives, fourteen thousand coaches, carry-

ing yearly six hundred million passengers, and one bill-

ion tons of freight. They cost about five billion dollars.

EOMAN NOTATION

15. The system of notation and numeration already

explained is commonly called the Arabic System. There

is still another system known as the Roman System.

16. In the Roman system of notation seven capital

letters of the alphabet and combinations of these letters

are used to express numbers. The letters and their

values are as follows :

I V X L C D M

1 5 10 50 100 500 1000

17. A bar placed over a letter increases its value a

thousand fold, e.g., V denotes 5000 ; X denotes 10,000.

18. When these symbols are used in combination their

values are governed by the following laws :

I. Each repetition of a letter repeats its value, e.g.,

XX denotes 20, XXX denotes 30, CO denotes 200, MMM

denotes 3000.

II. When a letter is placed after one of greater value,

its value is to be added to that of the preceding letter,

e.g., XI represents 10 and 1, or 11 ; VII represents 5 and

2, or 7 ; XVI represents 10 and 5 and 1, or 16 ; CXXI

represents 100 and 10 and 10 and 1, or 121.

III. When a letter is placed before another of greater

value, its value is taken from that of the letter of greater

value, e.g., IX represents 10 less 1, or 9; XL represents

50 less 10, or 40 ; XC represents 100 less 10, or 90.

IV. When a letter is placed between two letters of

10

PRACTICAL ARITHMETIC

greater value, its value is taken from that of the letter

which follows it, e.g., XIX represents 10 and 9, or 19;

CXC represents 100 and 90, or 190.

EXERCISE 5. WRITTEN

Express in Arabic notation :

1. XI

2. XX

3. XIV

4. XXX

5. XL

6. XVI

7. LV

8. LIX

9. LXXVIII

10. XLIX

11. XXVII

12. XCV

is. XLIV

14. LXXIV

is. CCLIV

16. CDLVI

17. DCIX

18. MCXL

19. MCXLV

20. MDLIV

21. MDLX

22. MDXLVI

23. MDCCXLIV

24. MMDCCXCIII

25. VCCCLXXVI

26. XDCCXCIX

27. DXLIV

28. MDCCLXXXIII

29. MMCCCCLXIV

so. MMMDCCXIX

EXERCISE 6. WRITTEN

Express in Roman notation :

1. 11

2. 17

3. 19

4. 42

5. 33

6. 12

7. 26

8. 54

9. 83

10. 75

11. 98

12. 73

13. 116

14. 240

15. 375

16. 480

17. 510

18. 450

19. 375

20. 741

21. 421

22. 943

23. 719

24. 1425

25. 1764

26. 5861

27. 24,854

28. 256,845

29. 1,450,819

so. 3,840,006

UNITED STATES MONET

19. In the money of the United States the unit is the

Dollar. In writing it is expressed by the sign $, e.g.,

$25 is read twenty-five dollars.

20. Our money system is based upon the same system of

tens and groups of tens which we studied in Arabic nota-

tion. That is, ten units of one order make a unit of the

next higher order.

21. Ten ten-cent pieces equal one dollar. Ten one-

cent pieces equal a ten-cent piece. A still smaller divi-

sion of our money which we do not commonly use is

called Mills. Ten mills equal one cent.

Ten cents is one-tenth of a dollar. One cent is one

one-hundredth of a dollar. One mill is one one-thou-

sandth of a dollar.

22. The period used to separate dollars and cents is

called the Decimal Point.

23. The following diagrams serve to show the arrange-

ment of dollars, cents, and mills as they are written:

2

"3 33 S3 00

^ "3 > '3 .33

M 4S p< -g oj A'STS

o g s

^-S^^-SoS

$245.245 $245.245

11

12 PRACTICAL ARITHMETIC

EXERCISE 7. ORAL

Read as dollars and cents :

1. $ 3.24 5. $ 25.06 9. $349.99 13. $ 542.89

2. $ 8.72 6. $ 91.07 10. $698.42 14. $ 560.90

3. $ 9.87 7. $ 92.09 11. $100.10 is. $1845.24

4. $10.25 8. $900.09 12. $ 99.99 16. $6291.98

Read as dollars, cents, and mills :

17. $5.842 20. $ 17.001 23. $981.701 26. $699.764

18. $3.205 21. $ 70.070 24. $909.701 27. $263.809

19. $4.998 22. $191.672 25. $340.034 28. $ 89.617

EXERCISE 8. WRITTEN

Express the following in figures, using the dollar sign

and decimal point :

1. Twenty dollars and fifty cents; thirty-four dollars

and five cents.

2. Eighteen dollars and thirty-five cents ; ninety-five

dollars and twenty cents ; thirty-one dollars and sixty

cents ; one hundred twenty dollars and four cents.

3. One hundred dollars and ten cents ; fifty-four dol-

lars and nineteen cents ; fifty-three dollars and fifty-five

cents ; nineteen dollars and ninety cents.

4. Eighty dollars and one cent, five mills ; fifty dollars and

fifty cents ; three hundred dollars and six cents, one mill ;

four hundred thirty-three dollars and thirty-three cents.

5. Five hundred dollars and three-tenths ; two hundred

dollars and thirty-three hundredths ; one hundred dollars

and three hundred thirty-three thousandths.

ADDITION

24. The growth of an apple twig in 1905 was 4 inches

and in 1906 it was 6 inches. How many inches did it

grow in the two years?

Addition is the process of finding the number that

is equal to two or more numbers taken together.

25. The result obtained by adding numbers is called

the Sum.

26. The sign of addition, + , is called Plus. When

placed between numbers it means that they are to be

added.

27. The sign of equality, =, when placed between

numbers shows that they are equal. Thus 7 + 3 = 10 is

read seven plus three equals ten.

28. Find the sums of the following, which include all

the combinations of two numbers from one to nine :

2 + 7 =

2 + 1 =

3 + 1 =

1 + 9 =

4 + 2 =

3 + 7 =

1 + 6 =

3 + 5 =

3 + 4 =

1 + 1 =

2 + 4 =

1 + 7 =

2 + 3 =

7 + 2 =

3 + 7 =

4 + 3 =

7 + 1 =

3 + 3 =

5 + 4 =

6 + 1 =

8 + 2 =

4 + 5 =

1 + 4 =

3 + 2 =

1 + 9 =

6 + 4 =

2+2 =

1 + 2 =

5 + 2 =

1 + 8 =

5 + 5 =

4 + 6 =

3 + 6 =

2 + 5 =

8 + 1 =

6 + 2 =

13

14 PRACTICAL ARITHMETIC

6+3= 4+4= 2+8= 1+3=

5+3= 2+6= 3+4= 4+1=

1 + 5 =

Practise adding these numbers daily until the sum of

any of these combinations can be told at a glance.

EXERCISE 9. ORAL

1. A man fed a colt 2 quarts of oats, a driving horse

4 quarts, and a draught horse 6 quarts. How many quarts

of oats did he use at a feeding?

2. If the morning and the afternoon each becomes 5

minutes longer during the second week in March, how

much longer are the days of the second week than the

days of the first week ?

3. If the cost of hauling Kansas wheat to the railroad

station is 3 cts. a bushel, and the freight to New York is

11 cts. a bushel, what is the total cost of transportation ?

4. A dairyman had 4 cows. One gave 5 quarts, one

7 quarts, one 8 quarts, and another 9 quarts of milk at a

milking. How many quarts did all give at a milking ?

5. A morning from sunrise to noon in September is

6 hours, and from noon to sunset is 6 hours. What is

the total length of the day ?

6. A ration for a cow is : corn and cob meal, 5 Ibs. ;

cotton-seed meal, 4 Ibs.; hay, 20 Ibs. What is the weight

of the entire ration ?

7. The number of cloudy days in January was 9, the

rainy days were 4. How many days were rainy and

cloudy ?

ADDITION 15

8. If a fruit cake requires 3 Ibs. of currants, 2 Ibs. of

raisins, and 1 Ib. of citron, how many pounds of fruit are

used in the cake ?

9. If the increase in temperature at Raleigh, N.C., in

1907 was 26 degrees from February to May and 14 degrees

from May to August, what was the total increase in tem-

perature during the six months ?

10. If the temperature decreases 8 degrees from July

to September and 33 degrees from September to March,

what is the total decrease in temperature ?

11. The number of senators from each of several sec-

tions of our country in 1890 was as follows : from the

New England States, 12; the Middle States, 8; the

Pacific States, 10. How many senators were there from

all these sections ?

12. The number of senators from the two largest sec-

tions of our country in 1890 was as follows : the South, 28 ;

the Northwest, 24. How many senators were there from

these sections?

13. A ration for a cow is 15 Ibs. of hay, 30 Ibs. of

silage, 4 Ibs. of cotton-seed meal, 3 Ibs. of wheat bran,

and 3 Ibs. of corn meal. What is the weight of the

entire ration ?

14. Count from 3 to 99 by threes.

15. Count from 4 to 100 by fours.

16. Count from 6 to 96 by sixes.

17. Count from 9 to 99 by nines.

18. At Raleigh, N.C., in 1907 the lowest temperature

for the month of October was 36 degrees, the highest

16 PRACTICAL ARITHMETIC

temperature was 45 degrees higher. What was the high-

est temperature ?

19. Two skilled laborers earned 83 and 85 respectively

a day. How much did the two earn together ?

20. Two unskilled laborers earned respectively 81.25

and 81.50 a day. How much did the two earn ?

21. The cultivation of an acre of corn costs 86, the fer-

tilizers 8 3, harvesting and other expenses 83. What is

the cost of the crop per acre ?

22. A ration for a horse weighing 1000 Ibs. when doing

moderately hard work is 6 Ibs. of corn, 8 Ibs. of oats, and

15 Ibs. of hay. What is the weight of the ration?

23. A ration for a fattening beef animal weighing

1000 Ibs. is 30 Ibs. of corn silage, 12 Ibs. of corn stover,

5 Ibs. of cotton-seed meal, and 4 Ibs. of cotton seed.

What is the weight of the ration?

24. If a man wishes to seed an acre for a meadow and

uses 11 Ibs. of timothy, 6 Ibs. of red top, and 5 Ibs. of

clover seed, how many pounds of seed does he sow on the

acre ?

25. If 1000 Ibs. of an average mixed stable manure

contain 5 Ibs. of nitrogen, 6 Ibs. of potash, and 3 Ibs. of

phosphoric acid, how many pounds of these plant foods

does it contain ?

26. If the plants in a ton of dry clover hay used 39

Ibs. of nitrogen, 37 Ibs. of potash, and 11 Ibs. of phos-

phoric acid in growth, how many pounds of these mate-

rials were used by the plants ?

27. If a ton of wheat straw used in growing 11 Ibs,

ADDITION 17

of nitrogen, 23 Ibs. of potash, and 4 Ibs. of phosphoric

acid, how many pounds of these materials were taken

from the soil ?

28. If a ton of oat grain used in growing 35 Ibs. of

nitrogen, 9 Ibs. of potash, and 13 Ibs. of phosphoric acid,

how many pounds of these materials were used ?

ARITHMETIC

STEVENS

LIBRARY

OF THE

UNIVERSITY OF CALIFORNIA.

GIFT OF

^ I

Class

A PRACTICAL ARITHMETIC

MAY 29 i9ii

GIFT

COPYRIGHT, 1909, BY

CHARLES SCRIBNER'S SONS

PREFACE

THE primary object of arithmetic is to enable the

student to acquire skill in computation. In addition to

the attainment of this essential end, great benefit is de-

rived from the exercise of the reasoning powers and

their consequent development. While the first of these

must ever remain the fundamental reason for the study

of arithmetic, and the second will always be held in

high esteem, there is a third major object which the

teaching of arithmetic may accomplish, one which is usu-

ally almost entirely ignored in the preparation of an

arithmetic ; namely, the incidental teaching of valuable

facts by basing the problems of the book upon the prob-

lems of real life.

In the preparation of this book, it has been the aim

of the authors to secure the maximum results in these

three functions of arithmetic teaching.

It is chiefly in the careful consideration which has been

given to the subject-matter of the problems, and to the

inferences that will unconsciously and unavoidably remain

in the mind of the pupil, that this book differs from other

arithmetics.

Skill in computation comes from learning a few methods,

followed by extensive drill or practice. Methods have

been carefully and clearly presented in this book, and

an abundance of drill problems provided.

The development of the reasoning powers comes from

work with problems requiring careful analysis before pro-

ceeding to the more mechanical solution. A large number

2191 55

VI PREFACE

of carefully graded thought problems, necessitating accu-

rate analysis, serves this end.

The special value of this book, however, depends upon

the fact that a large proportion of its problems bring out

clearly in their statement or in their solution important

facts bearing upon the practical activities of life. Since

agriculture is the one fundamental industry of America,

especial attention has been given to this subject, and a

large proportion of the thought problems are based upon

agriculture, without, however, in any way leading to

neglect of other industries.

The problems relating to agriculture are based upon

wholly reliable information, upon the most recent find-

ings of the State Experiment Stations and of the National

Department of Agriculture. The facts used in these

problems and the legitimate inferences which may be

drawn from them are trustworthy. In solving these

problems, the pupil will unconsciously absorb and retain

many valuable facts and principles relating to agricul-

tural practice, such, for example, as the value of seed

selection, purity and vitality, judicious use of fertilizers,

balancing of animal rations, crop rotation, prevention or

treatment for plant diseases, conservation of soil moisture,

preservation of soil fertility, prevention of insect injury,

economy in methods of harvesting, proper dairy methods,

the improvement of the herd by selection, poultry culture,

value of good roads, etc.

A feature of value is the outline problems to be com-

pleted by the pupils with data from their homes.

Teachers, parents and pupils are invited to write to the

authors of this book for information upon any agricultural

points involved.

THE AUTHORS.

RALEIGH, N.C., November, 1908.

CONTENTS

PAGH

NOTATION AND NUMERATION 1

The Arabic System 1

The Roman System 9

United States Money 11

ADDITION 13

Addition of United States Money .... .19

SUBTRACTION 29

Subtraction of United States Money 36

MULTIPLICATION 41

Multiplication of United States Money . . . .52

DIVISION 57

Short Division . . . . . . . . . 61

Long Division ......... 64

Division of United States Money 68

Cancellation . . .72

REVIEW PROBLEMS .74

DIVISORS AND MULTIPLES . . . ... . .86

Tests of Divisibility, Greatest Common Divisor, Least Com-

mon Multiple.

DECIMAL FRACTIONS 92

Notation and Numeration 92

Addition 95

Subtraction. .......... 97

Multiplication ......... 99

Division . . .. . . . . . . . 103

REVIEW PROBLEMS ......... 106

COMMON FRACTIONS . . . 113

Addition 120

vii

Vlii CONTENTS

PAGE

Subtraction 122

Multiplication . . . . . . . .125

Division 129

REVIEW PROBLEMS 138

ACCOUNTS AND BILLS ......... 147

DENOMINATE NUMBERS 150

Units of Length, Reduction, Metric Units of Measure,

Representation of Magnitudes, Surface Measure (English

and Metric), Surveyor's Measures, Measures of Volume

(English and Metric), Measures of Weight (English and

Metric), Measures of Time, Angle Measure, Counting,

Addition and Subtraction, Multiplication, Division.

REVIEW PROBLEMS 179

MEASUREMENTS 186

PRACTICAL MEASUREMENTS 198

Plastering, Painting, Paving, Carpeting, Papering, Masonry

and Brickwork, Wood Measure, Board Measure, Round

Logs, Temperature, Longitude and Time, Standard Time.

REVIEW PROBLEMS 216

PERCENTAGE . 227

Profit and Loss 256

Commission 260

Commercial Discount 263

Insurance . . . . 265

Taxes 268

INTEREST 275

Stocks and Bonds . 285

Bank Discount . . . . . 293

Partial Payments . . .296

RATIO .302

The Nutritive Ratio, Specific Gravity.

PROPORTION 308

Levers, Compound Proportion.

CONTENTS ix

PAGE

POWERS 318

ROOTS 321

MISCELLANEOUS REVIEW PROBLEMS 326

APPENDIX ........... 367

Surfaces of Solids, Volumes of Solids, Extraction of Cube

Root, Proof of Fundamental Processes by casting out

Nines, Arithmetical Progression, Geometrical Progression,

Tables of Measures, Weights of Produce, Interest Tables,

Cattlemen's Notation, Lumbermen's Notation.

\

PRACTICAL ARITHMETIC

NOTATION AND NUMERATION

EXERCISE l.-OBAL

1. How many ones in 2, 8, 9?

2. How many tens in 20, 30, 50?

3. How many tens and ones in 18, 36, 45, 47, 98 ?

4. How many one hundreds in 200, 400, 600, 900?

5. How many one hundreds, tens, and ones in :

876 425 743 437 982

123 896 456 847 225

378 549 874 953 629

6. How many one hundreds in this number, 1000?

7. What name is given to this number?

8. How many thousands, hundreds, tens, and ones in :

6387 4702 6512 5068 6728

7080 1400 8150 6740 4963

8824 1814 3096 2263 9184

9. How many thousands in this number, 10000?

10. How many ten-thousands, thousands, hundreds,

tens, and ones in :

50207 34291 23845 10205 23814

35842 78354 91846 35841 87961

26459 52796 87964 88249 18462

i

PRACTICAL ARITHMETIC

11. How many thousands in this number, 100000?

12. How many hundred-thousands, ten-thousands, thou-

sands, hundreds, tens, and ones in:

259132

660878

802136

271186

504001

275360

350006

116006

275253

495271

203841

134410

468796

398178

884192

1. Hundreds, tens, and ones written together form a

group or period, called Units' Period.

2. Hundred-thousands, ten-thousands, and thousands

written together form a period, called Thousands' Period.

3. The next period higher than thousands' period is

called Millions' Period ; the next higher, Billions' Period,

and the next Trillions' Period ; but rarely is there use for

these larger numbers.

4. The following diagram will aid in reading large

numbers. Read the numbers given :

NAMES OF

PERIODS :

PERIODS :

TRILL-

IONS

BILL-

IONS

"g

MILL-

IONS

THOU-

SANDS

I

UNITS

.1

al

ORDERS :

la*

!

la*

^!

Is*

III

la*

^

-2 *2

III

000

000

000

129

654

000

000

004

201

250

000

000

020

045

600

020

006

302

463

001

204

875

001

609

451

NOTATION AND NUMERATION 3

5. Numbers of more than four figures are usually

written with a comma between the periods, thus:

1,642,001 63,105,005 78,121

6. To read a number. Begin at the right and point

off into periods of three figures each ; then begin at the

left and read each period as if it stood alone, adding the

name of the period.

7. The place value of a figure. What effect does it

have upon the value of a figure to move it one place to

the left in its period? To move it one place to the right?

Moving a figure one place to the left increases its

value tenfold. Moving a figure one place to the right

decreases its value tenfold.

EXERCISE 2. ORAL

THE MEANING OF NUMBERS

There are 5 people in my neighbor's home : father,

mother, daughter, and 2 sons. In 20 such homes there

would be 100 people. In a small village of 100 homes

there are about 500 inhabitants. Ten times as many peo-

ple as this in one community would be 5000, and in 100

such towns together there would be 500,000 people.

The following numbers show the population of some

capital cities in 1900. Read the numbers and try to

realize their meaning :

1. Albany, 94,151 3. Richmond, 85,050

2. Harrisburg, 50,167 4. Trenton, 73,307

PRACTICAL ARITHMETIC

5. Dover,

6. Baltimore,

7. Augusta,

8. Boston,

9. Concord,

10. Providence,

11. Bismarck,

12. Pierre,

13. Lincoln,

14. St. Paul,

3,329 15. Jefferson City, 9,664

508,957 16. Madison, 19,164

39,441 17. Lansing, 16,485

560,892 18. Columbus, 125,560

19,632 19. Springfield, 34,157

175,597 20. Raleigh, 13,643

3,319 21. Jackson, 7,816

2,305 22. Tallahassee, 2,981

40,167 23. Phoenix, 5,544

163,065 24. Atlanta, 89,872

Read the following numbers, which express the corn

and wheat produced and the number of milk cows of cer-

tain states in 1906 :

CORN, BUSHELS

WHEAT, BUSHELS

MILK Cows

25.

North Carolina,

41,796,846

5,297,028

282,600

26.

New York,

22,685,000

9,350,180

1,826,211

27.

Georgia,

52,066,596

3,161,070

305,469

28.

Ohio,

141,645,000

43,202,100

919,100

29.

Mississippi,

40,789,207

17,610

329,664

30.

Iowa,

373,275,000

9,212,218

1,555,300

31.

Texas,

155,804,782

14,126,186

993,122

32.

Kansas,

195,075,000

81,830,611

729,274

8. Any one thing is called a Unit.

9. A unit or collection of units is called a Number.

10. Numbers representing whole units are called Whole

Numbers, Integral Numbers, or Integers.

NOTATION AND NUMERATION 5

11. Figures or Digits are symbols used to express

numbers.

12. The process of reading numbers is called Numeration.

13. Numbers may be expressed by Figures, Letters, or

Words.

EXERCISE 3. WRITTEN

Write these numbers in figures, using the comma to

separate periods :

1. Six hundred seventy -five.

2. Two hundred thirteen.

3. Four hundred ninety-six.

4. Two hundred twenty-nine.

5. Four hundred eight.

6. One thousand, three hundred fifty-two.

7. Six thousand, forty.

8. Eighty thousand, eighty.

9. Seven thousand, three hundred.

10. Thirteen thousand, four hundred fifty.

11. Ninety-nine thousand, nine.

12. Forty-four thousand, sixteen.

13. Four hundred six thousand, one hundred fifty.

14. Three thousand, fourteen.

15. Nine thousand, seventy-seven.

16. Fifty thousand, sixty-eight.

17. Eleven thousand, nine hundred seventy-three.

18. Seven hundred eighty-five thousand, two.

6 PRACTICAL ARITHMETIC

19. Ninety-two thousand, one hundred six.

20. One million, three hundred ninety-seven thousand.

21. Eight thousand, four hundred eighty- two.

22. Nineteen million, one hundred fifty-six thousand.

23. Eight million, six.

24. Five thousand, one hundred thirty-one.

25. Sixty-three million, sixty-eight thousand, seven.

14. The art of writing numbers is called Notation.

EXERCISE 4. WRITTEN

Write in figures the following numbers, which express

the wool production and the number of hogs in several

states, arranging in columns and using the comma between

the periods, as in Exercise 2.

POUNDS OF WOOL PRODUCED IN 1906

1. North Carolina, eight hundred seventy-one thou-

sand, two hundred fifty.

2. Alabama, five hundred sixty-eight thousand, seven

hundred fifty.

3. Montana, thirty-five million, eight hundred fifteen

thousand.

4. Florida, three hundred sixteen thousand, six hun-

dred two.

5. Wyoming, thirty-two million, eight hundred forty-

nine thousand, seven hundred fifty.

6. Texas, nine million, three hundred sixty thousand.

7. Missouri, four million, six hundred seven thousand,

three.

NOTATION AND NUMERATION 7

NUMBER OF HOGS IN 1907

8. New York, six hundred seventy-five thousand, five

hundred forty -five.

9. Iowa, eight million, five hundred eighty-four thou-

sand, five hundred.

10. Pennsylvania, nine hundred eighty-nine thousand,

six hundred eighty-five.

11. Kentucky, one million, two hundred thirteen thou-

sand, three hundred eighty.

12. Illinois, four million, four hundred forty-nine thou-

sand, seven hundred five.

13. Texas, two million, eight hundred sixty thousand,

eight hundred seventy-nine.

14. Ohio, two million, four hundred thirty-six thousand,

seven hundred ninety-seven.

15. Alabama, one million, two hundred fifty-one thou-

sand, two hundred fifty-one.

16. Nebraska, four million, eighty thousand.

The following are the distances between several impor-

tant cities. Write the numbers in figures and try to real-

ize what they mean.

17. By rail from Albany, N.Y., to Troy, N.Y., six

miles ; from Utica, N.Y., to Rome, N.Y., fifteen miles ;

from Syracuse, N.Y., to Rochester, N.Y., eighty-one

miles.

18. From St. Paul, Minn., to Portland, Ore., two

thousand fifty-three miles; from Cleveland, O., to Cin-

cinnati, O., two hundred sixty-three miles.

8

PRACTICAL ARITHMETIC

STREET SCENE IN ATLANTA, GA.

From a photograph.

Copyright, 1907, by Underwood & Underwood.

19. From Chattanooga, Teim., to New Orleans, La.,

iour hundred ninety-two miles ; from Nashville, Tenn., to

New Orleans, La.,

six hundred twenty-

four miles ; from

New Orleans, La.,

to Atlanta, Ga., four

hundred ninety-six

miles.

20. By water from

New York to Liver-

pool, three thousand

fifty-eight miles ;

from San Francisco

to Yokohama, four

thousand, seven hundred ninety-one miles.

21. From New York to Manila, sixteen thousand, five

hundred miles; from New York to Havana, one thou-

sand, four hundred twenty miles.

22. From New York to Strait of Magellan, six thousand

eight hundred ninety miles; from Strait of Magellan to

San Francisco, six thousand one hundred ninety-nine miles.

23. By rail from New York to Omaha, one thousand

three hundred eighty-five miles ; to San Francisco, three

thousand two hundred fifty miles.

24. The railroads of the United States aggregate one

hundred ninety-three thousand miles, bearing thirty-eight

thousand locomotives, fourteen thousand coaches, carry-

ing yearly six hundred million passengers, and one bill-

ion tons of freight. They cost about five billion dollars.

EOMAN NOTATION

15. The system of notation and numeration already

explained is commonly called the Arabic System. There

is still another system known as the Roman System.

16. In the Roman system of notation seven capital

letters of the alphabet and combinations of these letters

are used to express numbers. The letters and their

values are as follows :

I V X L C D M

1 5 10 50 100 500 1000

17. A bar placed over a letter increases its value a

thousand fold, e.g., V denotes 5000 ; X denotes 10,000.

18. When these symbols are used in combination their

values are governed by the following laws :

I. Each repetition of a letter repeats its value, e.g.,

XX denotes 20, XXX denotes 30, CO denotes 200, MMM

denotes 3000.

II. When a letter is placed after one of greater value,

its value is to be added to that of the preceding letter,

e.g., XI represents 10 and 1, or 11 ; VII represents 5 and

2, or 7 ; XVI represents 10 and 5 and 1, or 16 ; CXXI

represents 100 and 10 and 10 and 1, or 121.

III. When a letter is placed before another of greater

value, its value is taken from that of the letter of greater

value, e.g., IX represents 10 less 1, or 9; XL represents

50 less 10, or 40 ; XC represents 100 less 10, or 90.

IV. When a letter is placed between two letters of

10

PRACTICAL ARITHMETIC

greater value, its value is taken from that of the letter

which follows it, e.g., XIX represents 10 and 9, or 19;

CXC represents 100 and 90, or 190.

EXERCISE 5. WRITTEN

Express in Arabic notation :

1. XI

2. XX

3. XIV

4. XXX

5. XL

6. XVI

7. LV

8. LIX

9. LXXVIII

10. XLIX

11. XXVII

12. XCV

is. XLIV

14. LXXIV

is. CCLIV

16. CDLVI

17. DCIX

18. MCXL

19. MCXLV

20. MDLIV

21. MDLX

22. MDXLVI

23. MDCCXLIV

24. MMDCCXCIII

25. VCCCLXXVI

26. XDCCXCIX

27. DXLIV

28. MDCCLXXXIII

29. MMCCCCLXIV

so. MMMDCCXIX

EXERCISE 6. WRITTEN

Express in Roman notation :

1. 11

2. 17

3. 19

4. 42

5. 33

6. 12

7. 26

8. 54

9. 83

10. 75

11. 98

12. 73

13. 116

14. 240

15. 375

16. 480

17. 510

18. 450

19. 375

20. 741

21. 421

22. 943

23. 719

24. 1425

25. 1764

26. 5861

27. 24,854

28. 256,845

29. 1,450,819

so. 3,840,006

UNITED STATES MONET

19. In the money of the United States the unit is the

Dollar. In writing it is expressed by the sign $, e.g.,

$25 is read twenty-five dollars.

20. Our money system is based upon the same system of

tens and groups of tens which we studied in Arabic nota-

tion. That is, ten units of one order make a unit of the

next higher order.

21. Ten ten-cent pieces equal one dollar. Ten one-

cent pieces equal a ten-cent piece. A still smaller divi-

sion of our money which we do not commonly use is

called Mills. Ten mills equal one cent.

Ten cents is one-tenth of a dollar. One cent is one

one-hundredth of a dollar. One mill is one one-thou-

sandth of a dollar.

22. The period used to separate dollars and cents is

called the Decimal Point.

23. The following diagrams serve to show the arrange-

ment of dollars, cents, and mills as they are written:

2

"3 33 S3 00

^ "3 > '3 .33

M 4S p< -g oj A'STS

o g s

^-S^^-SoS

$245.245 $245.245

11

12 PRACTICAL ARITHMETIC

EXERCISE 7. ORAL

Read as dollars and cents :

1. $ 3.24 5. $ 25.06 9. $349.99 13. $ 542.89

2. $ 8.72 6. $ 91.07 10. $698.42 14. $ 560.90

3. $ 9.87 7. $ 92.09 11. $100.10 is. $1845.24

4. $10.25 8. $900.09 12. $ 99.99 16. $6291.98

Read as dollars, cents, and mills :

17. $5.842 20. $ 17.001 23. $981.701 26. $699.764

18. $3.205 21. $ 70.070 24. $909.701 27. $263.809

19. $4.998 22. $191.672 25. $340.034 28. $ 89.617

EXERCISE 8. WRITTEN

Express the following in figures, using the dollar sign

and decimal point :

1. Twenty dollars and fifty cents; thirty-four dollars

and five cents.

2. Eighteen dollars and thirty-five cents ; ninety-five

dollars and twenty cents ; thirty-one dollars and sixty

cents ; one hundred twenty dollars and four cents.

3. One hundred dollars and ten cents ; fifty-four dol-

lars and nineteen cents ; fifty-three dollars and fifty-five

cents ; nineteen dollars and ninety cents.

4. Eighty dollars and one cent, five mills ; fifty dollars and

fifty cents ; three hundred dollars and six cents, one mill ;

four hundred thirty-three dollars and thirty-three cents.

5. Five hundred dollars and three-tenths ; two hundred

dollars and thirty-three hundredths ; one hundred dollars

and three hundred thirty-three thousandths.

ADDITION

24. The growth of an apple twig in 1905 was 4 inches

and in 1906 it was 6 inches. How many inches did it

grow in the two years?

Addition is the process of finding the number that

is equal to two or more numbers taken together.

25. The result obtained by adding numbers is called

the Sum.

26. The sign of addition, + , is called Plus. When

placed between numbers it means that they are to be

added.

27. The sign of equality, =, when placed between

numbers shows that they are equal. Thus 7 + 3 = 10 is

read seven plus three equals ten.

28. Find the sums of the following, which include all

the combinations of two numbers from one to nine :

2 + 7 =

2 + 1 =

3 + 1 =

1 + 9 =

4 + 2 =

3 + 7 =

1 + 6 =

3 + 5 =

3 + 4 =

1 + 1 =

2 + 4 =

1 + 7 =

2 + 3 =

7 + 2 =

3 + 7 =

4 + 3 =

7 + 1 =

3 + 3 =

5 + 4 =

6 + 1 =

8 + 2 =

4 + 5 =

1 + 4 =

3 + 2 =

1 + 9 =

6 + 4 =

2+2 =

1 + 2 =

5 + 2 =

1 + 8 =

5 + 5 =

4 + 6 =

3 + 6 =

2 + 5 =

8 + 1 =

6 + 2 =

13

14 PRACTICAL ARITHMETIC

6+3= 4+4= 2+8= 1+3=

5+3= 2+6= 3+4= 4+1=

1 + 5 =

Practise adding these numbers daily until the sum of

any of these combinations can be told at a glance.

EXERCISE 9. ORAL

1. A man fed a colt 2 quarts of oats, a driving horse

4 quarts, and a draught horse 6 quarts. How many quarts

of oats did he use at a feeding?

2. If the morning and the afternoon each becomes 5

minutes longer during the second week in March, how

much longer are the days of the second week than the

days of the first week ?

3. If the cost of hauling Kansas wheat to the railroad

station is 3 cts. a bushel, and the freight to New York is

11 cts. a bushel, what is the total cost of transportation ?

4. A dairyman had 4 cows. One gave 5 quarts, one

7 quarts, one 8 quarts, and another 9 quarts of milk at a

milking. How many quarts did all give at a milking ?

5. A morning from sunrise to noon in September is

6 hours, and from noon to sunset is 6 hours. What is

the total length of the day ?

6. A ration for a cow is : corn and cob meal, 5 Ibs. ;

cotton-seed meal, 4 Ibs.; hay, 20 Ibs. What is the weight

of the entire ration ?

7. The number of cloudy days in January was 9, the

rainy days were 4. How many days were rainy and

cloudy ?

ADDITION 15

8. If a fruit cake requires 3 Ibs. of currants, 2 Ibs. of

raisins, and 1 Ib. of citron, how many pounds of fruit are

used in the cake ?

9. If the increase in temperature at Raleigh, N.C., in

1907 was 26 degrees from February to May and 14 degrees

from May to August, what was the total increase in tem-

perature during the six months ?

10. If the temperature decreases 8 degrees from July

to September and 33 degrees from September to March,

what is the total decrease in temperature ?

11. The number of senators from each of several sec-

tions of our country in 1890 was as follows : from the

New England States, 12; the Middle States, 8; the

Pacific States, 10. How many senators were there from

all these sections ?

12. The number of senators from the two largest sec-

tions of our country in 1890 was as follows : the South, 28 ;

the Northwest, 24. How many senators were there from

these sections?

13. A ration for a cow is 15 Ibs. of hay, 30 Ibs. of

silage, 4 Ibs. of cotton-seed meal, 3 Ibs. of wheat bran,

and 3 Ibs. of corn meal. What is the weight of the

entire ration ?

14. Count from 3 to 99 by threes.

15. Count from 4 to 100 by fours.

16. Count from 6 to 96 by sixes.

17. Count from 9 to 99 by nines.

18. At Raleigh, N.C., in 1907 the lowest temperature

for the month of October was 36 degrees, the highest

16 PRACTICAL ARITHMETIC

temperature was 45 degrees higher. What was the high-

est temperature ?

19. Two skilled laborers earned 83 and 85 respectively

a day. How much did the two earn together ?

20. Two unskilled laborers earned respectively 81.25

and 81.50 a day. How much did the two earn ?

21. The cultivation of an acre of corn costs 86, the fer-

tilizers 8 3, harvesting and other expenses 83. What is

the cost of the crop per acre ?

22. A ration for a horse weighing 1000 Ibs. when doing

moderately hard work is 6 Ibs. of corn, 8 Ibs. of oats, and

15 Ibs. of hay. What is the weight of the ration?

23. A ration for a fattening beef animal weighing

1000 Ibs. is 30 Ibs. of corn silage, 12 Ibs. of corn stover,

5 Ibs. of cotton-seed meal, and 4 Ibs. of cotton seed.

What is the weight of the ration?

24. If a man wishes to seed an acre for a meadow and

uses 11 Ibs. of timothy, 6 Ibs. of red top, and 5 Ibs. of

clover seed, how many pounds of seed does he sow on the

acre ?

25. If 1000 Ibs. of an average mixed stable manure

contain 5 Ibs. of nitrogen, 6 Ibs. of potash, and 3 Ibs. of

phosphoric acid, how many pounds of these plant foods

does it contain ?

26. If the plants in a ton of dry clover hay used 39

Ibs. of nitrogen, 37 Ibs. of potash, and 11 Ibs. of phos-

phoric acid in growth, how many pounds of these mate-

rials were used by the plants ?

27. If a ton of wheat straw used in growing 11 Ibs,

ADDITION 17

of nitrogen, 23 Ibs. of potash, and 4 Ibs. of phosphoric

acid, how many pounds of these materials were taken

from the soil ?

28. If a ton of oat grain used in growing 35 Ibs. of

nitrogen, 9 Ibs. of potash, and 13 Ibs. of phosphoric acid,

how many pounds of these materials were used ?