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I. C. S.
REFERENCE LIBRARY



A SERIES OF TEXTBOOKS PREPARED FOR THE STUDENTS OF THE

INTERNATIONAL CORRESPONDENCE SCHOOLS AND CONTAINING

IN PERMANENT FORM THE INSTRUCTION PAPERS.

EXAMINATION QUESTIONS. AND KEYS USED

IN THEIR VARIOUS COURSES



ARITHMETIC
MENSURATION AND USE OF LETTERS IN

FORMULAS
PRINCIPLES OF MECHANICS

MACHINE ELEMENTS

MECHANICS OF FLUIDS

STRENGTH OF MATERIALS

ELEMENTS OF ELECTRICITY AND MAGNETISM

HEAT AND STEAM

49852A



SCRANTON
INTERNATIONAL TEXTBOOK COMPANY



Copyright, 1897, by THE COLLIERY ENGINEER COMPANY.



Copyright, 1901, 1902, 1904, by INTERNATIONAL TEXTBOOK COMPANY.



Entered at Stationers' Hall, London.



Arithmetic, Parts 1-4: Copyright, 1893, 1894, 1895, 1896, 1897, 1898, 1899, by THE COL-

LIERY ENGINEER COMPANY. Copyright, 1901, by INTERNATIONAL TEXTBOOK

COMPANY.
Arithmetic, Part 5: Copyright, 1905, by INTERNATIONAL TEXTBOOK COMPANY.

Entered at Stationers' Hall, London.
Mensuration and Use of Letters in Formulas: Copyright, 1894, 1895. 1897, 1898, -by

THE COLLIERY ENGINEER COMPANY.
Principles of Mechanics: Copyright, 1901, by INTERNATIONAL TEXTBOOK COMPANY.

Entered atStationers' Hall, London.
Machine Elements: Copyright, 1901, by INTERNATIONAL TEXTBOOK COMPANY.

Entered at Stationers' Hall, London.
Mechanics of Fluids: Copyright, 1901, by INTERNATIONAL TEXTBOOK COMPANY.

Entered at Stationers' Hall, London:
Strength of Materials: Copyright, 1901, by INTERNATIONAL TEXTBOOK COMPANY.

Entered at Stationers' Hall, London.
Elements of Electricity and Magnetism: Copyright, 1894, 1897, by THE COLLIERY

ENGINEER COMPANY. Copyright, 1901, by INTERNATIONAL TEXTBOOK COM-
PANY.
Heat and Steam: Copyright, 1894, 1895, 1898, 1900, by THE COLLIERY ENGINEER

COMPANY. Copyright, 1902, by INTERNATIONAL TEXTBOOK COMPANY.



All rights reserved.



PRINTED IN THE UNITED STATES



BURR PRINTING HOUSE

FRANKFORT AND JACOB STREETS

NEW YORK



Y'l



PREFACE



Formerly it was our practice to send to each student
entitled to receive them a set of volumes printed and bound
especially for the Course for which the student enrolled.
In consequence of the vast increase in the enrolment, this
plan became no longer practicable and we therefore con-
cluded to issue a single set of volumes, comprising all our
textbooks, under the general title of I. C. S. Reference
Library. The students receive such volumes of this
Library as contain the instruction to which they are entitled.
Under this plan some volumes contain one or more Papers
not included in the particular Course for which the student
enrolled, but in no case are any subjects omitted that form
a part of such Course. This plan is particularly advan-
tageous to those students who enroll for more than one
Course, since they no longer receive volumes that are, in
some cases, practically duplicates of those they already
have. This arrangement also renders it much easier to
revise a volume and keep each subject up to date.

Each volume in the Library contains, in addition to the
text proper, the Examination Questions and (for those
subjects in which they are issued) the Answers to the
Examination Questions.

In preparing these textbooks, it has been our constant
endeavor to view the matter from the student's standpoint,
and try to anticipate everything that would cause him
trouble* The utmost pains have been taken to avoid and
correct any and all ambiguous expressions both those due
to faulty rhetoric and those due to insufficiency of state-
ment or explanation. As the best way to make a statement,
explanation, or description clear is to give a picture or a



iv PREFACE

diagram in connection with it, illustrations have been used
almost without limit. The illustrations have in all cases
been adapted to the requirements of the text, and projections
and sections or outline, partially shaded, or full-shaded
perspectives have been used, according to which will best
produce the desired results.

The method of numbering pages and articles is such that
each part is complete in itself; hence, in order to make the
x indexes intelligible, it was necessary to give each part a
number. This number is placed at the top of each page, on
the headline, opposite the page number; and to distinguish
it from the page number, it is preceded by a section
mark (). Consequently, a reference, such as 3, page 10,
can be readily found by looking along the inside edges of
the headlines until 3 is found, and then through 3 until
page 10 is found.

INTERNATIONAL CORRESPONDENCE SCHOOLS



CONTENTS



ARITHMETIC


Section


Page


Definitions


1


1


Notation and Numeration -


. 1


1


Addition


1


4


Subtraction


1


9


Multiplication


. 1


11


Division


1


16


Cancelation


. 1


20


Fractions


1


23


Reduction of Fractions


1


25


Addition of Fractions


1


28


Multiplication of Fractions


. 1


31


Division of Fractions


. 1


33


Decimals


. 1


37


Addition of Decimals . .'


1


39


Subtraction of Decimals


. 1


41


Multiplication of Decimals


. 1


42


Division of Decimals


. 1


44


Signs of Aggregation


. 1


52


Percentage '.


2


1


Calculations Involving Percentage . . .


. 2


4


Denominate Numbers


. 2


9


Measures


. 2


10


Reduction of Denominate Numbers . .


. 2


13


Addition of Denominate Numbers . . .


. 2


16


Subtraction of Denominate Numbers .


. 2


18


Multiplication of Denominate Numbers


. 2


20


Division of Denominate Numbers .


. 2


21


Involution


2


25


Evolution


, 2


28



vi CONTENTS

ARITHMETIC Continued Section Pagi

Square Root 2 34

Cube Root 2 37

Ratio . - 2 58

Proportion '. 2 61

Unit Method 2 66

MENSURATION AND USE OF LETTERS IN FORMULAS

Formulas . ' 3 1

Mensuration 3 13

Quadrilaterals 3 17

The Triangle 3 20

Polygons ..'..' 3 < 24

The Prism and Cylinder 3 32

The Pyramid and Cone 3 36

The Frustum of a Pyramid or Cone ... 3 37

The Sphere and Cylindrical Ring .... 3 39

PPINCIPLES OF MECHANICS

Matter and Its Properties 4 1

Motion and Velocity 4 5

Force 4 10

Gravitation and Weight 4 15

Work, Power, and Energy 4 20

Composition and Resolution of Forces . . 4 26

Friction 4 33

Center of Gravity 4 39

Centrifugal Force 4 43

Equilibrium 4 45

MACHINE ELEMENTS

The Lever, Wheel, and Axle ...... 5 1

Pulleys 5 7

Belts 5 12

Wheel Work . . 5 25

Gear-Calculations 5 34

Fixed and Movable Pulleys 5 42

The Inclined Plane .' 5 47

The Screw 5 53

Velocity Ratio and Efficiency 5 59



CONTENTS vii

MECHANICS OF FLUIDS Section Page

Hydrostatics 6 1

Specific Gravity 6 15

Buoyant Effects of Water 6 19

Hydrokinetics 6 22

Pneumatics 6 27

Pneumatic Machines 6 40

Pumps 6 47

STRENGTH OF MATERIALS

General Principles 7 1

Tensile Strength of Materials ...... 7 2

Crushing Strength of Material? 7 15

Transverse Strength of Materials .... 7 23

Shearing, or Cutting, Strength of Materials 7 29

Torsion . 7 32

ELEMENTS OF ELECTRICITY AND MAGNETISM

Introduction 8 1

Static Charges 8 3

Conductors and Non-Conductors 8 . 5

Electrodynamics 8 6

Magnetism 8 14

Electrical Units 8 26

Applications of Ohm's Law 8 50

Electrical Quantity 8 60

Electrical Work 8 61

Electrical Power 8 63

HEAT AND STEAM

Heat . . . '. 11 1

Steam 11 13



ARITHMETIC.

(PART 1.)



DEFINITIONS.

1. Arithmetic is the art of reckoning, or the study of
numbers.

2. A unit is one, or a single thing, as one, one bolt, one
pulley, one dozen.

3. A number is a unit, or a collection of units, as one,
three engines, five boilers.

4. The unit of a number is one of the collection of units
which constitutes the number. Thus, the unit of twelve is
one, of twenty dollars is one dollar, of one hundred bolts is
one bolt.

5. A concrete number is a number applied to some
particular kind of object or quantity, as three grate bars,
five dollars, ten pounds.

6. An abstract number t s a number that is not applied
to any object or quantity, as three, five, ten.

7. lake numbers are numbers which express units of the
same kind, as six days and ten days, two feet and five feet.

8. Unlike numbers are numbers which express units of
different kinds, as ten months and eight miles, seven wrenches
and five bolts.



NOTATION AND NUMERATION.

9. Numbers are expressed in three ways: (1) by words;
(2) by figures; (3) by letters.

10. Notation is the art of expressing numbers by figures
or letters.

11. Numeration is the art of reading the numbers which
have been expressed by figures or letters.

1

For notice of copyright, see page immediately following the title page,
12



3 ARITHMETIC. 1

13. The Arabic notation is the method of expressing
numbers by figures. This method employs ten different
figures to represent numbers, viz. :

Figures 0123456789

naught, one two three four Jive six seven fight nine
Names cipher,
or zero.

The first character (0) is called naught, cipher, or zero,

and when standing alone has no value.

The other nine figures are called digits, and each has a
value of its own.

Any whole number is called an Integer.

13. As there are only ten figures used in expressing
numbers, each figure must have a different value at different
times.

14. The value of a figure depends upon its position in
relation to other figures.

15. Figures have simple values, and local, or relative,

values.

16. The simple value of a figure is the value it expresses
when standing alone.

17. The local, or relative, value of a figure is the
increased value it expresses by having other figures placed
on its right.

For instance, if we see the figure 6 standing alone,

thus 6

we consider it as six units, or simply six.

Place another 6 to the left of it ; thus 66

The original figure is still six units, but the second
figure is ten times 6, or 6 tens.

If a third 6 be now placed still one place further
to the left, it is increased in value ten times more,

thus making it 6 hundreds 666

A fourth 6 would be 6 thousands 6666

A fifth 6 would be 6 tens of thousands, or sixty

thousand 66666

A sixth 6 would be 6 hundreds of thousands . . 666666
A seventh 6 would be 6 millions . . 6666666



1



ARITHMETIC



The entire line of seven figures is read six millions six
hundred sixty-six thousands six hundred sixty-six.

1 8. The increased value of each of these figures is its
local, or relative, value. Each figure is ten times greater in
value than the one immediately on its right.

19. The cipher (0) has no value itself, but it is useful
in determining the place of other figures. To represent the
number four hundred five, two digits only are necessary, one
to represent four hundred and the other to represent five
units ; but if these two digits are placed together, as 45, the 4
(being in the second place) will mean 4 tens. To mean 4 hun-
dreds, the 4 should have two figures on its right, and a cipher
is therefore inserted in the place usually given to tens, to show
that the number is composed of hundreds and units only, and
that there are no tens. Four hundred five is therefore ex-
pressed as 405. If the number were/<?r thousand five, two
ciphers would be inserted; thus, 4005. If it were four hun-
dred fifty, it would have the cipher at the right-hand side to
show that there were no units, and only hundreds and tens;
thus, 450. Four thousand fifty would be expressed 4050.

20. In reading figures, it is usual to point off the number
into groups of three figures each, beginning at the right-
hand, or units, column, a comma (,) being used to point off
these groups.



Billions.


Millions.


Thousands.


Units.








0i






1



















9
o






I


en




w






3


d




3


j




o


1




'S






S


1




S


|




EH


S

3







w




o


5




"o


^




o


O
j$


tn


"o


'S




tf>


S

(4-1

o


1


H

S


"o


w
a


n




1


tn

1


ID

"o




1


en


|


d
c

3


i


o


d
a


i


1


d
c


i


'S


3


fcn





a


e


Jjj


W


^H


EH


ffi


fH




4 3 2,1 9 8,7 6 5,4 3 2



\& pointing off these figures, begin at the right-hand figure
and count units, tens of units, hundreds of units; the next



4 ARITHMETIC. 1

group of three figures is thousands; therefore, we insert a
comma (,) before beginning with them. Beginning at the
figure 5, we say thousands, tens of thousands, hundreds of
thousands, and insert another comma. We next read millions,
tens of millions, hundreds of millions (insert another comma),
billions, tens of billions, hundreds of billions.

The entire line of figures would be read: Four hundred
thirty-two billions one hundred ninety-eight millions seven
hundred sixty- five thousands four hundred thirty-two. When
we thus reads, line of figures, it is called numeration, and if the
numeration be changed back to figures, it is called notation.

For instance, the writing of the following figures,

72,584,623,

would be the notation, and the numeration would be seventy-
two millions five hundred eighty-four thousands six hundred
twenty-three.

21. NOTE. It is customary to leave the "s" off the words
millions, thousands, etc. in cases like the above, both in speaking and
writing; hence, the above would usually be expressed seventy-two
million five hundred eighty-four thousand six hundred twenty-three.

22. The four fundamental processes of arithmetic are
addition, subtraction, multiplication, and division. They are
called fundamental processes because all operations in arith-
metic are based upon them.



ADDITION.

23. Addition is \he process of finding the sum of two or
more numbers. The sign of addition is -|-. It is read plus,
and means more. Thus, 5 + 6 is read 5 plus 6, and means
that 5 and 6 are to be added.

24. The sign of equality is = . It is read equals or Is
equal to. Thus, 5 + 6 = 11 may be read 5 plus 6 equals 11,
or 5 plus 6 is equal to 11.

25. Like numbers can be added; unlike numbers cannot
be added. 6 dollars can be added to 7 dollars, and the
sum will be 13 dollars; but 6 dollars cannot be added to
7 feet.



1



ARITHMETIC.



26. The following table gives the sum of any two
numbers from 1 to 12 ; it should be carefully committed to
memory:



1 and 1 is 2


2 and 1 is 3


3 and 1 is 4


4 and 1 is 5


1 and 2 is 3


2 and 2 is 4


3 and 2 is 5


4 and 2 is 6


1 and 3 is 4


2 and 3 is 5


3 and 3 is 6


4 and 3 is 7


1 and 4 is 5


2 and 4 is 6


3 and 4 is 7


4 and 4 is 8


1 and 5 is 6


2 and 5 is 7


3 and 5 is 8


4 and 5 is 9


1 and 6 is 7


2 and 6 is 8


3 and 6 is 9


4 and 6 is 10


1 and 7 is 8


2 and 7 is 9


3 and 7 is 10


4 and 7 is 11


and 8 is 9


2 and 8 is 10


3 and 8 is 11


4 and 8 is 12


and 9 is 10


2 and 9 is 11


3 and 9 is 12


4 and 9 is 13


and 10 is 11


2 and 10 is 12


3 and 10 is 13


4 and 10 is 14


and 11 is 12


2 and 11 is 13


3 and 11 is 14


4 and 11 is 15


and 12 is 13


2 and 12 is 14


3 and 12 is 15


4 and 12 is 16


5 and 1 is 6


6 and 1 is 7


7 and 1 is 8


8 and 1 is 9


5 and 2 is 7


6 and 2 is 8


7 and 2 is 9


8 and 2 is 10


5 and 3 is 8


6 and 3 is 9


7 and 3 is 10


8 and 3 is 11


5 and 4 is 9


6 and 4 is 10


7 and 4 is 11


8 and 4 is 12


5 and 5 is 10


6 and 5 is 11


7 and 5 is 12


8 and 5 is 13


5 and 6 is 11


6 and 6 is 12


7 and 6 is 13


8 and 6 is 14


5 and 7 is 12


6 and 7 is 13


7 and 7 is 14


8 and 7 is 15


5 and 8 is 13


6 and 8 is 14


7 and 8 is 15


8 and 8 is 16


5 and 9 is 14


6 and 9 is 15


7 and 9 is 16


8 and 9 is 17


5 and 10 is 15


6 and 10 is 16


7 and 10 is 17


8 and 10 is 18


5 and 11 is 16


6 and 11 is 17


7 and 11 is 18


8 and 11 is 19


5 and 12 is 17


6 and 12 is 18


7 and 12 is 19


8 and 12 is 20


9 and 1 is 10


10 and lisll


11 and 1 is 12


12 and 1 is 13


9 and 2 is 11


10 and 2 is 12


11 and 2 is 13


12 and 2 is 14


9 and 3 is 12


10 and 3 is 13


11 and 3 is 14


12 and 3 is 15


9 and 4 is 13


10 and 4 is 14


11 and 4 is 15


12 and 4 is 16


9 and 5 is 14


10 and 5 is 15


11 and 5 is 16


12 and 5 is 17


9 and 6 is 15


10 and 6 is 16


11 and 6 is 17


12 and 6 is 18


9 and 7 is 16


10 and 7 is 17


11 and 7 is 18


12 and 7 is 19


9 and 8 is 17


10 and 8 is 18


11 and 8 is 19


12 and 8 is 20


9 and 9 is 18


10 and 9 is 19


11 and 9 is 20


12 and 9 is 21


9 and 10 is 19


10 and 10 is 20


11 and 10 is 21


12 and 10 is 22


9 and 11 is 20


10 and 11 is 21


11 and 11 is 22


12 and 11 is 23


9 and 12 is 21


10 and 12 is 22


11 and 12 is 23


12 and 12 is 24



27. For addition, place the numbers to be added directly
under one another, taking care to place units under units,
tens under tens, Imndreds under hundreds, and so on.

When the numbers are thus written, the right-hand figure
of one number is placed directly under the right-hand figure
of the one above it, thus bringing units under units, tens
under tens, etc Proceed as in the following examples;



6 ARITHMETIC. 1

28. EXAMPLE. What is the sum of 131, 222, 21, 2, and 413 ?

SOLUTION. 131

222

21

2

413

sum 789 Ans.

EXPLANATION. After placing the numbers in proper
order, begin at the bottom of the right-hand, or units, col-
umn and add ; thus, 3 + 2 + 1 + 2 + 1 = 9, the sum of the
numbers in units column. Place the 9 directly beneath as
the first, or units, figure in the sum.

The sum of the numbers in the next, or tens, column
equals 8 tens, which is the second, or tens, figure in the
sum.

The sum of the numbers in the next, or hundreds, col-
umn equals 7 hundreds, which is the third, or hundreds,
figure in the sum.

The sum, or answer, is 789.

29. EXAMPLE. What is the sum of 425, 36, 9,215, 4, and 907 ?

SOLUTION. 425

36

9215

4

907



27

60

1500
9000

sum 10587 Ans.

EXPLANATION. The sum of the numbers in the first, or
units, column is 27 units; i. e., 2 tens and 7 units. Write 27
as shown. The sum of the numbers in the second, or tens,
column is G tens, or 60. Write 60 underneath 27 as shown.
The sum of the numbers in the third, or hundreds, column
is 15 hundreds, or 1,500. Write 1,500 under the two pre-
ceding results as shown. There is only one number in the
fourth, or thousands, column, 9, which represents 9,000.



1 ARITHMETIC. 7

Write 9,000 under the three preceding results. Adding
these four results, the sum is 10,587, which is the sum of 425,
36, 9,215, 4, and 907.

3O. The addition may also be performed as follows:
425
36

9215

4

907



sum 10587 Ans.

EXPLANATION. The sum of the numbers in units col-
umn = 27 units, or 2 tens and 7 units. Write the 7 units
as the first, or right-hand, figure in the sum. Reserve the
2 tens and add them to the figures in tens column. The
sum of the figures in the tens column plus the 2 tens
reserved and carried from the units column is 8, which is
written down as the second figure in the sum. There is
nothing to carry to the next column, because 8 is less
than 10. The sum of the numbers in the next column is
15 hundreds, or 1 thousand and 5 hundreds. Write down
the 5 as the third, or hundreds, figure in the sum and carry
the 1 to the next column. 1 -j- 9 = 10, which is written
down at the left of the other figures.

The second method saves space and figures, but the first
is to be preferred when adding a long column.

31. EXAMPLE. Add the numbers in the column below :
SOLUTION. 890

82



281

80
770

83
492

80
383

84
191



sum 3899 Ans.



8 ARITHMETIC. 1

EXPLANATION. The sum of the digits in the first column
equals 19 units, or 1 ten and 9 units. Write the 9 and
carry 1 to the next column. The sum of the digits in the
second column -|- the 1 carried from the first column is
109 tens, or 10 hundreds and 9 tens. Write down the 9 and
carry the 10 to the next column. The sum of the digits in
this column plus the 10 carried from the second column is 38.

The entire sum is 3,899.

32. Kule. I. Begin at the right, add each column
separately, and write the sum, if it be only one figure, under
the column added.

II. If the sum of any column consists of t^vo or more fig-
ures, put the right-hand figure of the sum under that column
and add the remaining figure or figures to the next column.

33. Proof. To prove addition, add each column from
top to bottom. If you obtain the same result as by adding
from bottom to top, the work is probably correct.



EXAMPLES FOR PRACTICE.

34. Find the sum of:

(a) 104 + 203 + 613 + 214.

(b) 1,875 + 3,143 + 5,826 + 10,832.

(c) 4,865 + 2,145 + 8,173 + 40,084.

(d) 14,204 + 8,173 + 1,065 + 10,042.

(e) 10,832 + 4,145 + 3,133 + 5,872.
(/) 214 + 1,231 + 141 + 5,000.

(g) 123 + 104 + 425 + 136 + 327.

(A) 6,354 + 2,145 + 2,042 + 1,111 + 3,333.



Ans.



(a) 1,134.

(6) 21,676.

(c) 55,267.

(d) 33,484.
(<r) 23,982.
(/) 6,586.
(JO 1,105.
(k) 14,985.



1. A week's record of coal burned in an engine room is as fol-
lows: Monday, 1,800 pounds; Tuesday, 1,655 pounds; Wednesday,
1,725 pounds; Thursday, 1,690 pounds; Friday, 1,648 pounds; Satur-
day, 1,020 pounds. How much coal was burned during the week ?

Ans. 9,538 Ib.

2. A steam pump, in one hour, pumps out of a cistern 4,200 gal-
lons ; in the next hour, 5,420 gallons ; and in 45 minutes more an addi-
tional 3,600 gallons, when the cistern becomes empty. How many
gallons were in the cistern at first ? Ans. 13,220 gal.



1 ARITHMETIC. 9

3. What is the total cost of a steam plant, the several items of
expense being as follows: steam engine, $900; boiler, $775; fittings
and connections, 225 ; erecting the plant, 125 ; engine house, 650 ?

Ans. 2,675.



SUBTRACTION.

35. In arithmetic, subtraction is the process of finding
how much greater one number is than another.

The greater of the two numbers is called the minuend.

The smaller of the two numbers is called the subtra-
hend.

The number left after subtracting the subtrahend from
the minuend is called the difference, or remainder.

36. The sign of subtraction is. It is read minus,
and means less. Thus, 12 7 is read 12 minus 7, and means
that 7 is to be taken from 12.

37. EXAMPLE. From 7,568 take 3,425.
SOLUTION. minuend 7568

subtrahend 3425



remainder 4143 Ans.

EXPLANATION. Begin at the right-hand, or units, column
and subtract in succession each figure in the subtrahend
from the one directly above it in the minuend, and write
the remainders below the line. The result is the entire
remainder.

38. When there are more figures in the minuend than
in the subtrahend, and when some figures in the minuend
are less than the figures directly under them in the sub-
trahend, proceed as in the following example:

EXAMPLE. From 8,453 take 844.

SOLUTION. minuend 8453

subtrahend 844



remainder 7609 Ans.

EXPLANATION. Begin at the right-hand, or units, col-
umn to subtract. We cannot take 4 from 3, and must,



10 ARITHMETIC. 1

therefore, borrow 1 from 5 in tens column and annex it to
the 3 in units column. The 1 ten = 10 units, which added
to the 3 in units column 13 units. 4 from 13 = 9, the
first, or units, figure in the remainder.

Since we borrowed 1 from the 5, only 4 remains; 4 from
4 = 0, the second, or tens, figure. We cannot take 8 from 4,
so borrow 1 thousand, or 10 hundreds, from 8 ; 10 hundreds
+ 4 hundreds = 14 hundreds, and 8 from 14 = 6, the third,
or hundreds, figure in the remainder.

Since we borrowed 1 from 8, only 7 remains, from which
there is nothing to subtract ; therefore, 7 is the next figure
in the remainder, or answer.

The operation of borrowing is placing 1 before the figure
following the one from which it is borrowed. In the above
example the 1 borrowed from 5 is placed before 3, making
it 13, from which we subtract 4. The 1 borrowed from' 8 is
placed before 4, making 14, from which 8 is taken.

39. EXAMPLE. Find the difference between 10,000 and 8,763.
SOLUTION. minuend 10000

subtrahend 8763



remainder 1237 Ans.

EXPLANATION. In the above example we borrow 1 from
the second column and place it before 0, making 10 ; 3 from
10 = 7. In the same way we borrow 1 and place it before
the next cipher, making 10; but as we have borrowed 1
from this column and have taken it to the units column,
only 9 remains from which to subtract 6 ; 6 from 9=3.
For the same reason we subtract 7 from 9 and 8 from 9
for the next two figures, and obtain a total remainder of
1,237.

40. Rule. Place the subtrahend (or smaller) number
under the minuend (or larger} number, in the same manner



Online LibraryInternational Correspondence SchoolsI.C.S. reference library; a series of textbooks prepared for the students of the International Correspondence Schools, and containing in permanent form the instruction papers, examination questions, and keys used in their various courses (Volume 1) → online text (page 1 of 39)