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PI
OR
«
w
PRIMARY ARITHMETIC
ixciiUDBra
ORAL, SLATE, AND WRITTEN EXERCISES.
BY
^EV. D. H. MACVICAR, LL.D.,
Principal Prebbytf.rian CoLLKaE, Montreal.
* ^•^ »
TORONTO :
CANADA PUBLISHING COMPANY,
MONTREAL :— DAWSON BROTHERS.
1880.
'm
cy
Entered according to Act of Parliament of Canada, in the Vear 1879, by
Dawson Brothers, in the Office of tha Minister of Agriculture.
uiRAirr
I
I-AVA^-^
PREFACE.
THE objects specially uiined at in this work are to train th«
pu})il to accuracy and rapidity in the operations of the
four elementary rules of Arithmetic, to accustom him to habits
of careful ob!:^ervation on the methods of solving practical
problems, and to render him so familiar with fundamental
principles and processes as to r^ ike advanced work natural and
easy.
The lollowiiujf points indicate tlie plan of the book:
1. In every subject the lirst steps are presented objectively,
followed by sutlicient slate and written exercises to define and
fix lirmly in the mind of the pui)il the truths illustrated.
2. The work from the beginning is so arranged that each
step forms a natural and complete preparation for the step fol-
lowing. Hence tlio pupil is led to understand clearly the prin-
ciples on which each operation depends before he is re<juired
to perform it.
;j. By the use of Arithmetical Tahks an unlimited number of
exomples in abstract numbers is given, affording the teacher
the best means for dasH drill, and for keeping pupils employed
at their seats, while giving them sufficient practice in writing
numbers neatly and accurately.
4. Tlx' oral and written exercises are carefully graded, and
are of die most practical nature. The use of Canadian money
is introduced in Addition and continued throughout the book.
Siriple examples in denominate numbers are also given as
applications in Multiplication and Division, thus making the
pupil familiar, at an early stage of his work, with what is
practical. * • ' ,-, o o ->
5
8
ii
PRE FA CE.
5. The nature of fractions is presented objectively, and the
pupil taught clearly how to represent various fractional units,
how to change a fraction from one fractional unit to another,
how to change wholes into any given fractional units, and given
fractional units into wholes. After this, exercises are given
requiring, iu the simplest form, the use of addition, subtrac-
tion, multiplication and division of fractions.
These pages, while purely elementary, are so complete as ta
give the child such a knowledge of fractions as will fit him to
perform the operations ordinarily occurring in prujtical life.
6. The book closes with denominate numbers, giving all ti
tables the pupil requires to know, with carefully graded exer-
cises illustrating each table.
Hints and directions to teachers are not introduced through-
out the work, because they would prove injurious to the pupil,
for whom it is exclusively intended. Full instructions and a
complete method of presentation will be found in the Teach-
er's Edition of the Elementary and Complete Auith-
METios, by M. Mac Vicar, Ph.D., LL.D., Principal of th:^ State
Normal School, Potsdam, N. Y., published by Taintor Brothers,
Merrill & Co., New York. The present work is specially
adapted for use in Canadian Schools, while based upon the
Elementary Arithmetic j- .st named, which was prepared by
Dr. M. Mac Vicar and the undersigned.
D. H. Mac Vicar.
Montreal, January, 1879.
CONTENTS.
Page
Notation and Numeration — Numbers from 1 to 10 5
Exercise in use of Signs » 10
Numbers from 10 to 100 U
Numbers from 100 to 1,000 17
Numbers above 1,000 ....tr 19
Definitions, Bules , , 24
Boman Notation 25
Addition 27
. Addition Tables 31
Definitions, Rule 46
Subtraction 47
Definitions, Bule 64
Multiplication 65
Definitions, Rules 77
Applications, Canadian Money « 79
Measures of Weight -. 81
Divisioii ,... 83
DefinitioUii, Rule 102
Applications, Dry Measure 103
Liquid Measure 104
Exercises on Exact Division, greatest common divisor. . . 105
Exercise on Multiples 106
Fractions, Oral Exercises 107
Reduction , 112
Addition 117
Subtraction c > 118
m
It
CONTHNTij.
Multiplication 119
Division ,. 123
Definitions 126
Denominate Numbers, Canadian and United States Money. 127
English and other Money 129
Exercises in Units ofWeight 131
Units of Length 133
Exercises in Units of Surface 135
Exercises in Units of Volume 137
Units of Capacity 1 39
Units which vary in Size 143
Units of Time I44
Answers >,,,,, , . , , 145,
u ::
%
119
. 123
. 126
. 127
129
131
133
135
137
139
143
144
145»
ARITHMETIC
NUMBERS FROM 1 TO 10.
ONE.
1 . The following illustrates the method of presenting num-
bers from one to ten, Tlie teacher should vary the illustra-
tions by the use of diflferent objects and of the Numeral Frame
and blackboard.
1. Show me one book. One boy. One pencil. One desk.
One window. One slate.
3. Show me one hand. One door. One finger. One knife.
One head. One ear. One eye.
3. What is a single thing called ? Name a single thing.
4. One means a single thing. The figure 1 stands for one.
T VV^O.
2. 1. Show me two fingers. Two thumbs. Two girls.
Two boys. Two ink bottles. Two slates. Two books.
2. How many eyes have you ? How many ears ? How many
hands ? How many feet ?
3. One dog and one dog are how many ? One and one are
how many ? Two dogs less one dog are how many ?
4. Two desks less one desk are how many ? Two slates less
one slate ? Two less one are how many?
5. Two means one and one. The figure 2 stands for two.
6
NOTATION AND yVMERATIf)N.
THREE.
3, 1. Show me three boys. Three windows. Three fiujrers.
2. Three dogs less one dog are how many ? Three books less
one book ? Three less one are how many ?
3. How many are two and one? How many ones in twoV
In three ? How many twos iu three, and what left?
4. Count three. Name three boys. Three girls. 2 and 1
are how many ? 1 and 1 and 1 are how many ?
5. Two and one make three. The figure 3 stunds for
three.
FOUR.
4t 1. Show me four balls on the Numeral Frame. Three
balls. Two balls and two balls.
2. Two hats and one hat are how many ? Three hats and
one hat ? Two hats and two hats ?
3. How many hats taken from four will leave one? Will
leave two*? Will leave three ? Will leave four ?
4. How many two boys in four boys? How many three
boys, and how many left ?
5. Three and one make four. The figure 4 stands for
four,
FIVE.
6. 1. Show me five balls on the Numeral Frame. Four
balls. Three balls and two balls.
2. How many are two desks and one desk ? Two desks and
two desks ? Four desks and one desk ?
3. Five fishes less one fish are how many ? Less two fishes ?
Less three fishes ? Less four fishes ?
4. How many are 2 and 1 ? 2 and 2 ? 4 and 1 ? 3 and 2?
3 and 1 ? 2 and 2 and 1 ?
6. Four and one make five* The figure 5 stands for five.
.1
NOTATION AND NUMERATION.
SIX.
6. 1. Sliow me six balls on the Numeral Frame. Three
balls and two balls. Five balls and one ball.
3. Six trees less one tree are how many ? Six trees less two
trees ? Six trees less three trees ?
3. Two books and one book are how many? Two books and
three books ? Two books and four books ?
4. 3 and 1 are how many ? 3 and 2? 3 and 3 ? 6 less 1 arc
how many ? 6 less 3 ? 6 less 3 ? 6 less 4 ? 6 less 5 ? .
5. Five and one make six. The figure stands for 8/a?«
SEVEN.
7. 1. Show me seven balls on the Numeral Frame. Five
balls and two balls ? Six balls and one ball ?
2. Six plums less one plum are how many ? Less two plums ?
Less three plums ? Less five plums ?
3. How many 3 plums in 7 plums, and how many left ? How
many two plums, and how many left ?
4. 3 and 1 are how many ? 4 and 2 ? 4 and 3 ? 5 and 1 ?
5 and 2? 3 and 3?
5. Six and one make seven. The figure 7 stands for
seven.
I
EIGHT.
8. 1. Show me eight balls on the Numeral Frame. Four
balls and three balls. Two balls and six balls.
3. Eight peaches less one peach are how many ? Less two ?
Less three ? Less ^our ? Less five ? Less six ?
3. How many fours in eight ? How many twos ? How many
threes, and how many left ? How many ones?
4. 6 and 1 are how many? 3 and 2? 3 and 3? 7and 1?
6 and 2? 5 and 3? 4 and 4?
5. Seven and one make eight. The figure 8 stands for
eight.
8
NOTATION AND NUMERATION,
NINE. •
O. 1. Show me nine balls on the Numeral Frame. Six
balls and three balls. Four balls and three balls.
2. Five leaves and one leaf are how many? Five leaves and
\ hree leaves ? Eight leaves and one leaf ?
i). 6 and 1 are how many ? 4 and 2 ? 4 and 3 ? 4 and 4 ?
4 and 5? 3 and 6? 2 and 7? •
4 How many are 5 less than 9 ? 3 less than 9 ?
5. How many 3's in 0? How many in 9? How many in 8,
and what left? How many 2's in 4 ? How many in 8 ?
6. 3 and 2 and 2 are how many? 4 and 1 and 3? 2 and 3
nnd 4 ? 4 and 2 and 2 ? 5 and 1 and 2 ?
7. Eight and one make nine. The figure 9 stands for
nine*
TEN.
10. 1- Show me ten balls on the Numeral Frame. Six
halls and four balls. Three balls nnd five balls.
3. How i.iany are 9 cherries and 1 cherry V 8 cherries and
3 cherries? 7 cherries and 3 cherries ? G cherries and 4 cher-
ries ? 5 cher.'ies and 5 cherries ?
3. How many 5 cherries in 10 cherries? How many 3 cher-
vieH? How many 4 cherries, and how many left?
4. In how many ways can you make 10 cherries into two
i!:roups of cherries ?
5. 10 cherries less 3 cherries are liow many ? Less 1 ?
Lnss4? Less 2? Less 9? Less 5?
6. 7 and 2 are how many ? 7 and 3 ? 7 and 1 ? 5 and 2 ?
5 au'l 4 ? 5 and 3 ? 5 and 5 ? 8 and 1 ? 8 and 2 ? 4 and 2 ?
7. Nine and one make ten. The figures 10 stand for ten.
The figure O, which is oa,lleJ clplun' or zero^ has »»o value
m itself.
U.
in the c
\
Co
ydi
NOT AT 10 N' AND i\ UJI E RATION.
le. Six
ves and
and 4 ?
ny in 8,
2 and 8
mds for
ne. Six
lies and
i 4 cher-
jT 3 cher
into two
Loss 1 V
5 and 2 ?
and 2 V
'or ten .
»o valiif
I
EXERCISE IN MAKING FIGURES.
I Jl . C^opy neatly from this picture of a slate all the figures
in the order in which they are given.
/?Y'
'j-- /
■J :J .;' 4
7 /
'' ■':J ■>
■y -J o
J -T J cV U -/- '^ />
^ / /'S S-6
^/ ^ ^ o 6 <r :^ 2
3yJ ; f ^^ :^/) s^
Continue to copy these figure?^ until you can make them on ^
yov. ilate as well us they are made here.
10
NOTATION AND NUMERATION.
EXERCISE ON USE OP SIGNS.
12. 1. The sign + stands for and. Thus, 3+4 is read,
3 and 4*
3. The sign = stands for make or equal. Thus, 5 + 3 = 7
is read, 5 and 2 make 7, or 5 and 2 equal 7.
3. The mark (?) placed after the sign = means that the
answer is to be found.
Thus, 6 + 3 = ? means that 9, the number that 6 and 3 are
together equal to, is to be found.
Copy the following on your slate ; find the answers and write
them in place of the question marks :
8+2 = 'i 3+2 = 1 7+-^-? 2+2 = f
4+2=9 6+2=9 8+2=? 9+1=?
2
4+3=? 7+8=? 2+3=? 5+3=?
8+3=? 6+3=? 4+8=? 8+2=?
5+4=? 2+4=? 6+4=? 8+4=?
4+4=? 7+2=? 9+1=? 6+4=?
4+5=? 2+5^? 5+5=? 8+5=?
5+8=? G+4=? 8+2=? 7+3=?
ON,
rs.
^4 is read,
.8,5 + 2 = 7
IS that the
and 3 are
I and write
NOTATION AND N U M E B ATI N. 11
NUMBERS FROM 10 TO 100.
EXERCISE IN GROUPING.
13. 1. Make on your slate a group of 5 marks ; of 7 marks ;
of 9 marks ; thus :
3. Make in the same manner on your slate a group of
4 marks ; of 6 ; of 8 ; of 3 ; of 9 ; of 5 ; of 10.
3. Put on your slate two groups of ten marks each, thus :
4. Make each of these groups into two equal groups. How
many groups do they now make? How many in each group?
5. Make on your slate a group of ten marks and 1 mark ; a
group of ten marks and of 3 marks ; thus :
1 ten and 1.
1 ten and V.
Eleven,
Twelve.
6. What does Elecen mean? What does Tioelve mean?
7. Make in the same manner on your slate a group of tea
and three ; ten and four ; and so on, thus :
Iten and 3*
1 ten and 4.
Thirteen*
Fourteen,
8. What does T/nrteen mean ? Fourteen ? Fifteen f Sixteen t
Seventeen? Eighteen? Nineteen? Twenty?
9. Eleven objects are how many more than ten? Twelve
than eleven ? Thirteen than twelve ? Seventeen than sixteen ?
10. Give the names of the numbers from one to tioenty, thus :
One, Two, Three, Four, etc.
12
NOTATION AND NUMERATION,
NUMBERS FROM 10 TO 20.
14. 1. Write the figure that stands for one, 1,
2. Write the figures that stand for ten, 10,
1 ten and 1 are Eleven, Written, J 1,
3. Write the figures that stand for ten. For ttvo,
1 ten and '^ are Twelve, Written, 12,
4. When two figures are written side by t^ide, what does the
one on the right denote ? Tlie one on the left ?
5. Write the figures for 1 t( i and 3. For 1 ton and 4. For
1 ten and 5. For 1 ten and 7.
6. What figures stand for 1 ten and 2 ? For 1 ten and 9 ?
For 1 ten and 4 ? For 1 ten and 8 ?
7. Repeat this table :
1 ten and 1 are Eleven,
1 ten and 2 are Twelve,
1 ten and 'i are Thirteen,
1 ten and 1 are Fourteen,
1 ten and ,-> are Fifteen.
1 ten and (i are Sixteen,
1 ten and 7 are Seventeen,
1 ten and H are Fiijhteen,
1 ten and f> are Nineteen.
8. Ten and one are how many V Twelve and one ? Fourteen
and one ? Seventeen and one ?
9. Seventeen less one are how many? Tliirteen less one?
Nineteen less one ? Fifteen less one ?
10. 11 + 1 are how many V 17 + 1? 15 + 1? 13 + 1? 18 + 1?
13 + 1? 14 + 1? 10 + 1? 19 + 1?
11. Write the figures that stand for eleven. For twelve. For
seventeen. For thirteen. For nineteen.
NOTATION AND NUMERATION.
13
EXERCISES IN GBOUFING.
15. 1. Make on your slate 3 groups of ten marks, and 3
groups of ten marks, thus :
%
t«HS»
3 tens.
' = Twenty.
S
-[ = Thirty.
2. Wiiat does Twenty meaal Thirty? Forty?
3. Make iu the same manner 4 groups of ten marks • 8 groups
of ten marks ; 6 groups of ten marks.
4. What does Fifty mean ? Sixty ? Seventy ? Eighty ?
Ninety ?
6. How many is sixty more than fifty ? Fifty than forty ?
C. Four tens are how many? Seven tens? Five tens?
Tlireetens? Nine tens?
7. Make on your slate 10 groups of ten marks each.
Ten yroups of
ten marks aach,
1 Hundred
marks.
8. What is meant hy 1 hundred marks? 1 hundred
hooks? 1 hundred boys? 1 hundred men?
9. How many does 9 groups of ten marks lack of being
1 hundred marks? groups of fen marks?
10. A group of 8 boys, one of 9 boys, and one of 3 boys, will
together make how many groups of ten boys ?
11. 8 apples, 3 apples, 5 apples, and 9 apples, will make how
many groups of ten apples
14
NOTATION AND NUMERATION,
WRITING AND READING TENS.
16. 1. Write the figures that stand for ten.
9 and 1 are ten. Written 10,
2. What two figures stand for ten ? How are they wfttten ?
Which is on the left hand ? Which is on the right hand ?
'd. Make ten marks on your slate two times :
Thus, llilllllll IIIIIIIHI
4. Write the figures that stand for two tens,
2 t^ns are twenty. Written 20,
5. Make ten marks on your filate 3 times ; •! times ; 5 times ;
6 times ; 7 times ; 8 times ; 9 times ; 10 times.
6. How would you write the figures that stand for three tens,
four tens, five tens, six tens, seven tens, eight tens, nine tens ?
7. Repeat this tabl^ :
2 tens are twenty* 6 tens are sixty,
3 tens are thirty, 7 tens are seventy,
4: tens are forty, 8 tens are eighty ^
5 tens are fifty, tens are ninety,
10 tens are 1 hundred.
o. What two figures together stand for eig7it tens ? Which
is on the left hand ? Which is on the right hand ?
9. How many are 3 tens ? 6 tens ? 9 tens ? 4 tens ?
17.
Express in figures :
10. Two tens. 13. Three tens.
11. Four tens. 14. Five tens.
12. Six tens. 15. Nine tens.
19. Read the following :
60. 30. 70. 30. 50.
16. Eight tens.
17. Four tens.
18. Seven tens.
90. 60. 40. 70. 90.
^'.
NOTATIOX AND N IT ME RATIO N.
15
s.
wfttten ?
md?
5 times ;
ree tens,
6 tens?
y*
Which
bens.
3ns.
tens.
00.
NUMBEBS FROM 20 TO 100.
17. 1- Write the figures that stand for two tens andon^.
2 tens and 1 are Awenty^ouf, Written 21,
3. Write the figures that stand for three tens and one,
3 tens and 1 are Thirty -one* Written SI,
3. Write the figures that stand for four tens and one. For
six tens and one. For nine tens and otw,
4. How many are 2 tens and 1 ? 3 tens and 1 ? 7 tens and 1 ?
5 tens and 1 ? 8 tens and 1 ? 9 tens and 1 ?
5. Write the figures that stand for two tens and two,
2 tens and 2 ar, Twenty-^wo, Written 22,
G. Write the figures that stand for 4 tens and 2. For 6 tens
and 2. For 8 tens and 2. For 9 tens and 2.
7. How many tens in Twenty "two, and how many over?
In Thirty-two ? In Seventy-two ?
8. How many are 2 tens and 6 ? 3 tens and 87 6 tens and 5 ?
8 tens and 4?
9. How many are 30+7? 40 + 9? 80+5? 70 + 6? 60 + 3?
90+2?
10. How many are 20+1? 25 + 1? 27+1? 32 + 1? 36 + 1?
56 + 1? 89 + 1?
11. How many are 37 less 1 ? 56 less 1 ? 74 less 1 ? 80 less
1? 931688 1?
12. Name the numbers in orde . from one to on>e hundred ;
thus, one, two, three, etc.
13. Bead the following numbers :
20 15 17 70 11 33 56 18 29 80
57 79 68 94 57 86 79 99 41 45
IG A > TA T I .V .1 yn y umera ti o x.
Ill
ARITHMETICAL TABLE No. 1.
18. 1. Copy on your slate columns A and B of this table.
Read each number on your slate.
1.
A.
B.
c.
B.
E,
F.
C^.
H.
■
(9'
■J.
/
7-^
/
4
/
/
V
'V
/
1
9.
8.
4.
•
^ , /
^ ■■/
6.
V.
/ ■
-V
' /
•1, "-
/ ^
/
;• \
\ ■;
/ ^^
8.
9.
10.
0.
■ / r
— ■■ _v
//■
*
2. Coi)y on another part of your slate columns B and C, the»
C and D, and so on, Head the numbers as before.
N
2.
are
3.
dred "
4.
>«i
I !
NO TA TION A ND N UME K A TION. 17
NUMBERS FROM 100 TO 1000.
*;«
lO. 1. Write the figures that express ten tens*
10 tens are one hundfcd. Written 100»
2. How many ciphers used to exvess one hundred? Where
are they written V Where is the 1 written ?
3. Express by figures two hundred ; four hundred; six hun-
dred ; seven hundred ; five hundred ; nine hundred
4. Express by figures eleven tens,
11 tens are one hundred and ten* Written 110.
5. IIow many ciphers used to express one hundred ten ?
6. Write by figures 13 tens; 15 tens; 17 tens; 19 tens; 21
tens ; 20 teno ; 25 tens ; 59 tens.
7. ITow many ciplicrs used* to express 30 tens? 50 tens?
60 tens? 40 tens? 90 tens?
8. Write by figures one hundred foi-ty ; five hundred eighty ;
eight hundred seventy ; four hui.v«red twenty.
9. Express by figures ten tens and one,
10 tens Bind 1 are one hundred and one. Written 101.
10. How many ciphers used to express one hundred onef
Where wrii,ten?
Express by figures the following numbers :
11. Three hundred one; five hundred one; nine hundred
one ; seven hundred one.
12. Three hundred four ; six hundred two ; eight hundred
five ; two liundred nine ; nine hundred nine.
13. Two hundred sixty-one ; five hundrod seventy-nine.
14. Nine hundred nine ; nine hundred ninety-nine.
18
NOTATION AND N UM E li A Tl N,
SLATE EXER'^" >.
20. Copy on your slate and read the following :
(1-)
(3.)
(3.)
(4.)
(8.)
309
406
506
905
906.
107
SOS
805
902
805
402
405
608
607
909
301
402
302
806
606
205
209
6O4
8O4
907
(6.)
(7.)
(8.)
(9.)
(10.)
120
140
131
289
454
S60
670
523
973
'897
fy20
380
474
884
898
560
760
882
579
555
820
680
796
845
999
Express in figures the following :
11. Two hundred five.
20.
Eight hundred fifteen.
12. Five
hundred seven.
21.
Nine hundred
nine.
13. Seven hundred two.
22.
Two hundred \
sixty.
14. Eight hundred twenty
23,
Six hundred e
ighty-ono.
15. Six hundred ninety.
■ 24.
Five hundred
thirty-five.
16. Four hundred sixty.
2.1
Eight hixndred fifteen.
17. Three hundred seven.
26.
Two hundred
seventy-four.
18. Two
hundred eighty.
97.
Six hundred s
xty-!\ine.
19. One hundred twenty-one. 28.
Two hundred
e;gli1y-on(?.
NOT A T i O A A.\B N UME RATIO N,
19
(6.)
906
805
909
606
907
NUMBERS ABOVE 1000.
SLATE EXERCISES.
21. 1. Expreas in figures ten hundreH,
10 hundred are one tJiousand, Written 1,000*
2. How many ciphers used to espress one thousand ? Where
ere they written ? What place from the right of the number
does the 1 occupy ?
3. Write in figures three thousand ; five thousand ; eight
thousand ; nine thousand ; 4 thousand ; 6 thousand.
4. Express in figures ten thousand,
10 thousand are written 10,000,
5. How many ciphers used to express ten thousand? What
place from the right does the 1 occupy ? What separates the
10 from the three ciphers ?
G. Write in figures fifty thousand ; seventy thousand ; lorty
thousand ; 50 thousand ; 80 thousand.
7. TTow many ciphers must be placed to the right of 13 to
make ii denote 13 thousand ?
Espress in figures the following numbers :
8. Fifteen thousand. 13. Twcnty-four thousand.
0. Tliiity-five tliousand. 14. Eigliiv-six thousand.
10. Nine thousand two. 15. Five thousand nine.
11. Seven thousand fifty-five. 10. (5ne thousand eighty-one.
12. Forty-six thousand one 17. Seventy-two thousand five.
18. Twonty-ono thousand seven hundred ninety-nine.
19. Forty-four tliouf<and three hundred fifty.
20. Two hundred thirty-six thousand.
20
NOTATION AND NUMERATION,
NUMERATION TABLE.
22. 1. What place does the figure 6 occupy in 49G? The
figure 9? The figure 4?
2. The places in a number denote the orders of units.
Thus, in 946, the 6 in the^>«^ place from the right represents
units of the first order, the 4 in the second place units of the
second order, the 9 in the third place units of the third order.
3. The orders of units in a number are formed into groups
of three. Each group is called a Period,
4. The figures in the first period on the right represent
unltSf in the second period thoiisandSf in the tliird period
millions, as shown in the following
4'
9
TABLE.
r i>
l!
Periods.
3d
2d.
1st.
>- Millioi
*
IS.
Th
ousands.
^
Units.
Names
r
— >
^
<M
<H
«M
OF
o
o
o
Orders ^
n3
OF
0)
«w
«f-i
a>
«H
<M
a>
CM
«M
>H
O
o
ti
o
o
S-,
o
o
Units.
en
m
73
—4
CO
01
T3
!/3
ai
a
<u
O
d
<o
C
a
<D
<o
a
ff
0)
a
C
v
I w
&H
O
W
H
O
w
H
o
r2
4
3
6
9
«
.$
5
7
7
2
6
1
Numbers
4
8
5
3
7
7
to be read.
9
8
6
8
8
4
7
-4
3
2
8
tei
5. Read the foregoing numbers.
. 6. How do the names of the orders of units in the first period
compare with those of the second and third periods?
7. What is the general name for the three orders in the first
period? In the second period? In the third period?
NOTATION AND NUMERATION.
21
The
SLATE EXERCISES.
SJ3. Read aud copy the following on your elate:
(1-)
(2.)
(3.)
800009
63^707^
850609
j^802500
815019 -
6^80074.
606002 -■
3709^06
460668
9700000
2602300
2680308
(4.)
(«.)
(6.)
78036
83252 ■■
952^36
Jj-002
500^
87330
609036
82568^
309^62
60903
87303
235984
240089
593820
480002
24, Read and analyze the following, thus :
Ex. 1. 340 cents = 3 hundreds 4 tens and 6 ones.
Analysis. 340 cents means 3 groups of one hundred cents, 4 groups of
ten conta, and C single cents, or it may mean 34 groups oXten cents and 6
single cents.
2.
95 birds.
10.
1480 tables.
18.
586.
3.
430 men.
11.
5700 spikes.
19.
1907.
4.
342 sheep.
13.
4097 books.
30.
5081.
5.
70 inkstands.
13.
48079 nails.
21.
93040.
C.
654 \vindows.
14.
496 beds.
23.
60473.
7.
899 houses.
15.
2009 lamps.
23.
102490.
8.
94 canary birds.
10.
3075 oxen.
24.
70840.
9.
593 robins.
17.
1936 boots.
25.
430603.
22
NOT ATI N A XD X UME RATIO N,
SLATE EXERCISES.
25. Copy tlie following numbers, placing them in columns,
units under units, tens under tens, etc. Read each number,
pointing it off into periods.
1. ^886^; 89^63; 568; 820^0.
2. 8043; 2000; 2090 4; 7^001.
8. 4000 J/-; 100601; 3080; 800^.
2(5. Copy and analyze on your slate the following :
Tuus, 9846 = 9000 + 800 + 4O + 6.
3070 = 3000 + 70.
(1)
(8.)
(3.)
63595
93940
60904
49583
86900
593006
36826
525708
6O64OO
37043
40238
8500954
4. How many tens in 674, and how many remaining? In
809 V In 8G8 ? In 4840 ? In 1040 ?
5. How many hundreds in 9584, and how many remaining?
In 6362? In 5905? In 93609?
(i. Read as one number 800 + 90 + 9 ; 5300 + 50 + 7.
7. If a cipher in annexed to 8, how many will it then repre-
sent ? If 3 ciphers ? If 4 ciphers?
8. Change 5 to five thousand ; to five hundred thousand.
NOTATION AND NUMERATION.
23
BEVIEW AND TEST EXERCISE.
27. 1. How many tens in oO? In 80? In 70 ? In 90?
2. Fiow many tens in 35 and liow many left? In 48? In 63?
In (19? In 97? In 84? In 73?
3. How many tens in 100? In 300 ? In 500 ? In 800?
4. How many tens in 140? In 250? In 870? In 560?
5. How many tens in 39G and how many left? In 674? In
594? In 360? In 983? In 999?
0. How many hundreds in 600? In 400? In 900? In 1200?
In 2400? luooOO? In 9900?
7. How many lumdreds in 436 and how many left ? In 815 ?
In 586? In 1607? In 5406? In 8852?
8. Commence at the right and read each order in 683640992.
9. Analyze into separate orders (26) 73986.
10. How many thousands in 85000 ? In 93000? In 50000?
11. How many thousands in 46825 and how many left ? In
93462? In 289704? In 100602?
Express in figures the following :
12. One tliousand. One thousand one. Two thousand nine.
Eight thousand sixty. Four thousand twenty.
13. Eleven hundred. Twenty-five hundred. Twelve hun-
dred five. Eighty-six hundred sixteen.
14. Ten tons. One hundred tens. Ten tens three. Five
hundred tens fifteen. Eight hundred two tens.
15. Ten thousand. Ten thousand seven. Eighty thousand.
Twenty thousand fifty-three.
1(). Eighty-three thousand sixty. Seventy thousand four
hundred seven. Ninety-seven tnousand fifty.
17. Six million three thousand seventy-one. Seven hundred
eight million fifty thousand nine.
18. Five hundred million 5 thousand eighty-nine.
19. 200 million 19 thousand 5 hundred 6.
20. Seventy million 70 thousand 4 hundred sixty three.
21. Four hundred six million 50 thousand five.
24
;V" OTA TI X A XD X UMEB ATIO N,
2G. 70050050.
27. 400008008.
Read the following numbers :
22. C)0070;J0. 24. 830000604.
23. 20G00040. 25. 40060010.
DEFINITIONS.
28. A Unit is a single thing, or group of single things re-
garded us one ; as, one desk, one foot, one ten, one hundred.
2t). A Nnnibev is a unit, or collection of units ; as, one
boy, three tables, tino, five hundred.
«50. The Unit of a Nil in her \s one of t\iG things num-
bered ; thus, the unit cf seven yards is one yard, of throe men
is one man, of eight is 07ie.
a 1 . F'iyures are characters used to represent numbers.
3ti. Notation is the method of writing numbers by figures
or other characters.
I5J5. Nnnieration is the method of reading numbers
which are expressed by figures or other characters.
RULES.
34. Nmneration. — T. Begin at the right and separate the
number, by inserting commas, into periods of three figures each.
II. Begin at the left and read the hundreds, tens, and ones of
mch period, giving the name of each period, except the last.
35. Notation. — Begin at the left and write the figures ex-
pressing the hundreds, tens, and ones of each period in their
proper order, filling icith ciphers all periods or places where no
significant figures are given.
The Arabic Not at ion f presented in the preceding pnges,
was introduced into Europe by the Arabs, who had obtained it
from the Hindoos. Tlie following is the method which was
used by the Romans.
S
R MA iX NOT ATI N.
^5
ROMAN NOTATION.
J?6. The Roman Notation employs, in expressing numbers,
seven letters and a dasli.
Letters, I, V, X, L,
M.
C, D,
T7- » f\ T-- rn 1-1- r* One Five One
Values, One, Five, Te., lufty, ^^^^^^^ hundred, thousand.
'*fcf
1
i
Laivs of Moman Notation.
Any number can be written by using the above seven letters
and a dash, in accordance with the following laws :
1." Repeating a letter repeats its value.
Thus, I denotes one ; II, two ; III, three ; X, ten ; XX, two
tens, or twenty.
2. When a letter is placed next to the left of one of greater
value, the difference of their valiies is t?ie number e^iypressed.
TliiiH, IV donoteo 5 less 1, or 4; IX denotes 10 less 1, or 9 ;
XL denotes 50 less 10, or 40.
8. When a letter is placed nectt to the right of one of greater
value, the sum (f their values is the number expressed.
Tims, VI denotes the sum of 5 and 1, or 6; XI denotes the
sum of 10 and 1, or 11 ; LX denotes the sum of 50 and 10, or GO.
4. A dash j)l"ccd oiwr a lifer, or letters, multiplies the value
expressed by one thousand.
Thus, X denotes ten thousand, IV denotes four thousand,
L fifty thousand, XVIII eighteen thousand.
Exi>rcss in Roman Notation the following :
1. Three.
2. Seven.
3. Four.
4. Nine.
T). Twelve.
0. Seventeen.
7. Nineteen.
8. Fift(>on.
9. Twenty.
10. Fourteen.
II. Thirty-three.
13. Forty.
1.'?. Forty-four.
14. Sixty.
15. Fifty-nine.
26 ROMAN NOTATION.
EXERCISES IN ROMAN NOTATION-
87. Read each of the following numbers :
1.
X. 8.
L. ir>. CII.
32. DC.
^.
XI. 9.
VL. 10. ex.
23. CD.
o
O.
IV. 10.
XL. 17. XC.
34. Die.
4.
XIX. 11.
LX. 18. CXX.
25. DCV.
5.
XIV. 13.
LIX. 19. CL.
26. DC(^XV
0.
IX. 13.
LVIII. 20. CIL.
37. M.
7.
XXIV. 14.
LXXXIV. 31. CIC.
28. CM.
A\
'rite in Ronuiu Notation the following numbers :
1.
Twentv-four.
7. One hundred nine.
13. 10001
2.
Seventy-nine.
8. Five hundred four.
14. 3005.
3.
Eighty-three.
9. Three hundred seventy
15. 5009.
4.
Ninety-four.
10. Seven hundred six.
10. 2084,
5.
Fifty-seven.
11. Two hundred eighty.
17. 1877.
6.
Thirty-nine.
13. Four hundred two.
18. 1854.
Read each of the following numbers
1.
X.
6.
L.
11.
MDCCCLXXVII.
16.
D.
2.
V.
7.
XX.
12.
MMDCLXIX.
17.
XV.
3.
XI.
8.
LX.
13.
MCCLIX.
18.
TS.X
4.
vi.
9.
C.
14.
MMMDLVIII.
It).
XXV
5.
IV.
10.
OX.
15.
MCDXVII.
20.
XD.
Express in Roman Notation tlie following :
1. Ten thousand.
2. Four thousand.
3. Six thousand.
4. Two thousand.
5. Nine thousand.
6. Eight thousand five hundiod.
7. Five tliousand two hundred.
8. Three thousand six hundred.
9. Ten thousand one hundred.
10. One thousand fiftv-rine.
DN.
DC.
CD.
Die.
DCV.
DCCXV
M.
CM.
3. 10001.
14. 3005.
5. 5009.
[G. 2084,
.7. 1877.
8. 1854.
I. D.
\ XV.
I. XXX.
'. XXV.
». XD.
mdred.
1(1 rod.
lulrod.
lied.
ADDITION.
OEAL AND SLATE EXERCISES.
38. 1. Add 3 pears aud 5 pears.
Three pears and five pears are added thus :
Tilings are added by putting them together.
2. Three pears and five pears are how many ? 3 and 5 are
how many ?
, 3. Add 7 blocks and 3 blocks, thus :
7 btocka
+ 3 blocks =
lO blocks*
4. Seven blocks and 3 blocks are how many ? 7 and 3 are
how many ?
5. Finding how many two or more groups of objects will
make when put together is called Addition f and the number
found is called the SifiH.
Find tlio sum :
6. Of 4 caps and 3 caps.
7. Of 3 pencils and 3 pencils.
8. Of 2 desks and 4 desks,
9. Of 5 ])ens and 2 ])ens.
10. Of 4 chairs aud 5 chairs.
11, Of 3 tables and G tables,
12, Of 5 books and 4 books,
13, Of 2 boys aud boys,
14, Of girls and 4 girls.
15, Of 7 blocks and 3 blocks.
i^
\
1
28
AD D IT 10 X,
SLATE EXERCISES.
30. 1. Find, by making- marks ou your slate, the sum of
7 marks and 6 marks ; thus,
7 marlk's
tnarks
10 tnarlis nud 3 marks.
1 tell and 3 =
Find in this wav tlie pum :
2. Of markf and 5 marks,
8. Of 8 marks and 9 marks.
4. Of 7 marks and 4 marks.
Thirteen,
5. Of 9 marks and 3 marks.
C. Of 4 marks and 9 marks.
7. Of 9 marks and 9 marks.
Copy on your slate and find, by using objects, the sum for
each example in the following exercises :
^ + .? = ? 8+l = 'i 5+l='i
7-ri=? 0+1 = ^ G+l-^'r
6+3 = ?
2+3 = ?
2+3 = ?
J + c? = ?
2+J^ = ?
3+4 = ?
8+2
3+2
9
9
r)+2
9+2
/T
■:•>
9 + 3
9
9
/v
7+3
i+3
r>
3+.^ =
6+4 =
9
9
7+4
9+4
9
9
t
9
«
9
9
9
9+1 = ?
4+1=?
7+2 = ?
6+2 = ?
6+3 =
8+3 =
5+4
4+4
9
9
9
40.
how mar
SOLUTK
which is 8
1. A 1
cows has
3. In i
many tr(
4. 'l b(
much di
5. In J
pupils ai
0. At
ADDITIOX,
29
lie sum of
d 3 marks.
?ll.
id 3 marks,
id 9 marks,
id 9 marks.
le sum for
9
9
+ .? = ?
3
'+.? = ?
ORAL EXERCISES.
40. 1. Mary had 5 apples and lier brother gave her 3 more ;
how many apples had she then ?
SoLUTiox.— She had as many apples as the sum of 5 apples aucl 3 apples,
which is 8 apples.
2. A man has G white cows and 3 black ones ; how many
cows has he in all ?
3. In a o-arden there are 7 peach trees and 3 apple trees ; how^
many trce3 are there of both kinds ?
4. I bought a coat for 8 dollars and a hat for 5 dollars ; how
much did I give for both ?
5. In a certain class there are 4 hoys and 5 girls ; how many
pupils are there in the class ?
G. A boy rode 6 miles in the cars and 3 miles in a carriage ;
how many miles did he travel?
7. There were 7 mugs upon a shelf and Ada placed three
more there ; how many mugs were then on the shelf?
8. Six birds wore l^pon a tree, and four more alighted ; how
many birds on the tree ?
0. Edward caught four trout in one brook, two in another,
and three in anotlier ; how many trout had ho in all ?
10. A turkey weighed G pounds, but afterwards gained two
pounds ; what did tlu) turkey then weigh ?
11. If a house has 7 windows on one side, and four on
anot)ier, how many windows has it in all ?
13. Five caps are hanging in a row, and soon four more are
hung up ; how many caps in all ?
115. A poor man earned five dollars by sawing wood, one dol-
lar by carrying coal, and four dollars by planting a garden ;
how many dollars did he earn in all ?
14. A flag has 4 red stripes and 5 white stripes ; how many
stripes has it in all?
15. Frank had 9 cents and his sister Jessie gave him 3 more ;
how many did he then have ?
80
ADDITION.
SLATE EXERCISES.
41. Copy on your slate and find, by using objects, the sum
for each example in the following exercises :
5+6 ?
2+4 ?
2+5--
7+4 =
= 9
•
-9
«
6+8-?
4+5 = ?
5+5 ?
8+4-?
8+3-'i
6+3-1
6+2 =
6+7 =
= 9
•
= 9
•
3
9+5 = ?
4+6 = ?
5+6 ?
7+6 = ?
7+3 = '>
5+6 = 1
5+7 =
8+7 =
•
= 9
•
3
7+7-^?
7+2 = ?
9+7 ?
6+7 = ?
3+8-?
6+8-1
5+8 =
4+8 =
= 9
•
= 9
•
4
9+7-?
9+S-?
4+8-?
8+8-?
4+9 ?
7+9-?
3+0 =
4+9 =
= 9
= 9
•
5
6+9"?
8+9 ?
5+9 ?
0+9 ?
6
7+7 = ? c9+£^ = ? 6N-^-? 5+5 = ?
9+5 = '} 5+G = ? 9+7 = ? S+7 = ?
5
3
9
2
6
3
1
8
8
4
7
4
6
5
5
ADDITION,
31
}; the Slim
+ 5--
+^-
+6
+ 6
+ 7
+ 7
9
9
9
ADDITION TABLES.
42. Practice on each of the following tables separately.
Thus, jpy the numbers on your slate in the order given, find
the .sums and write tlieni under the numbers, then erase them
and write them again and again from memory.
Tahte
"/
Twos.
5
o
O
4
8
1
3
2
3
2
2
9
G
2
7
9
2
2
8
2
2
Taftfe of Threes,
5
6
2
3
4
3
3
3
3
3
1
7
G
8
9
3
3
3
3
Ta6/e
of
I'ours,
3
8
3
6
2
4
4
4
4
4
7
9
3
9
1
4
4
4
4
4
Table
«/
rives.
G
3
1
8
5
5
5
5
5
5
7
4
3
8
9
5
5
5
5
5
Table
o/^
i'tjces.
5
1
8
3
6
6
6
6
6
6
3
4
8
9
4
6
6
6
6
G
Table of Sevens.
3 4 7 9 1
7 7 7 7 7
5
9 8 2
6
7
7 7 7
Table of Eights.
7
8
5 3 4
7
8
8 8 8
8
9
8
3 1
8 8
6
8
Table of Xiuos.
9
8
4
6
5
8
3
9
9
9
9
9
1
7
6
5
9
9
9
9
9
9
f
33 ADDITJOX,
OBAL EXEBCISES.
43. 1. John had one cluster of four grapes, another of
seven, and another of three ; how many grapes had he ?
Solution.— lie had as mauy grapes as the sum of 4 grapes, 7 grapes, aud
3 grapes, which is 14 grapes.
2. Norman had four red tops, two blue tops, and five white
tops ; how mauy tops had he ?
3. My house contains 2 parlors, 1 sitting room, 1 dining
room, 1 kitchen, 4 chambers, 5 bedrooms, and an attic ; how
many rooms iu all does it contain ?
4. A man takes two daily papers, four weekly papers, and
three monthly papers ; how many papers does he take in all ?
5. My garden has six rows of beans, four rows of peas, and
three rows of turnips ; bow many rows does it contain?
6. A farmer has a spade worth three dollars, a mallet worth
one dollar, a hatchet worth one dollar, and a gun worth five
dollais; how many dollars are they all worth?
7. 1 have four gold rings, eight brass rings, and two silver
rings ; how many rings have I ?
8. Oliver has 4 slate pencils, and Kate has G lead pencils and
5 slate pencils ; how many pencils have both ?
0. A farmer has 9 cows and 8 oxen ; how many cattle has he
mallV
10. Harvey paid 10 cents for a slate, 2 cents for a pencil, and
6 cents for a sponge ; how much did they all cost ?
11. A man bought a saddle for dollars, a bridle for 3 dol-
lars, and a whip for 1 dollar ; how much did they all cost ?
13. What is the sum of 5 + 8 + 4 + 3?
13. There are 3 pears on one i)]ate, 5 on another, and 9 on
another ; how many pears on the three plates ?
14. Warren's mother gave him 15 cents, he earned 9 cents,
and found 7 cents ; how many cents did he then have ?
15. A lady has 7 Iron spoons and 3 more silver spoons than
iron ones ; how many spoons has she in all ?
5.
:f
17.
18.
•f2ai
19.
additic
20.
800+:
21.
70+4(
i
ADDITION,
i33
notlier of
grapes, and
five white
1 dining
tittic ; liow
)apers, and
ko iu all ?
f peas, and
tin '.'
allet worth
worth five
I two silver
pencils and
lattle has he
a pencil, and
lie for 8 dol-
all cost ?
ler, and 9 on
rued 9 cents,
lave ?
f spoons than
OBAI. EXEBCISBS.
44. 1. How many ones are there in 11 and 4 ? in 7 and 8 ?
10 and 5? in 13 and 7? •
3. How many ones are there in 27 and 6? in 36 and 6 ? in 55
d 7? in 66 and 7? in 93 and 8?
8. How many are 3 and 1 ? 11 and 3? 34 and 6 ? 33 and 3?
and 3? 81 and 5?
4. How many are 3 and 7? 13 and 5? 33 and 6? 74and3?
106 and 4? 643 and 4? 553 and 4?
5. How many are 8 and 7 ? 16and7? 35and7? 75and7?
465 and 7? 18 and 8? 36 and 8? 346 and 8?
6. How many are 9 and 3? 49 and 3? 59 and 3? 9and6t
70 and 6? 339 and 6? 469 and 6?
7. How many are 8 and 7? 38 and 7? 36 and 7? 9 and 8?
e»and8? 859 and 8?
8. Add by 3's from 1 to 33 ; thus, 1, 3, 5, 7, 9, 11.
Add
0. By 3's from 3 to 50.
10. By 3's from 4 to 74.
11. By 3'8 from 3 to 78.
13. By 5's from 3 to 84.
13. By 5'8 &om 6 to 96.
14. By 7's from 3 to 87.
15. By 6's from 5 to OS.
16. By 7'8 from 4 to 89.
17. Add by O's from 3 to 105 ; from 5 to 87 ; from 7 to 119.
18. Add from 1 to 76 by repeating the successive additions
•f 3 and 3 ; thus, 1, 3, 6, 8, 11, 13, etc.
19. Begin with 4 and add to 105 by repeating the successive
additions of 3, 8. and 4.
20. How many are 30 + 5? 60-f7? 300+40+6? 700 + 90+3?
800+30+4? 600+50+7?
31. How many are 30 + 40? 50 + 60? 70 + 40+6? 80+30?
70+40? 90+80? 80+60+8? I
34
ADDITION.
SLATE EXERCISES.
45. Copy on your slate and find the sum for each example
ID the folluwiui? exercises :
1
f
% ■
AM '
ii i
1^1
Ifl i
300+50+G •? 700-
^60+4 ?
600+40+9-? 900-
^50+6 = ?
500+80+1 ? 900-
^70+5-?
2
503+50 '? 308+50 ?
504+ 60-?
66+iOO ? 88+600 ?
13+800-?
80+ 504=? 80+509-?
80+209=?
3
33+5 ? 47+8-?
55+9=?
63+5-? 57+8-?
75+9 = ?
83+5 ? 67+8-?
85+9 ?
73+5 ? 77+8-?
65+9=?
4
37+6+6+6=9 . 42+
■5+5+5 ?
59+4+4+4-? 26+8+8+8=?
25+9+9+9 = ? 34+
.f+Y+7 = 9
57+5+5+5 ? 65+3+3+3=?
i
%
shown
table,
copy a
ADDITION.
ARITHMETICAL TABLE No. 2.
ch example
■800=-^
+9 = 1
+ 9 = ?
+5> = ?
+5
'+7
1+3
*
= 9
= 9
1.
A.
B.
c.
D.
E.
F,
G.
H.|
i\/ / ,-1 _ ^ , /' 1
1 > >
/
' 'y
7
4^ !
J2^.
3.
2
.i^
.//
U.
6
7'
4.
1
1
)
iV
9
/
') J
S'
6
5,
6
-- — '
/
/
- A/
■> /
1. )
9
y
_2
«•
•z.
7
}
:')
/
/
y 9
/
/
1
a
9.
10*
9
/
s-
6
J 9
CJ^
4 1
46. Copy neatly on your slate examples from this table, aa
shown on next page. Make the figures as they are in the
table. Find the sum of each example, then erase them, and
copy and find the sum again and again.
'1?§-
36 ADDITION.
SLATE EXEBCISE TABLE NO. 2.
Columns of Three Figures,
4r7. 1. Commence with column A, opposite J, and copy
three figures for the first example ; then opposite "4^ and copy
three more for the second example ; then opposite 5, and copy
tliree more for the third example. Continue in this way to the
bottom of the column and you will have on your slate :
1
"' i
I I
(1)
(2)
(3)
(4)
(5)
(0)
(7)
(8)
o
5
2
4
6
8
4-
5
6
2
4-
6
3
4
5
8
2
I
6
3
A
5
8
9
2. Copy examples from each of the other columns in the same
manner and find the sum for each example.
Columns of Four or Moi'e Fiyures,
48. 1. Commence with column .1, opposite i, and copy
the required number of figures for the first example. Copy the
second, third, etc., examples in the same manner as those with
three figures.
2. Copy in this way from each column in the table, examples
with four figures in a column ; then five figures ; six figures ;
seven figures ; eight figures.
Note.— The teacher should illaptratc on the blackboard, tojonngpapilt,
the method of copying examples from this and following tables.
The ])upU Bhonid bo required to practice on examples with three and
four numbcff; until he can give the sums almost at sight of the flgurei ;
longer columnB can then be given.
Definite work from thie* and 9nbfteqnent tables should be asHigned to the
popil to prepare, on hie slate or on paper, at his seat and at home.
ADDITION,
87
\ 2.
If and copy
2f and copy
3f and copy
is way to the
ilate :
5
8
(8)
5
8
9
B in the same
SLATE AND BOABD EXERCISES.
49. Find the sum of Explanation.-I. The sum of 7, 9, and
8 ie found by forming groups of ten. Thua,
the 7 and make 1 ten uud 6, and thiB 6 and
8 make 1 ten and 4. Hence, 7, 9, and 8
make 2 tens and 4.
2. The Bum of 7, 9, and 8 is the same
whether these figures represent unita^ tens,
or hundreds, etc. Hence, when their sum
ie found, if they repreeein, units, as in the
first example, the sum is units ; if tliey represent tens, as in the second ex-
ample, the sum is tens ; it hundreds, hundreds, etc.
50. Analyze on your slate each of the following sets of
numbers, thus :
(1)
(3)
(3)
8
80
800
9
90
900
7
70
700
24
240
2400
8SS9 =-8000+500+30+9.
3080 = 3000+ 80.
7402 = 7000+4.00+ 2.
res.
i, and copy
Copy the
18 those with
(1)
6740
8042
4305
(2)
5578
6909
7025
(3)
3063
6704
5380
(4)
68953
70507
38005
(5)
70406
40069
80340
(6)
37506
93540
60320
6 1 . Find the sum in each of the following examples :
)le, examples
six figures ;
o young puplli,
lies.
ith three and
of the figure! ;
assigned to the
lome.
1.
TO + 5.
4. 7200
+ 80 + 4.
7. 90 + 60.
2.
800 + 60 + 3.
5. 6003
+ 400.
a 700 + 600.
3.
600 + 80 + 9.
6. 70 + 50.
9. 5000 + 9000.
(10)
(11)
(12)
(18)
(14) (15)
80
400
9000
40000
9000 4005
60
700
5000
80000
6000 7008
20
800
7000
30000
8000 2006
50
600
8000
90000
6000 8009
38
ADDITION-,
I \
SLATE AND BOARD EXERCISES.
52. 1. Find the sum of 245, 508, ;05, and 25i).
Explanation.— 1. Wo write the numbers so that
figures reprcs-eutiug the tauiu ortlcr of units stuud iu
the t-ame column.
2. We add the units' column, as in (4:9), naming
only the successive sums, thus, (», 14, ri, 2r. We write
the 7 unitx under the units' column.
3. We add the 2 teiL-^oi the uuits' column to the tens'
column, adding the tens' column by narainp, a- before the successive sums;
thus, 2, 7, 10, 22. 2G tens, or 2 hundred and 6 tens. We write the 6 (ens under
the tens' column.
4, We add the 2 hundred to the hundred's column, and proceed as with
the units and tens. We write the 18 hundred under the hundred'sjfolumu.
245
508
795
259
1807
r
**J5. Copy on vour slate and add and explain, as above, each
of the following examples :
(3)
(3)
(4)
i'^)
(6)
(7) .
50:}
00
370
2075
48060
52708
00
660
8080
59083
3501
970
759
63
0708
702
983
5839
93
605
635
7538
70839
90780
58
457
78
3789
5909
038
543
43d
6497
25394
30348
45570
(8)
(9)
(10)
(11)
(13)
(13)
?M
209
8437
5674
805
8500O
8970
9500
589
8009
93
3905
8008
8877
03
730(50
7158
40038
57
634
437
7950
8390(5
9(5077
0:53
3735
6895
30509
506
4940
59V)8
476
703
4877
2398
82596
755
65
4325
7 -37
7433
8579
979
420
512
44553
740
31164
vM:
ADD IT [0 lY.
39
ES.
here so that
liis stand iu
1:9), naming
t. \Vc write
1 to the teas'
L'yt*ive sums ;
3 6 (ens under
ceed as with
ed'sjfolumu.
ibovc, each
(7) .
52708
5830
96780
038
45570
(13)
85000
3905
40038
90077
4940
82590
8579
31104
ARITHMETICAL TABLE No. 3.
''ft
1.
^
JB»
€?•
s^«
£;•
r.
^
A
/
• /
'J
J
/
■J cV
■ /
7
6
7
\
1
1
7\
6 \
S
/
^
8.
4.
;«•
6.
1
/.
^■^^
d~'
O
/
K.
^
' 1
/'/ /
.f
. )
r
/
8.
o
•J
/
9
rO
9.
■ /
/■ /^'
9
/I./
/
A'
//
10.
1
/y
.■/ d'
(•
9
s
54. Copy examples as shown on next page from this table
and from Table No. 2, on page 35. Continue this practice until
you can add rapidly and accurately.
Answers to examples from the Tables are t,Mvon at the end of the book.
r-
40 ADDITION.
1
EXAMPLES FROM TABLES NO. 2 AND
3.
1
Exercises tvith Ntunbers of Two Figures.
1
5
■l J
(8)
(9)
30
54
54
26
65. 1. CJopy examples with two numbers from Table No. %
page -35, then from Table No. 3, page 39.
Use columns A and B. Commence opposite 1, and take
two numbers for the first example, then opposite 2, and take
two more numbers for another example, and so on to the
bottom of the table. The examples taken in this way from
columns A and B, Table No. 8, are as follows :
(1) (2) (3) (4) (5) (6) (7)
65 53 20 67 42 36 65
63206742366530__
2. Copy in this manner examples from columns b and c ;
c and D ; d and E ; £ and f ; f and o ; a and n.
3. Copy in the same way examples of three numbers ; four
numbers ; five numbers, etc. Find the sum for each example.
Exercises with Ntunbers of Three or More Figures,
66. 1. For lumbers of three figures use any three columns
that follow each other, as abc, def.
2. For numbers of four places use any four columns that fol-
low each other, as BCDE, BFOH.
3. Commence with examples of three numbers, then take
four, five, aud so on up to eight numbers.
4. Copy the numbers from the table in the same manner as
those of two figures. Thus, the examples with three numbers
from columns abc, Table No. 3, are as follows :
(1)
(3)
(3)
(4)
(5)
(6)
(7)
(8)
658
537
205
673
428
360
657
304
537
205
673
428
360
657
304
540
205
673
428
360
657
304*
540
265
ADDITION,
41
AND 3.
\ires,
able No. 2,
, and take
f and take
on to the
way from
(0)
64
26
B and c ;
bere; four
L example.
Figures,
e columns
s that fol-
then take
manner as
3 numbers
m
WBITTEN EXERCISES.
57. 1. Howmanypoundsinthreeloadsof hay, each weigh-
ing 2325 pounds? In five loads, each weighing 1983 pounds ?
2. How many acres in four farms, each containing 198
acres?
3. A fanner sold 293 bushels of wheat to one man, 185 to
another, and 86 to another. How many bushels did he sell?
4. Henry Scott sold a span of horses for $275, a carriage for
$395, and harness for $65. How much did he receive ?
5. A farmer has 95 sheep in one field, 187 in another, and 264
in another. How many sheep has he in all 1
6. A merchant sold 175 yards of cotton on Monday, 386 yards
on Tuesday, 139 yards on Wednesday, 98 yards on Thursday,
216 on Friday, and 397 on Saturday. How many yards did he
selliuall?
7. A man sold a house for $8894, a horse and carriage for
$586, and seven tons of hay for $95. How much did he receive
for the whole?
8. Peter Eaton paid for a tub of butter $24, for eight cords
of wood $49, and four barrels of flour $36. How much did he
pay in all ?
9. How many pounds of butter in five tubs, each weighing
85 pounds ? In three tubs, each weighing 78 pounds ?
10. Wliat is the sum of $472, $843, $366, and $95? Of
$307, )^283, $94, $569, and $85 ? Of $836, $1372, $995, and
$48?
11. How many bushels in three loads of wheat, each contain-
ing 83 bushels ? In seven loads, each containing 69 bushels ?
12. A grocer bought three cheeses, each weighing 54 pounds,
and four, each weighing 69 pounds. How many pounds did he
buy in ail ?
13. Find the sum of $356, $257, $423, and $87. Of $936,
$504, $240, $50, and $203. Of $504, $641, $237, $2140, and
$731.
i
I
42
ADDITlOy
1 ;
CiLNADIAN MONEY.
58. 1. The Sign | stands for the word dollars. Thus,
|9 is read nine dollars.
2. The letters c^ stand for cents* Thus, 24 ct. ia read
twenty-four cefUs.
3. ^^^^en dollars and cents are both given, the cents are
expressed by writing them after the dollars with a period
between them. Thus, $5 and 37 ct. are written $5.37.
4. When the number of centa is lesB than 10, a cipher must
occupy the first place at the right of the period. Thus, $15
and 9 ct. are written |15.09.
5. In arranging numbers for addition, dollars must be
placed under dollars and cents under cents, in such order that
the periods in the numbers stand in the aame column ; thus,
(1)
(2)
^3)
142.69
$840.36
$9v,..D5
8.25
93.08
60.32
346.54
307 03
300.04
Add as If there were do periode in the numbere, and in the sum place
a period between the second and third fi^Tire from the right. The figures
•n the left of the period express dollars, those on the right cents.
59. Read, arrange and add the following :
1. $6.36 ^ $99.43 + $507 + $70.50.
2. $364.03 + $30.52 + $709 80.
3. $3.00 _ $805.30 4- $34.09 + $600.04.
4 $490.08 + $5.25 + $46 -f $208.07.
Express the following in figures and with the proper signs.
6. Thirteen dollars and forty-eight cents.
6. Two himdred three dollars and seventy cents.
i. Four dollars and seven cents.
8. Eight hundred dollars and forty cents.
m
ADDITION.
43
SLATE EXERCISES.
00. Copy and find the sum of each of the following :
(1)
(2) ,
(3)
(4)
{^)
$30T.0-2
$S00.G0
$583.
$37.06
$573.
84.09
905.07
609.00
802.40
65.32
500.00
32.06
28
75.
802.05
400.75
708.39
436.90
90.03
850.73
239.08
400.05
800.07
342.79
90.50
(6)
(<)
(B)
(9)
(10)
$900.05
$26.80
1854.05
1389.
$101.01
57.
13.14
60.2:^.
57.65
79.
406.13
590.
100.10
105.10
255.39
73.00
268.39
530.05
780.23
893.
5.59
85.
8.5.70
96.0*5
500.
260.
703.04
705.04
40S.
46.90
Read, arrange on your slate in columns, and find the sum :
11. Of !i;8.25, $27.48. $13.06, ;^407.39, and $80.05.
12. Of $273.06. $75, $306.02, $.500, and SS30.73.
13. Of .t.506. $39, $G<>2.15, $290.87, and $730.42.
Express the following in figures and with the proper sigps :
14. Seven dollars and nine cents. Eighty-four dollars and
six cent??.
15. Two hundrt'd ten dollars ar ' three cents.
16. One dollar and nine cents. Five dollars and ninety cents.
17. Sir hundred thirty dollars and eight cents.
18. Use the sign $ and express Al' cents ; 79 cents ; 95 cents ;
8 cents ; 4 cents ; 1 cent.
19. 79 cents ; 50 cents ; 7 cents ; 6 cents ; 10 cents ; 9 cents..
20. One hundred one dollars and one cent.
21. One thousand one dollars and one cent.
\
u
ADDITION.
WBITTEN EXERCISES.
<$1. 1. Bought twelve pounds of sugar for $1.68, two
pounds of tea for $1.90, and eight pounds of butter for $2.40.
"What did the whole cost ? ->
2. Paid $1.15 for cheese, $4.93 for coflee, $3.85 for flour, and
$7.09 for potatoes. How much did I pay in all ?
3. Sold three barrels of apples for $12.75, fifteen bushels
turnips for $3.75, and four cabbages for 60 cents. How much
-did I get for the whole ?
4. Paid one man $38.02, another $307.45. How much did I
pay in all ?
5. Henry bought a gun for $17.70, a pair of skates for $3.45,
and a hunter's knife for $2.45. How much did the whole cost ?
6. Bought a coat for $22.85, and a hat for $5.54. How much
did I pay for both ?
7. A lady paid for goods in one store $14.86, in another
■$37.79, and in another $6.05. How much did she pay in all?
8. A grocer sold to one man $84.63 of groceries, to another
$16.20, and to another $9.07. How much did he sell in all ?
9. Bought three books for $5.73, six quires of paper for
90 cents and a gold pen for $6.85. How much did they all
cost?
10. Ada paid for a dress $23.34, a hat $5.87, a shawl $17.64,
and ll pair of gloves $1.95. How much did she pay in all ?
11. James sold 2 barrels of apples for $6.95, a bushel of
pears for $3.45, and 4 baskets of peaches for $4.25. How much
did lie get for the whole ?
12. George bought 10 cords of wood for $43.50, a tub of
butter for $20.75, and 17 bushels of potatoes for $8.50. What
was the cost of the whole ?
13. A farmer received in one year $806.95 for wheat, $256.38
for corn, and $95.86 for oats. How much did he receive in all 1
14. Paid for wheat $736.25, for oats $121.10. How much did
I pay f o" all ?
i,^
ADDITION.
45
$1.68, two
3r for $2.40.
)r flour, and
•en bushels
How much
much did I
es for $3.45,
whole cost ?
How much
in another
pay in all ?
B, to another
lellinall?
)f paper for
did they all
lla^vl $17.64,
ly in all ?
a bushel of
How much
,50, a tub of
18.50. What
'heat, $256.38
eceive in all ?
[ow much did
WHI'x'TEN EXERCISES.
Gli. 1. Thomas Austin bought 3 horses for $527, cows for
$181, and 12 sheep for $63.85 ; what did he pay for all?
2. A man gave to his wife $1145, to his daughter Jano
$205.60, to his daughter Agnes the same amount, and to liis
son $305.58 ; how much money did he give to all ?
3. lu a certain city there are 5 schools ; in the nrst are 789
pupils, in the second and third, each 935, in the 2o;'rth 1100,
and in the fifth 886 ; how many pupils in the five schools?
4. Elmer earned $80.29, his father gave him $47.13, then he
earned $62.08 more ; how much money had he ?
5. If I deposit $207.18 in a bank on Monday, $466.97 on
Tuesday, $136.08 on Wednesday, $37.20 on Thursday, $200.28
on Friday, and $1060 on Saturday, how many dollars do I
deposit in the six days ?
6. A man buys a village lot for $2652, upon which he builds
a house which cost him $1907.75, he pays $20.32 for fencing,
$49.09 for having his lot graded, and $35.48 for laying a side*
walk ; how much money will pay for all ?
7. James Thompson owed one man 26 dollars and 4 cents, he
owe^ another man 475 dollars and 90 cents, another $1406 and
8 cents ; what is the amount of his indebtedness ?
8. John Bedford went to the grocery and bought the follow-
ing items : 2 barrels of fldur for $13.75, 13 pounds of butter for
3 dollars and 8 cents, 4 g^lons of syrup for $4.60, 25 pounds
of meal for $3 and 7 cents, and 13 gallons of vinegar for
6 dollars and 30 cents ; what did he pay for all ?
9. A nurseryman sold 185 peach trees, 3146 apple trees, 230
plum trees, 2024 cherry trees, 876 pear trees, 256 quince trees,
and has still remaining 4892 trees ; how many trees did he
have before he sold any ?
10. William Henderson paid for groceries for the week $7.89,
for meat $2.37, for other articles $2.05, and for a suit of clothes
$28.75 ; how much did he pay in all ?
*
i
i
I
i
It
46
ADDITION.
\ \
DEFINITIONS.
63. Addition is the process of uniting two or more num-
bers into one number.
64. Addends are the numbers added.
65. The Sum or A^nount is the number found by addi-
tion.
66. The Process of Addition, when the sum is greater
than ten, consists in forming units of the same order into
groups of ten, so as to express their amount in terms of a
higher order.
67. The Sign of Addition is + , and is read plus. When
placed between numbers, thus, 8 + 3 + 6 + 2 + 9, it means that
tliey are to be added.
68. The Sign of Equality is =, and is read equal; thus,
9 + 4 = 13 is read nine plus four equal thirteen.
RULE.
69. /. Write the numbers to he added in such a manner thM
figures representing the same oi'der of units stand in the same
column.
II. Add each column separately, commencing with the units.
Ill When the sum, of any column is expressed by two or more
figures, place the right-hand figure binder the column, and add
the number expressed by the remaining figures to the next
column.
IV. Write under the last column its entire sum.
Proof. — Add the numbers by commencing at the top of the
columns. If the results agree, the work is probably correct.
m
lore num-
SUBTRACTION
OBAL EXEBCISES.
70. 1. If 3 pears be taken from 8 pears, how many will t-e
left?
3 pears taken from
8 pears leaves
3. Things are Subtracted by taking them away.
3. 9 books less 5 books are how many ? Less 2 books ?
4. Henry has 8 pears and James has 5 ; how many more
pears has Henry than James 1
8 pears
5 pears
compared toith
3 pears
shows that Henry has
more than James.
5. How many are 8 pears greater than 5 pears ?
6. Comparing two numbers, to find how many the one num-
ber is greater than the other, is called Subtraction*
The greater of the two numbers compared is called the
Miimendf the lesser the Subtrahend,
11. The number which indicates how many the minuend is
greater than the subtrahend is called the Difference,
8. The Sign (— ) stands for the word less; thus, 7—3 = 4
is read, seven less three equal four.
I
I) <
I
ill
'f
I
48 SUBTRACTION.
SLATE EXEBCISES.
71* Copy the following exercises and practice on each sepa*
rately. Thus, find the differences and write them under the
numbers, then erase them and vrrite them again and again from
memory.
S9S68479
11111111
4. A
•8
wards
3
5
6
7
9
10
4
8
5. R
i.
I
i
I
■3
2
i.
i
ence ii
G.
ilOW 111
7. h
5
4
7
9
10
8
11
6 1
more r
I
§.
I
i.
3
3
s
i
8. L
more t
5
7
9
11
•4
10
6
8
IS
9. A
manv :
10.
I
I
I
4
4
■5
d
4
4
more ^
11. '
how 11]
6
9
11
8
13
10
7
14 '
13.
and th
6
5
5
5
5
•6
6
5
5
13. 1
pike, {
14.
12
10
8
13
15
11
14
7
orange
1 (^
6
6
6
6
6
6
6
6
10,
dollan
S r li Tli Ar TION, 49
ORAL EXERCISES.
72. 1. James had six cIovCkS and sold two of them to
George ; how many doves had he then left ?
Solution.— He had aa mauy doves as the dilTei-ence between 6 doves and
a dovt'fl, which is 4 doves.
2. Jolin had a knife with four blades, but he broke three of
tiieiii ; how many blades did the knife then have?
3. Nine girls werci. playing together, but five of them were
called home by their mothers ; how many remained?
4. A wheel had twelve spokes, but three of them were after-
wards broken out ; how many spokes were left ?
5. Robert is 11 years old and Mary is 7 ; what is the differ-
ence in their ages?
C. One cat caught eleven mice and ar )ther caught three ;
how many more mice did one catch than the other ?
7. Ivan has eight rabbits and Hubert has five ; how many
mon^ nibbits has Ivan than Hubert?
8. Laura has 6 dolls and Mabel has only two ; how many
more dolls has Laura than Mabel ?
9. A long ladder has 17 steps and a short one has 8 ; how
many more steps has the long ladder than the short one?
10. A jeweler has 19 gold rings and 5 silver ones ; how many
more gold rings has he than silver ones ?
11. There were 18 apples on a tree, but the wind blew off W;
how many apples were then left ?
13. A farmer set thirteen fence-posts ; six of them were oak
and the' rest cedar ; how many were cedar?
13. Samuel caught seventeen fish ; three were perch, three
pike, and the rest trout ; how many trout did he catch ?
14. A boy had nine cents and gave five of them for an
orange ; how many cents had he left ?
15. William had 15 dollars and gave away 6; how many
dollars has he left ?
. ' ii
W
1 I
.? . 1
if
F
n
M
I
?
50
SUB TEA OTIO N,
SLATE EXEHCISES.
73. Copy the following exeriises and practice on each sep-
arately, as directed in (71). Continue the practice until you
can give the differences at sight of the numoers.
12
9
8
11
10
IS
u
16
7
7
7
7
7
7
7
7
13
IS
11
9
8
10
16
u
17
8
8
8
8
8
8
8
8
10
13
11
-<- <..■'
3
17
14
16
12
9
9
9
9
S
9
9
9
8 12
3 4
6
6
17
8
4
13
2
12
8
18
3
11
9
•
9 16
7 6
7
5
12
8
s
18
7
IS
9
18.
9
12
4
18 19
9 3
27
4
35
2
—
4!)
5
28
3
2S
2
S9
6
SUBTRACTION,
51
OBAL EXEBCISES.
74. 1. How many are 8 less 6 ? 11 less 6 ? 14 less 6 ?
2. How many are 16 less 7 ? 13 less 7 ? 9 less 7 ? 15 less 7 ?
lCless7? 14 less 7? 39 less 7?
3. How many will remain if 8 be taken from 8 ? From 10 ?
From 14 ? From 17 ? From 12 ? From 16 ? From 29 ?
4. How many are 11 less 9 ? 17 less 9 ? 13 less 9 ? 19 less 9 ?
12 less 9 ? 18 less 9 ?
5. How many are 13-8? 17-9? 26-5? 13-5?
15-7? 24-3? ^9-4? 86-3? 99-9?
6. If 7 tens be taken from 9 tens, how many tens will remain?
8 tens less 3 tens are how many ? 80 — 20 = how many ?
7. Express in figures 5 ter^; 8 tens; 6 tens; 12 tern;
15 tens ; 9 tens ; 18 tens ; 26 tens; 57 tens ; 16 tens.
8. Express 9 tens and 5 tens each in figures. 9 tens less 5 tens
are how many ? 90 less 60 are how many ?
9. Eighty trees less 50 trees are how many trees?
10. Express in figures 7 hundred ; 4 Tiundred ; 12 hundrei,;
\% hundred; \% hundred ; 2^ hundred; 1 A hundred; \^ hun-
dred.
11. Express 9 hundred and 3 hundred each in figures.
8 hundred less 3 hundred are how many ?
12. Nine hundred less one hundred are how many ?
13. Thirteen tens less seven tens are how many? 130 less 80
are how many? 120 lees 90 are how many ?
14. Fifteen hundred less eight hundred are how many?
1500 less 800 are how many ? 1400 - 600 = how many ?
15. A farmer had 9 hundred bushels of wheat and sold
hundred ; how many bushels had he left V 900 — 000 =
how many ?
1(5. Express in figures thousand ; 8 thousand ; 19 thousand.
17. Seven thousand less five thousand are how many ? 7000
less 5000 are how many ? 6000 — 2000 = how many ?
= 1 i!
52
S UBTRA CTION,
SLATE EXERCISES.
75. Copy on your slate and perform tlie sut>tTactio& Id eacli
of the following exercises, thus :
7
70
700
7000
500
5000
4
40
400
4000
300
3000
8
30
300
3000
200
2000
Observe, that when 4 is takon frow 7, the reniainder Is 3 ;
hence 4 nnits taken from 7 units the remairaor must be 3 units,
4 tens or 40 taken from 7 tens or 70 the remainder must be 3
tens or 30, and so on with hundred, thousands, and so forth.
60
800
8000
- » '
60
600
6000
80
300
3000
- 3 .
20
200
2000
900
9000
120
110
180
150
500
5000
60
70
50
80
7000
5000
9000
- 4 -
1400
1200
1600
4000
3000
7000
800
300
900
70
9
79
- 5 ■
000
80
7
687
80
4
84
400
50
2
453
6
907
502
7008
2004
5804
2301
8976
8242
6598
2178
9786
2514
SUB TE A CTION.
53
SLATE EXERCISES.
76. Separate each of the fallowing numbers into two parts,
so that one part will consist of 1 ten, or of 1 ten and the units
of the number, thus :
^iO ^ 20 + 10. 78 = 60-*-18. 359 = 340 + 19.
Continue to separate in this manner, on your slate, the foDowing num-
bers, until you can ^ve the parts at sight of each number.
20
60
31
1
71
62
33
73
24
40
30
61
32
92
63
28
64
70
90
91
52
72
93
54
94
50
21
41
82
22
43
74
44
80
51
81
49
2
53
88
34
84
36
65
26
56
77
43
98
29
85
25
96
97
67
78
28
69
45
55
36
37
27
38
39
99
75
76
66
87
67
68
59
49
95
46
86
47
i^
58
89
79
77. Write on your slate in irregular order the tens from 10
to 90 and subtract 2 from each, thus :
I
■ I
il
t
40
20
60
JO
70
50
80
10
90
2
2
2
2
2
2
2
2
2
88
18
58
28
68
48
78
8
88
Observe^ that in each example we simply subtract 2 from 10; thus, in
taking 2 from 40 the 40 la regarded as 30+ 10, and the 2 taken from the 10,
leaving 8, this 8 added to the 30 gives the remainder 38.
Subtract in this manner successively 1, 2, 3, 4, and so on up
to 9. When the remainders are found, erase them and write
them again and again from memory, until you can write them
at sight of the two numbers.
1
1
W !
M
64 SUBTRACTION.
SLATE EXERCISES.
78. Write on your slate in irregular order the tens and
1 unit from 21 to 91 inclu3ive, and subtract 3 from each num-
ber, tlius :
31
_2
19
Observe, that in each example the number A:om which the 2 is snbtracted
is separated into two parts, as in (76). Thus, in subtracting 3 ft-om 31, the
31 is regarded as 30+11, and the 3 is taken from 11, leaving 9 ; adding this
9 to the 30 giva the remainder 39.
Subtract in this manner successively 3, 4, 5, 6, 7, 8, and 9
from each of these numbers. In each case, when the subtrac-
tion is performed, erase the remainders and write them again
and again from memory.
Practice in this way upon each of the following exercises :
31
51
81
2
2
2
d9
49
79
91
61
41
71
2
2
2
2
89
59
39
69
42
72
32
52
82
22
62
92
J
J
_3
3
J
8
J
J
Practice as directed, upon subtractings 3, then erase it and
practice in the same manner upon 4, then 5, then 6, 7, 8, and 9,
58
4
83
4
33
4
63
4
93
4
43
4
23
4
73
4
Practice upon 4 as directed, then 5, then 6, 7, 8, and 9.
84
34
64
24
74
44
94
54
6
5
5
5
5
5
5
5
Practice upon 5 as before, then upon 6, 7, 8, and 9.
SUBTRACTION,
55
SLATE 'HIXEHCISES.
79. Practice as directed in 1(78) ou the following exercises :
1
76
46
86
86 6G
£6
56
96
7
7
7
7 7
7
7
7
After practicing upon 7, erase it and use 8, then 9.
2
47
67
57
97
37
87
27
77
8
8
8
8
8
8
8
8
Subtract 9 from each number iu the same manner.
3
38
58
98
48
78
28
68
88
9
^
_9
J
9
_9
9
9
80. Analyze the numbers and perform the subtraction iu
each of the following examples, thus :
Find the difference between 85 and 47.
Observe, that the 7 units in the
BQbtnthend cannot be taken from
the 6 units in the minuend. Hence
we separate the minuend into 70+
15 and take the 7 units from the 15
units, and the 4 tens, or 40, from the 7 tens, or 70, leaving 38, the difference
between 85 and 47.
Minuend,
Subtrahend,
Difference,
85 = 70+15
47 = 40 + _7
88 = 30+ 8
Perform in this way the following subtractions :
1. 53 - 26. 6. 85 - 37. 11. 361 - 34.
2. 82 - 55. 7. 63 - 44. 12. 284 - 58.
8. 61 - 27. 8. 52 - 25. 13. 757 - 29.
4. 95 - 79. 9. 31 - 13. 14. 368 - 35.
5. 64 - 35. 10. 82 - 46. 15. 471 - 43.
W \\
I !'
I. '
1^
56 S UB TR A C Tl X.
OKAL EXERCISES.
81. 1. How many will remain if 6 be taken from 11?
6 from 21 ? « from 41 ? G from 91 ? from 141 ?
2. How many will remain if 5 bo taken from 13 ? 5 from 23 ?
5 f ]oni 53 ■? 5 from To ? 5 from 253 '?
3. What number must be added to 7 to make 14? To make
34 ? To make 44 ? To make 84 ? To make 134 ?
4. There are 24 hours in a day ; if you sleep 7 hours, how
many liours are you awake ?
5. I sold a cow for 38 dollars, which was 9 dollars more than
it cost ; how many dollars did it cost?
6. A man paid 49 dollars for some hay and 7 dollars for some
straw ; how much did the hay cost more than the straw?
7. A tree had 73 apples on it, but the wind blew ofT 8'of
them ; how many remained on the tree?
8. There were 82 houses in a certain town, but 6 of them
were destroyed by fire ; how many houses remained?
9. There were 55 persons on a train of cars, and at a certain
Station 5 got olf and 13 got on ; how many were then ou the
train ?
10. Amy has 27 lines to read in her primer and she has read
C ; how nnuiy more lines has she to read?
11. Judson caught 39 trout, but the 7 largest fell back into
the Walter ; how many did he have to cany home?
12. Farmer Esty had 132 sheep ; five of them were black and
the rest white ; how many were white?
13. A school contains more boys than girls, and there are
8vT boys ; how many girls are there?
14. There wero 230 houses in a village, but a fire burned 8
of them ; how many remained?
15. 283 minus 5 are how many? 357 minus 9? 574 minus
8? 613-7? 115-9? 845 -G? 88-9? 97G - 7 ? 89-3?
37-8? 317-4?
10. An orchard has 7 more apple trees than cherry trees, and
there are 73 apple trees ; how many cherry trees are there ?
»r->t:i -ittiiitiimmtami ...v
SUBTRACTION,
57
SLATE AND BOABD EXERCISES.
82. Find the difference between 437 and 179.
Minuend,
Subtrahend,
Difference,
437
m
258
Explanation. — 1, We write the lesser
number under the greater, eo that units of the
same order are in the same column.
2. Since 9 units cannot be taken from 7 units,
we regard the minuend 437 as 420+ 17, and take
the 9 wiits from 17 units, leaving 8 units.
3. Since 7 tens cannot be taken from the 2 tens that are left in the minu-
end, we regard the 490 of the minuend as 800+120, and take 7^cn*or70
from the 12 tens or 120, leaving 5 tent or 60.
4. We take the 1 hundred from the 3 hundred left in the minuend, leav-
ing 200 ; hence the difference between 437 and 179 is 258.
Proop, 179 + 258-437.
83. Perform the subtraction in each of the following exam-
ples, anc' sxplain and prove as above.
1.
Take 248 from 524.
18.
3759-
1985.
2.
Take 385 from 732.
19.
8362-
4766.
3.
Take 59G from 963.
20.
6425-
3847.
4.
Take 478 from 654.
21.
4231 -
■ 1777.
5.
Take 289 from 467.
22.
9443-
6888.
6.
Take 653 from 821.
23.
7333-
3556.
7.
Take 361 from 533.
24.
5555 -
3666.
8.
Take 487 from 762.
25.
8232 -
■ 6444.
9.
Take 555 from 743.
26.
6524-
2879.
10.
Take 296 from 854.
27.
9365-
A987.
11.
Take 359 from 532.
28.
3694 -
2867.
13.
Take 89 from 2311.
29.
6325 -
4838.
13.
Take 425 from 613.
30.
4363-
1795.
14.
Take 96 from 3624.
31.
9564-
8298.
15.
Take 587 from 936.
82.
5346-
3769.
IG.
Take 293 from 462.
83.
2436-
857.
17.
Take 69 from 4326.
34.
8363-
976.
'•^
I) •!
:%i ^1 '■
f I
58
SUB Tit A CTION.
SLATE EXERCISES.
84. Find the difference between oOO and 7.
500
__7
493
Explanation.— There are no units from which to take
the 7 ttnits, hence we regard the 500 as 400 + 90 + 10, and
take the 7 units from the 10 units, leaving 3 units. Ilence
we have remaining 400+90+3 = 493, the diflference between
500 and 7.
PROOf, 493+7 = 500.
85. Perform the subtraction in each of the following exam-
ples, and explain and prove as above.
(1)
30
(3)
800
(3)
500
(4)
600
(5)
900
(6)
400
4
2
5
6
3
7
(7)
7000
(8)
9000
(9)
3000
(10)
8000
(11)
6000
(13)
4000
8
4
5
3
6
9
(13)
4000
(14)
6000
(15)
8000
(16)
3000
• (17)
9000
(18)
5000
37
25
63
57
74
46
(19)
150
(30)
1200
(21)
1800
(32)
210
(23)
510
(34)
710
4
7
5
3
2
8
(35)
1900
(36)
8100
(27)
8000
(88)
5100
(29)
3100
(30)
61000
53
69
37
02
74
41
(31)
7004
(32)
13000
(33)
4000
(34)
61000
(;]5)
11000
(3G)
10000
807
0008
502
7004
8006
3003
r
I
1.
2.
3.
5.
9.
10.
^1 : !•'
SUB TRA CTIOX.
5i
ARITHMETICAL TABLE No. 4.
1.
A.
B.
C.
D.
£«»
F.
a.
in
i d
I
1 ■>
!
! ^
i
1
'J
/
^'
/
n
V
/
'■1
/
V
/
/■
/
/
•y
/
/
/'
/
/
/ }
S'
y/
s
/
r
/
\
J
J
/
/I/ ■
/,
/'
5
,/
{
:y
1
y ■
1
A, ^
/ 1
/ ■ ;
/
— i
/
2.
3.
4.
5.
0.
t.
&
9.
10.
; )
nr
! i
•"H
I
8(>. Copy examples as shown on next page from tliia table
ftnd from Table No. 2, on page 35. Continue this practice until
you can find accurately, almost at sight of the figures, the dif'
ference between any two numbers.
60
SUB TEA CTIOX.
EXAMPLES FBOM TABLE NO. 3.
lHjcet'cises with Numbers of Two i'iguresm
87. 1. Use columns A and 13, Take for the first exam-
ple the figures opposite 1 and 2, for the second example the
figures opposite 2 and 5, etc. Write the lesser number under
the greater. The examples from columns A. and S are the
following :
(1)
(2)
(3)
(4)
(5)
(6)
l7)
(8)
(0)
65
53
67
67
42
65
65
54
54
63
20
20
42
36
36
30
30
26
2. Copy examples in the same manner from B and c ; c and
D ; D and e ; E and F ; F and 6 ; 6 and h.
3. Copy new examples, taking one number from columns A
and B and the other from oolomnB B and C, thna:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
65 53 20 73 42 60 65 30 59 65
5837_567283657j4026
4 Copy examples in iiis way, taking the numbers from
columns b and c, and c and d ; c and d, and D and E ; D and E,
and E and f ; e and f, and f and o ; f and 6, and G and h.
Eocercises with Numbers of Three or more Figures,
88. 1. Copy examples with numbers of three figures from
columns ABC in the same manner as the first set with tAvo
figures, then from columns BCD, CDE, def, efg, fgh.
Examples with numbers of four or more figures may be
copied in the same way by using the required number of
columns.
2. Use for one number columns ABC and for the other num-
ber columns bcd ; then BCD and cde ; and so on.
SUBTR A CTION.
61
WRITTEN EXERCISES.
St>. 1. Henry has $74 and James has $29. How many
dollars lias Henry more than James?
2. What is the difference between $436 and $279 ? Between
11824 and $968 ? Between $1035 and $632 ?
3. A man had $935 in the bank, and took out $369. How
many dollars had he then left in the bank ?
4. A grocer bought 482 pounds of maple sugar, and sold 295
pounds of it. How much has he still left ?
5. I had $145 in my pocket-book and paid out of it to one
man $49, to another $48. How much had I then left ?
G. A man owning 934 acres of land, sold to one man 283
acres, to another 215. How many acres has he still left ?
7. A boy had 41 marbles and bought 62 more ; he then lost
49 of them. How many had he left ?
8. A grocer bought two tubs of butter, the first containing 63
pounds, the second 85 pounds ; he sold out of the first 29 pounds,
out of the second 48 pounds. How many pounds has he left
in all?
9. A grain merchant bought three lots of wheat as follows :
584 bushels, 239 bushels, and 463 bushels ; he then sold out of
what he bought 1098 bushels. How many bushels has he left ?
10. A farmer has in one stack of hay 28 tons, in another 53
tons, and in another 47 tons ; he has sold in all out of the three
stacks 99 tons. How many tons has he left ?
11. A merchant had a piece of cloth containing 469 yards ;
he sold to one man 132 yards, to another 184 yards, and to
another 62 yards. , How many yards of the piece had he then
left ?
12. A man deposited in the bank at one time $238, at another
$ 172, and at another $684 ; he drew out in all $1097. How
much has ho still left in the bank ?
13. A farmer had 143 tons of hay and sold 19 tons ; how
many tons has he left ?
li
Hi
•4
ij .,
62
SUBTRA CTION.
CANADIAN MONEY.
90. 1. Take $18.67 from $43.35.
$43.25
_18^
$24.58
Explanation.— 1. Write the leeeer number nnder the
^eater, so that the periods are in the same column.
When there are no centg, place two ciphers on the right
of the period.
2. Subtract as if there were no periods, the 1867 from
the 4S25, and place in the remainder a period between the second and third
figure from the righ^
3. I'Tie figures to the right of the period express the number of cents, and
those to the left the number of dollars ; hence the remainder is read, twenty-
four dollars and fifty-eight cents.
Perform the subtraction in the following :
(2)
$49.76
23.51
(7)
$835.21
586.59
(3)
$97.35
43.14
(8)
$362.04
128.17
(4)
$83.52
81.27
(5)
$58.93
29.65
(9) (10)
$730.42 $2034.07
583.90 1293.69
(6)
$387.26
159.84
(11)
$430^V05
2083.97
ii^l
12. I was to pay a man $3.19 and gave him a 5 dollar bill.
How much change did I receive ?
13. Sold a load of wheat for $87.52 and received in pay only
$43.95. How much am I yet to receive ?
14. Bought a book for $2.35 and gave the bookseller $10.
How much change did he return V
15. A man owed me $37.43 ; he has paid $12.97. How much
is still due me ?
16. A boy went into a grocery with $12, and paid for sugar
$2.13, for tea $1.85, for butter $3.47, and for flour $4. How
much of the $12 had he left ?
17. A man earns $18 a week and his family expenses are
$13.42. How much docs he save each week?
SUBTRA CTJ Ou\.
63
WBITTEN EXERCISES.
01« 1. A man had in his purse $413.52, and paid a debt of
^85.68. How much had he left in his purse?
2. Bought a coat for $29.75, a vest for $4.83, and paid on
both $23.27. How much is yet to be paid ?
;j. William Robertson lent his neighbor $405.45, on which
be has received $239.87. How much has he yet to receive?
4. A farmer sold a firkin of butter for $52.35, a cheese for
$19.07, and a load of wheat for $83.25. He paid out of the
money received $67.93. How much had he then left ?
5. Henry Mills bought a horse for $253, a harness for $37.45
and a buggy for $207. He paid on the whole $283.87. How
much is yet to be paid ?
6. Out of $792.32 I paid a debt of $409.72. How much have
I left ?
7. Sold a horse for $247, and took in exchange a yoke of
oxen at $97 and a lot of sheep at $68.75. How much is still
•lie me?
S. Alexander Smith deposited in the bank $630.48, and after-
wards drew out $375.87. How much has he in the bank ?
9. A merchant sold a lady 12 yards of cloth for $17.39,
7 yards of ribbon for $2.95, a shawl lor $29.17, and gloves for
!jtl.35. She paid on the whole bill $36.83. How much did she
leave unpaid ?
10. A farmer bought rf'cow for $87, a lot of sheep for $203.85,
and a span of horses for $264. He paid on the whole $352.97.
How much has he yet to pay ?
11. Out of a 60 dollar bill I paid $2.35, $7.84, $23.27 and
$8.05. How much of the bill have I left ?
12. A lady had $99.50 \ len she went into a grocery. She
paid $7 for sugar, $20.39 ior butter, $2.13 for spices, $9 for
flour and $39.67 on an old account. How much of her money
had she left?
'Si
II
1
• -
H
•4
4
•^i'
( r
11
64 SUBTRACTION.
DEFINITIONS.
1)2. Subtraction is the process of finding the diflference
between two numbers.
93. The Minuend is the greater of two numbers whose
difference is to be found.
94. The Subtrahend is the lesser of two numbers whose
difference is to be found.
95. The Difference or Remainder is the result ob-
tained by subtraction.
The Process of Subtraction consists in comparing two
numbers and resolving the greater into two parts, one of which
is equal to the difference of the two numbers.
90. The Sign of Subtraction is — , and is reRd minus.
It indicates that the number written after it is to be taken from
the number written before it ; thus, 12 — 5 = 7.
BULE.
97. / Write the subtrahend under the minuend, placiuff
units of the same order in the same column.
II. Begin at the rights and find the difference between the units
of each order of the subtrahend and the coi'responding order of
the minuend, and write the restdt beneath.
III. If the numhrr of units of any brder of the subtrahend is
greater than the number of units of the corresponding order of
the .rdnucnd, increase the latter by 10 and subtract ; ttien dimin-
ish by 1 the units of the next higher order of the minuend, and
proceed as before.
VTXOOY.—Add the remainder to the srthtrafiend ; if tJie sum is
eqiial to the minuend, the work if probably correct.
2. 2 tir
3. 6 til
4. The
read 3 tin
5. Exp
and the s
3ti
4ti^
6. FinI
7. WlJ
adding ll
said to /I
8. TaJ
times an
piicatm
9. Till
cand, 1
10. tI
is to bo 1
11. M
ProdiM
MULTIPLICATION.
ORAL EXERCISES.
98. 1. 3 lines + 3 lines + 3 lines are how many lines?
— 4- ■" 4- ^ are 9 lines.
Three times 3 lines arc 9 lines.
3. 2 times 3 lines are how many? 5 times 3 lines?
3. 6 tim«s 3 pears are how many pears V 7 times 3 pears ?
4. The SiffU x stands for the word tunes. Thus. 5x3 is
read 3 times 5, and means 5 4-5 + 5.
5. P]xpres3 each of the following by using both the sign x
and the sign 4- . Thus, 3 times 4 = 4x3 = 44-44-4,
3 times 4.
4 times 0.
2 times 8.
5 times 4.
4 times 7.
C times 5.
6. Find by adding how many 2 times 6 are ; 4 times 7.
7. When we memorize these results and can tell without
adding how many 2 times 6, 4 times 7, and so on &t3, we are
said to nniltiplij.
8. Taking one number, by using memorized ronults, as many
times as there are ones or units in another, is called I\Ialti~
plication.
9. Tlie nuinber taken or multiplied is called the Multipli-
cand, Thus, in 5 times 9, the 9 is the multiplicand.
10. The number that shows how many times the multiplicand
is to be taken is calliul the Multiplier.
11. The result obtained by multiplying is * called the
I^roduct, -
Ni
» \
i
. tf
I
I
h
66
'■}
MULTIPLICATION.
ORAL EXEBCISES.
99. 1. Five boys went fishing ; each caught two fishes,
which they put in the same basket ; how many fishes were in
the basket ? 2 + 2 + 3 + 3 + 3 = ? How many are five 3's ?
2. A man planted two rows of trees in his garden ; if there
were three trees in eacli row, how many were there in all ?
3 + 3 = ? How many are two 3's ?
3. Simon picked two clusters of grapes, each cluster contain-
ing 4 grapes ; how many grapeg did he pick? 4 + 4=:? How
many are two 4's ?
4. Edith's mother gave her 4 books, and each book had three
pictures; how many pictures in all? 3 + 3 + 3 + 3 = ? How
many are four 3's ?
5. There are three clover-leaves on a stem ; how many leaves
shall I have if I pick five stems? 3 + 3 + 3 + 3 + 3=? How
many are five 3's ?
6. Ralph's father gave him six dollars a mouth for three
months; how many dollars did he get in all? 6 + 6 + 6 = ?
How many are three 6's ?
7. If a class learn four pages at one lesson, how many pages
will they learn at four lessons? 4 + 4+4+4 = ? How many
are four 4's ?
8. A man sold five hats, getting four dollars for each hat ;
how many doll ars did he get in all ? 4 + 4 + 4 + 4 + 4 = ? How
many are five 4's ?
9. If five leaves are on one twig, how many leaves will be
on six such twigs? 5 + 5 + 5 + 5 + 5 + 5 = ? Hoav many are
8ix5'8?
10. If one chest liPs five drawers, how many drawers will
four chests have ? 5 + 5 + 5 + 5 = ? How many are four 5's ?
11. ir there are four eggs in each nest, how many eggs will
there bo i a sflfvcn nests ? 4 + 4 + 4 + 4 + 4 + 4 + 4 = ? How many
are seven 4'8 ?
31 UL TIP Lie A TION.
67
fishes,
were in
if there
in all?
contain-
? How
lad three
? Ho\T
luy leaves
? How
for three
f6 + 6 = ?
finy pages
low many
each hat;
= ? How
s will be
Qany are
ivers will
»ur 5's ?
pggs will
ow many
SLATE EXEBCISES.
100. Copy separately each of the following tables :
Find the product for each example by addition and write it
on your slate thus :
5y<S = 5+3+5 = 15.
5^3 = 5+5+5+5+5 = 25.
Table of Twos.
2^2 2x6
2x5
2xjf.
2x8
2x7
2x8
2x9
Table
of Fours.
J/-XS
J^xG
^x3
^xS
j^x7
Ji.x2
^x^
^xQ
Table
of Tlirces.
8xfj,
8x8
8x2
8x5
8x6
8x7
8x8
8x9
Table of Fives.
5x2
6x3
5x6
5x5
5x^
5x7
5x8
5x9
101. Write each of the foregoing tables on your slate with-
out the sign x . The table of twos, lor example, should be
written thus :
4>
2
2
5
2
8
2 ■ 2
8 6
Jf- 'r
2
9
Find the product of each pair of numbers as before t\nd write
it under the numbers. Then eruse all thc^^ic i>roduc;f:-i and con-
tinue to rewrite them from memory, until you can wiile them
at sight of the numbers.
iW.
•tt
68
MULTIPLICATIO X
SLATE EXEBCISES.
102. Find the product for the following examples and ex-
plaii> each example thus :
(1) 4x3. Four multiplied by 3 are 13.
(3) 40 X 3.
Four teiu multiplied by 3 arc 13 tens
, or 120.
Table o
(3) 400 X 3.
3r 1300.
Four hundred mu
Itiplied by 3 are
13 hundred,
0x3
6x4
6x8
Table
of Twos applied.
6x5
3x3
30x5
300x3
3000 X 6
3x8
30x3
300 X 6
2000 X 2
Table oj
3x4
30x7
300x9
3yoo X 8
0x3
3x6
30x4
200 X 5
3000 X 5
9x0
2x9
20x8
200x7
2000 X 7
9x4
9x8
Table
of Tlireea applied.
30x4
300x8
3000 X 6
30000 X 9
30x7
300x3
3000 X 8
30000 X 7
13x3
30x5
300x9
3000 X 5
30000 X 5
13x5
30x9
300 X 7
3000 X
30000 X 8
30x6
300x3
3000 X 4
30000 X 6
104
out the
,
Table
of JTour
.V applied.
6
o
40x2
400x7
4000 X 5
40000 X 9
40x5
400x4
4000 X 9
40000 X 5
hj
40x8
400 X 8
4000 X 6
40000 X 8
Find
under
them 1
40x6
400x3
4000 X 8
40000 X 3
40x9
400 X 9
4000 X 4
40000 X 7
Table
of Fives applied.
50x7
500 X 6
nOGO X 4
50000 X 8
m-A
50x9
500x8
5000 X 9
50000 X 3
60 X J
50 X 5
500 X 4
nooo X 5
50000 X 6
60 X
50x8
500x0
5000 X 7
50000 X 2
60 X
M UL TIP LICATIO N,
69
J 'K
SLATE EXEECISES.
10.*5. Copy Beparately each of tlie following tables and find
the product for each example by addition.
Thus, Ox 4 - + G + 6 + G = 24.
I' 'I
Tahlr
ot
Sixes,
Table of
Sevens.
Table of Eights.
Ox 2
OxG
7x3
7x8
8x4
8x7
Gx4
0x8
7x5
7x2
8x3
8x3
0x8
Cx7
7x7
7x6
8x0
8x5
Cx5
Gx9
7x4
7x9
8x8
8x9
Tahlv
of
Xlnes,
J'able of Tens.
Table of Elevens.
9x8
9x7
10x5
10 xG
11x3
11x6
9x0
9x3
10x7
10x3
11x5
11x4
9x4
9x9
10x4
10x9
11x3
11x9
9x8
9x5
^
10x8
Table of
10x3
Twelves.
11x8
11x7
12x2
12x4
12 X
3
13
x6
13x10
12x5
12x7
12 X
8
13
x9
13x11
1 04. Write each of the foregoing tables on your slate with-
out the sign x thus :
6
G
C
6
6
G
6
6
3
4
8
5
6
3
7
9
Find as before the product of each example and write it
under the numlxTS. Then erase all these products and rewrite
them from memory as in (101). ♦
Tftblc of Sixes applied.
60^3
60x5
60x7
60x4
GOO X 3
600x8
GOO X G
600x9
GOOO X 5
6000 X 8
6000 X 6
GOOO X 9
60000 X 7
60000 X 9
60000 X 4
60000 X 8
I
i i.:ll
■ i
tiki
M
70
MULTIPLICA TION,
SLATE EXERCISES.
105. Copy each of the following examples and find the
products.
Thus, 4007 X C = 24043. Observe, when you multiply the
7 units by 6, you have 4 tens and 2 iinits^ which you write in
the tens and units place ; when you multiply the 4 thousands
hy 0, you have 24 thousands.
707x3
707x5
707x3
808x3
808x7
808x4
9009x5
9009 X 8
9009 X 3
Table of Sevens applied.
7007 X 6 70707 x 7
7007 X 9 70707 x 5
7007x4 70707x8
Table of Eights ajyplied.
8008 X 6 80808 x 2
8008 x 5 80808 x 8
8008 X 9 80808 x 4
Table of Nines applied.
90909 X 2 90909 x 9
90909 x 6 90909 x 5
90909 X 4 90909 x 8
700707 X 8
700T07 X 6
700707 X 9
80808 X 6
80808x9
80808 X 7
90909 X 6
90909 X 9
90909 X 7
106. Find the product for each of the following examples
and name the tables you apply in each case.
Thus, 90705 x 8 = 372115. In multiplying the 5 units by the
8 the table of Jives is applied, in multiplying the 7 hundreds by
the 3 the table of sevens is applied, in multiplying the 9 ten-
thousands by the 3 the table of nines is applied.
1. 30906x7.
2. 80405x3.
3. 20003x8.
4. 20705x8.
5. 50908x4.
C. 80306x7.
7. 90305x7.
8. 30806x9.
9. 70409x5.
Multiply and explain the following :
10. 10x4. 11. 100x7. 13. 1000x8. 13. 4x10.
3.
4.
5.
0.
17.
18.
19.
30.
MULTIPLICA TION.
SLATE EXERCISES.
71
107. 1. Multiply 483 by 6.
483
6
2898
Explanation.—!. The number to be multiplied contains
4 hundred 8 tens and 3 units^ and each of these parts are to
be taken 6 time,':*.
2. Six times 3 units malte 18 unity, or 1 ten and 8 units.
We write the8 units in the units' place and reserve the 1 ten
to add to the tens.
3. Six times 8 tens vasikc 48 tens, whicli, with the 1 ten reserved, make
49 tens or 4 hundred and 9 tens. We write the 9 tens in the tent?' place, and
reserve the 4 hundred to add to the hundreds.
4. Six times 4 hundred make 24 hundred, which, with the 4 hundred re-
served, make 28 hundred or 2 thousand 8 hxindred.
Multiply and explain in this manner each of the following
examples :
2.
385 by 3.
7.
5934x8.
12.
80360 X 3
3.
092 by 7.
8.
230G X 4.
13.
59007 X 6
4.
864 by 6.
9.
8509 X 5.
14.
30835 X 4
5.
497 by 4.
10.
6083 X 7.
15.
79068 X 5
G.
853 by 9.
11.
3095 X 9.
10.
99999 X 7
17. Multiply 83604 by 7 ; by 9 ; by 3 ; by 8 ; by 5.
18. Multiply 509307 by 3 ; by 5 ; by 7 ; by 8 ; by 2 ; by 9.
19. Multiply 83 hundred by 10 ; by 6 ; by 9.,
20. Multiply 903 thousand by 7 ; by 5 ; by 3 ; by 8.
(!
)l
1%
n
21.
70707 X 5.
30.
3333;) X 7.
39.
80808 X 9.
22.
30303 X 8.
31.
88888 X 9.
40.
79065 X 7.
33.
90909 X 6.
32.
55555 X 3.
41.
38 409 X 5.
24.
50508 X 9.
33.
44444 X 8.
42.
02537 X 3.
25.
90009 X 7.
34.
77777x4.
43.
90900 X 0.
36.
99999 X 4.
85.
23222 X 5.
44.
43925 X 8.
27.
66666x5.
86.
80907 X 6.
45.
89374 X 9.
28.
50505 X 6.
37.
39564 X 9.
46.
59648 X 5.
39.
83092 X 8,
38.
80709 X 2.
47.
83095 X 7.
in.
73
J/ U L Tl Phi C A TI X.
1' I
OBAL AND WBITTEN EXERCISES.
108. 1. A mason earned 13 dollars a week and spciit 4
dollars ; how mucli did lie save in G weeks ?
Solution.— He saved G times the difference between $12 and $4, which
is $48.
2. flow man}' are 2 times 7, ])lus r> ""i times 8, plus 7?
6 times 8, plus 3 ? 7 times 13, plus 9 ?
3. How many are 5 times 6, minus 4? 4 timet; '■'<, iiinus 6?
4 times 11, minus 9 ? 8 times 7, minus 8 ?
4. At 40 rents a yard, wliat would 7 yards of cambric cost ?
1?. yards? 13 yards? 8 yards? 10 yards?
5. How many cents will 13 doves cost, at 9 cents apiece ? At
11 cents apiece ? At 13 cents apiece ?
6. Bought 15 barrels of apples, at $3 a barrel, and a barrel
of crackers for $5 ; how much did the whole cost ?
7. A merchant sold 7 coats at !f5l3 apiece, 8 vests at i?4 each,
and 10 yards of broadcloth at $7 a yard ; how much did he re-
ceive for the whole ?
8. Bought 13(5 chairs at $3 each, 8 sofas at $25 each, and
9 tables at $9 each ; how much did the whole cost ?
9. Gave $39 each to 6 men, paid for 39 yards of cloth at $4 a
yard, and for a coat |30 ; how much money have I spent?
10. At 5 dollars a cord, what will 39 cords of wood cost?
87 cords? 384 cords? 79 cords?
11. In a week there are 7 days ; how many days in 4 v^ecks?
In 8 weeks ? In 6 weeks ? In 33 weeks ?
13. Bought 13 boxes of soap, each containing 39 bars ; how
many bars in all ?
13. What is the cost of 13 acres of land at |30 an acre? At
$59 ? At $84 ? At $1 85 ? At $507 ? At $953 ?
14. Jacob Mclntyre can earn 100 dollars a month, and it costs
him 63 dollars a month to upport his family ; how much can
he save in one year ?
109.
257
10
2570
3. Placii
In the
ber by 1(
Multip
1. Mul
2. Mul
3. Mui
4. Mu
110.
(1)]
EXPLA
inp;acii)li
in the iSec
2. In (:
muUiplio(
in tlic un
cipher.
Obser
plicaud
Knits ai
manner
MULTIPLICA TION,
73
\i
SLATE EXERCISES.
109. Multiply 357 by 10.
Explanation.— 1. In 267 the figure 7 expresses 7 ^initSy
the figure 5 expresses 5 tens^ and the figure 2 expresses
2 hundred.
2. Each of these figures will express 10 limes what they
now do if moved one place farther to the left.
3. Placing a cipher at the right of 257 moves each figure one place farther
io the left ; hence multiplies each order in 257 by 10.
257
10
2570
In the samo manner annexing two ciphers multiplies a num-
ber by 100 ; three ciphers by 1000, and so on.
Multiply and explain in this manner each of the following:
1. Multiply 93 by 10 ; by 100 ; by 1000 ; by 10000.
2. Multiply 709 by 100 ; by 10000.
3. Multiply 490 by 10; by 100 ; by 1000; by 10000.
4. Multiply 9730 by 1000 ; by 10000.
110. Multiply 59 by 30.
(1)
{First step, 59x10= 590.
[Secmdstep, 590 x 3=1770.
,n\ j Both steps in
{ one operation,
59
30
1770
Explanation.— 1. In the First Step in (1) 59 is taken 10 times by annex-
ing a cipher ; hence 590 is 10 times 59. Now, by faking 590 three times, as
in the Second Step, we have 30 times 59 ; Jicncc HiO is 30 times 59.
2. In (2) we unite the two stej)s in one oponition by regarding the W} as
mullipiied by 10, or as 59 tens, and multiplying by 3 ; hence we write a cipher
in the units place in the product, and write 3 times the 59 to the left of tho
cipher.
Obseroe, that to multiply by hundreds we regard the multi-
plicand as expressing hundreds, and hence write ciphers in the
nnits and tens place in the prodtict. We proceed in the same
manner in multij)lying by thousands, and so on.
4
i
t
K
%
uH
1%
i ■
m
ft
h
74
MULTIP Lie A TI N.
SLATE EXERCISES.
111. Multiply and explain cacli of the following examples r
1.
85x50
37 X 4000
5007 X 60000
2.
73x80
95 X 7000
8045 X 30000
o
92 X GO
4G3 X 9000
3906 X 70000
4.
54 X 90
627 X 5000
4509 X 50000
5.
367 X 30
890 X 3000
7000 X 90000
6.
509 X 70
70x40
8009 X 40000
7.
76 X 200
90x60
9300 X 20000
8.
39 X 400
800 X 700
5090 X 80000
112. Multiply 783 by 45.
(1)
783 Multiplicand.
45 Multiplier.
783 X 5
783x40
3915 1st partial product.
31320 2d partial product,
35235 Whole product.
(3)
783
45
3915
3132
35235
Explanation.— The multiplier 45 = 40 + 5; hence we multiply the 783
first by 5, then by 40, and add theee two products as shown in (1), giving
85335, which is 40 + 5 or 45 times T83.
Observe, tliat when multiplying by the 40 the cipher at the
right of the product need not be written, as shown in (2). The
position of each figure in 3132 under 3915 indicates what order
it represents. Thus, the 2 is placed under the tens in 3915;
hence we know that it expresses 2 tens.
Multiply and explain each of the following :
1.
476 X 53.
«.
839 X 78.
fj.
587 X 95.
4.
396x37.
5.
6.
7.
8.
705 X 69.
389 X 84.
936 X 78.
598x42.
9.
837 X 635.
10.
954 X 827.
11.
386 X 349.
13.
749 X 594.
1.
5.
tT
8.
~^
lO.
717
12.
i 1
113.
Mi
1. Coi
in addit
EPG, PG
For e
diately
M
Take!
BCDEP,
Takel
the rigl
^ULTI PLICA TION,
75'
ARITHMETICAL TABLE No. 8.
tnples :
00
)00
)00
[)00
ooo
000
000
1000
!5
ply the 783
I (1), giving
ler at the
(2). The
fhat order
> in 3915;
< 635.
<827.
<349.
<594.
A.
B.
c.
i>.
li.
F.
G.
H.
1.
J.
1.
1
6'
9
2
5
8
4
6
3 9
a.
4
5
3
7
9
6
5
3
8
9
7
3
6
4
6
3
8
9
2
5
2
5
9
8 5
4 8
7 2
3.
4.
5.
8
3
4
1
6
9
3
5
9
7
2
9
7
3
3
8
5 9
2 6
«.
7.
6
5
7
9
2
4
8
4
9 3
8.
9
5
2
1
4
8
6
4
8
G
5
7
9
5
7
9
6 8
3 7
o.
10.
7
4
4
8
2
9
7
5
9
4
4
8
8
6
5
8
9 4
5 9
11.
12.
9
7
5
8
7
(7t
o
9
4
8
6
113, Copy examples from this table as follows :
Multiplicand three figures ; Miiltiplier one,
1. Commence opposite 1 and take multiplicands in order, aa
in addition (^1\ from columns ABC, then from bcd, cde, dep,
EFG, FGir, GHI, and hij.
For each example take as the multiplier the figure imme-
diately under the right-hand figure of the multiplicand.
Multiplicand five figures ; MnltipUer one.
Take multiplicands in order from columns abode, then from
BCDEP, CDEPG, DEFGII, EFGHI, FGHIJ.
Take for multipliers, as before, the figure immediately under
the right-hand figure of the multiplicand.
* II
%
X%
'4,
76
31 UL TIP Lie A TION..
; I
li
SLATE EXERCISES.
Multiplicand four fi (J lives ; Multiplier two*
114. 1. Take the multiplicands from Table No. 5, as be-
fore directed. Use first columns abcd, then bcde, cuef, defg,
EFGii, FGiii, and onij.
Take as multipliers the two figures immediately under the
two right-hand orders of the multiplicand:^. The first live
examples taken in this way from columns abcd aro :
1692
68
4368
59
2759
37
5937
63
8463
95
I ;
LI •
3Iulti2*lic(fnd six figures ; 3Iultipliei' four,
2. Take the multiplicands first from columns abcdep, then
BCDEFG, CDEFGII, DEFGHI, and EFGIIIJ.
Use as multipliers the f<mr figures immediately under the
four right-hand orders of tlie multiplicands. The first four
examples from columns abcdef are :
I
169258
6886
430833
5963
275903
3748
593748
0392
3. James Wood sold 64 acres of land at 58 dollars per acre ;
how much money did he receive? Ans. (^3712.
4. If a railroad car goes 26 miles an hour, how far will it run
in 48 hours at the same rate? Ans. 1248 miles.
5. A tailor has a jiiece of cloth containing 126 yards ; how
much will he have left after cutting from it 9 suits, with 4 yards
in each suit? -<4?w. 90 yards.
6. If one acre of land cost $285, what will 27 acres cost at
the same rate? Ans. $7695.
7. There are 5280 feet in one mile ; how many feet in 345
miles? Ans. 182 1600 feet.
IV.
the mill
Hght-h\
multipX
prodij\
Pr(
muUh
red.
MULTIPLICA TION.
77
DEFINITIONS.
115. 3laltiplication is the process of taking one number
as many times as there are units in another.
1 1 <>. The Multiplicand is the number taken, or multi-
plied.
117. The Multiplier IB the number which, denotes how
many times the multiplicand is taken.
118. The Vroduct lathe result obtained by multiplica-
tion.
BULES.
1 19. I. Wiiu tJie multiplier under the multiplicand, so tJiat
units of the same order stand in the same column.
To multiply by numbers less than 10.
II. Begin at the right hand, and multiply each order of the
multiplicand by the multiplier. Write in the product, in each
case, the units of the result, and add the tens to the next higher
result.
To multiply by 10, 100, 1000, etc.
HI. Annex as many ciphers to the multiplicand a^ there are
ciphers in the multiplier.
To multiply by numbers greater than 10.
IV. Multiply the multiplicand by each significant figure in
the multiplier successively, beginning at the right, and place the
right-hand figure of each partial proi net under the order of the
multiplier used. Add the partial products, which icill give the
product required.
Proof. — 1. Repeat the work. 2. Use the multiplicand as
multiplier ; if the results are the same, the xoork is probably cor-
rect.
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78 MULTIPLICATION,
WRITTEN EXERCISES.
130. 1. A drover bought 56 cows at 38 dollars eacli, and
49 oxen at $59 each ; what did he pay for all ?
2. There are 80400 seconds in one day ; how many seconds
are tliere in 397 days ? Ans. 25G60800.
3. A grocer has 48 boxes of r dsins, each box containing 36
pounds ; how many pounds in all the boxes ?
4. A flour merchant sold 286 barrels of flour, each barrel con-
taining 196 pounds ; Low many pounds did he sell ?
5. lu a certain orchard are 15 rows of apple trees ; there are
12 trees in a row and 4500 apples on each tree ; how many
apples on all the trees ? Ans. 810000 apples.
G. One man owes another $118. He gives in part payment
6 sheep at $4 per h?ad, and 3 cows at |27 apiece ; how much
does he still owe him ? Am. $13.
7. A farmer bought 7 cows at $35 each, a span of horses for
$225, 4 calves at $5 each, and a colt for $45 ; what did he pay
for all? Ans. $535.
8. How many lemons in 350 boxes, if each box contains 274
kmons? u4?^s. 95900 lemons.
9. How much would a man earn in 19 years, if he received
a salary of 975 dollars a year ? Ans. $18525.
10. A man bought at one time 14 tons of hay at 16 dollars a
ton, at another time 24 tons at 18 dollars a ton ; what did he
pay for all ? Am. $656.
11. How much more must be given for 96 head of cattle at
47 dollars per head, than for 28 liorses at 155 dollars each ?
12. If 05 ])ushc]s 0^' oats can bo raised on one acre of ground,
how many bushels ran be raised on 96 acres?
13. If a cotton mill manufactures 789 yards of cloth in one
day, how many yards can it make in 805 days?
14. The piufits of a bank amount to $8500 per month ; how
much will they amount to in 15 months ?
3.
APPLICATIONS.
CANADIAN MONEY.
121. Canadian Money is tlic legal currency of the
Domiuioii of Canada. It is composed of dollars, cents, and
mills. The doU<ir is the unit.
The silver coins of the Dominion are the fifty-cent piece, the
twenty-five-cent piece, the ten-cent piece, and the five-cent
piece. The only copper coin is the one-cent piece. The mill
is not coined ; it is used only in computation.
Table of Units.
10 mills (m.) make 1 cent . .
100 cents " 1 dollar . .
SI = 100 ct. = 1000 m.
ct.
1. How many cents in $7?
S()T.UTif)N.— Since in $1 there are 100 ct., in $7 there must be 7 times
100 ct., which are 700 ct.
Obstrvc, that since |1 = 100 ct. = 1000 m., any member of dollara are
expres^si'd \v. cents by annexing two ciphers., in mills by annexing three
ciphers {.\{i9).
2. In $9 how many certs? How many mills? How many
mills in $5?
8. ExprnsH $13 in cents ; $G in mills ; $26;] in cents ; $84 in
mills; $24 in cents.
4. James has $9 all in 5-cont pieces ; how many 5-cent pieces
has he ? How many cents ? How many mills ?
Observe^ mills arc written aftci centb ; IhuB, !f7.4i)5, read 7 dollars 49 cents
5 millt*.
5. Read, $72,439; $37.9.30; $803,072; $300,009; $.570;
I3.C89; $.093; $40,300; $83,007.
0. How many mills in 8 cents? In 25 ct? In $1? In $7?
In $3.43?
7. Express $1 in mills ; $3 ; $1.36; $4.32 ; $.84.
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MV L TIP Lie ATI O iV.
\ ':
WEITTEN EXEECISES.
122. 1. Find the cost of 8 yards of cloth at $2.45 for each
yard. '^
Explanation.— 1. Since 1 yard cost $2.45, 8 yards must
cost 8 times $2.45, whicli are $19.60.
2. We find 8 times $2.45 by multiplying as if there were
no period between the 2 and 45.
3. We put a period in the product two places from the
rig/U, and prefix the sign ($) to the whole.
}?2.45
8
nd.GO
«?
Multiply and explain in this manner the following :
(2)
(3)
(4)
(5)
(6)
$4.87
$9.37
$32.82
$25.49
$8.57
5
9
14
37
28
7. Sold a horse for $195.80, and 45 bushels of wheat at $1.39
a bushel ; how much did I receive for both ?
8. Bought 59 sheep at $3.27 each ; how much did I pay for
the whole ?
9. Find the cost of 45 yards of cloth at $2.85 a yard.
10. At $.435 a pound, what are 73 pounds of coffee worth?
11. A farmer sold 753 bushels of wheat at $1.83 a bushel,
and paid out of what he received $893.57. How much had he
left?
12. A lady bought 7 yards of ribbon at $.45 a yard, 18 yards
of silk at $2.25 a yard, 2 pairs of gloves at $1.50 each, and G4
yards of cotton at $.14 a yard. How much did she pay for the
whole ?
13. A merchant sold in one day 532 yards of cotton at 15 ct.
a yard, 89 yards black clotli at $2.45 a yard, 150 yards of ribbon
at 25 ct. a yard, 3 shawls at $10.75 each, and 47 yards of silk at
$1.85 a yard. What was the amount of all that ho sold during
the day ?
14. What is the cost of 15 cords ef wood at $5.50 a cord?
MULTIPLICATION.
81
MEASUEES OP WEIGHT.
123. Ti*oy Weight is used in weighing gold, silver, and
precious stones, and in philosopliical experiments.
Table of Units.
24 grains (gr.) make 1 pennyweight . pwt.
20 pennyweights " 1 ounce . . . . oz.
13 ounces " 1 pound .... lb.
I I
124. Avoirdupois Weight is used in weighing gro-
ceries and all heavy and coarse articles.
lb.
cwt.
T.
Table of Units.
10 ounces (oz.) make 1 pound . . .
100 pounds " 1 himdredweight
20 cwt. or 2000 lbs. " 1 ton ... .
1 pound contains 7000 grains Troy.
Observe, the old ton of 2240 lb. is still in use.
The following denominations are also used :
100 pounds of grain or flour make 1 cental.
100 pounds of dry fish ** 1 quintal.
100 pounds of nails " 1 cask or keg.
196 pounds of flour •* 1 barreJ.
200 pounds of pork ** . barrel.
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125, 1. How many ounces in 4 lb. 9 oz. Troy?
Solution.— Sine*! In 1 lb. Troy there are 12 oz., in 4 lb. there must be 4
times 12 oz., which is 48 oz. ; 48 oz. plus 9 oz. equal 57 oz.
2. How many ounces in 7 lb. Troy ? In 8 lb. ? In 12 lb. ?
3. How many pennyweights in 3 oz. ? In oz. ? In 10 oz.?
Iu7oz.? In 3 oz. 5 pwt.?
4. In 4 lb. 3 oz. Avoirdupois, how many ounces?
5. How many pounds in 3 T. 170 lb.? In 5 ^J\ 84 lb. ? In
14 T. 230 lb. ?
6
82
.Y ULTiPLICjiTlO X,
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WRITTEN EXERCISES.
126. 1 How many pennyweights in 8 lb. 5 oz. 7 pwt.?
8 lb. 5 oz. 7 pwt.
12
101 oz.
20
Solution.— 1. Since 12 oz. make 1 lb., in
any number of pounds there are 12 times
as many ounces as there are pounds. Hence
we multiply the 8 lb. by 12, giving 96 oz.,
to which we add the 5 oz., giving 101 oz.
2. Again, since 20 pwt. make 1 oz., in
any number of ounces there are 20 times as
many pennyweights as there are ounces.
2027 ])%n.
Henc^ we multiply the 101 oz. by 20 and add in the 7 pwt., giving 2027 pwt.
2. How many grains in 11 oz. 6 pwt. 18 gr. ?
3. What will be the cost of 6 lb. 15 pwt. of goid-dust at $1
a pennyweight ?
4. In 5 cwt. 14 lb. 8 oz., how many ounces?
5. How many pounds in 8 T. 12 cwt. ?
6. What will 2 lb, 5 oz. of candy cost at 2 cents an ounce ?
7. What will be the cost of 1 T. 3 cwt. 75 lb. of Lay at one
cent a pound ?
8. How many pounds in barrels of fiour?
9. Express 8 lb. 8 oz. 17 pwt. in grains.
10. What will be the cost of 5 kegs and 1 1 lb. of naiiH at
4 cents a pound ?
11. Express 8 cw . 29 lb. 14 oz. in oiuaces.
13. In T. 15 oz., how many ounces?
13. What mnst I pay for 28 bar^'els of pork at 12 cents a
pound ?
14. Find the cost of 4 cwt. 56 lb. of sugar at 1 1 cont.s a
pound, and 2 quintals of fish at 7 cents a pound.
15. If it tak-- i <y/.. 4 pwt. of metal to make one tublospo'^r.,
liow many penny vvi-ights will make 18 tablespoons ?
10. How many pcjunds? in lo cwt. ? How many ouncea?
2.
iSw-
%^^'jf,^
wt.?
1 lb,, in
12 times
Hence
1? 96 oz.,
101 oz.
oz., in
iines as
ounces.
2027 i)wt.
t at !|1
unce?
7 at one
r.*'^ liw ^(t
cents a
cont« a
Icsno-^n,
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DIVISION
OUAL EXJSBCISES.
127* 1. In 12 marks how many groups of 4 marks?
l!i marks
3 ffroti2iS of 4 tnarh'Sm
2. IIow \\\u.ny fours iu twelvc'l
8. How many times 3 marks in 15 marks.
/.T marks
fi times 3 mnrhs.
4. TTow many iJtri'es in fifteen?
5. How many times can 6 pears be taken from 18 pears?
(). How many times are 5 ])ears contained in 15 peuirs?
7. The fiign -f- stands for the words "How many times.'*
Thus 15-;-o is read, Iioio maiij/ times 5 in 15.
8. Express by the sign -f- the following :
How many times " in 24?
Bow many times 7 in 35?
How many G's in 30 ?
How many i)'s in 45?
0. Find by subtraction how many 8's in 24.
Thus, 24 - 8 = 10, 10 - 8 :-^ 8, 8 - 8 = 0.
10. Find in the same way how many O's in 54 ; 7's in 50.
il. How could you find how many O's in 54 witluuit sub-
tracting ?
Vi, Finding, by using memorized results, how r.Miny times
one nnml)er is contained in another, is called Division.
13. The number divided is called the Diriflmtl.
14. The number used to divide is called ihe Dirisor.
15. The result found by division is called tlie Quotient,
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DIVISION,
OBAL EXERCISES.
1 28. 1. At 2 cents apiece, how many pencils can I buy for
8 cents.
Solution.— As many pencils as 2 cents are contamed times in 8 cents,
which are 4.
2. How many times 2 cents are 16 cents? 18 cents?
3. At 5 cents per pound, how many pounds of rice can I buy
for 25 cents ? For 40 cents ? For 35 cents ?
4. How many times 3 pounds arc 18 pounds? 27 pounds? "
5. At 4 dollars a pair, how many pairs of boots can be bought
for 36 dollars ? For 28 dollars ?
6. If one top cost 3 cents, how many can I buy for 18 cents ?
For 24 cents? For dO cents?
7. At 4 cents a quart, how many quarts of milk can I buy for
16 cents ? For 24 cents ? For 80 cents ?
8. How many tuucs 3 pears are pears ? 187 pears ? 12 pears 'i
16 p'^ars ?
9. At 4 t^ ]^ars a yard, how many yards of broadcloth can be
bought for 20 dollars ? For 36 dollars ?
10. 28 apples are how many times 4 sipples ?
11. How many times can 4 apples be taken from 20 applen?
From 24 ai)ples? From 36 apjdes?
12. If a n rin tvavol 4 miles in one ho:.r, bow long will it take
him to travo' 45 miles ?
13. How many times 5 mib-i j-re 15 niles? 25 miles? 35
miles ? 55 miles ?
14. TTow many times 3 dollars in 21 d !Jai'=<? In 27 dollars?
In 18 dollars ?
15. If a yard of ribbt)n cost 4 cents, how many yaids can be
bought for 24 cents ? For "3 cents ?
16. How many times 5 bws'aels are 30 bushels? 40 bushels ?
30 bushels? OObusUels? 45 bushels?
I buy
1
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DIVISION.
85
SLATE EXEBCISES.
129. Copy and practice on each of the following exercises,
thus :
3)_8 2)J^ 3)_4 3)_10 2)Jj6 2)_6
1. Observe, the number before the curved line is the divisor
and the one after the dividend. Thus, 2 ) 18 means the same
as 18-^3, and is read 18 divided by 2, or How many 2's in 18?
Observe, also, the quotients are found by using the multipli-
cation table.
2. Write the quotients under the dividends thus :
2)_8 2)J2 2)4 2n0 2)J^ 2)^
3
6
2
8
Having found and written the quotients in this way, erase
them and write them again and again from memory.
Practice in this manner on each of the following exercises.
2)6
2)12
2)2
^)_8
2)16
2)10
2)8
2)20
2)14
2)22
2)18
2)24
3)3
8)24
2
3)18
3)6
3)12
3)_27
8)9
8)30
3)15
8)24
3)21^
3)33
4)12
4)20
3
4)4
4)28
4)44
4)24
4)32
4)8
4)36
4)40
4)10
4)_48
5)^0
5)25
4
5 ) 15
5)5
5)_85
5)20
r3)_45
5)00
5 ) 40
5)55
5)J0
5)50
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DIVISION,
- ;
OBAL AND SLATE EXERCISES.
/
130. Find how many 2's in GO, or divide 60 by 3.
Explanation.—!, We know,
as fliown in the First step, that
in ()0 there are 10 dxcs. We
know aloo, as phown in the Sec-
ond step, that there are 3 twos in
6 ; consequently in 60 there are 10 times 3 twos or 30 tivos. Hence GO-i-2-30.
First step, 60 = 10 sixes.
^Second step, 6-f-2 = o.
Hence 60-^3 - 10 times 3, or 30.
Divide and explain in this way each of the following exam-
ples : »
I. How many 2's in 14? In 40? In 400? In 4000? In
40000 ?
3. How many 3's m 13? In 130? In 170? In 1400? In
16000'^ In 18000?
3. Divide 800 by 3 ; 9000 by 3 ; 36 by 4- ; 24000 by 4.
4. How many 5's in 35? In 1500? In 10? In 1000? In
250? In 4500? In 35000?
5. How many 3's in 18? In 180? In 18000? In 3100?
6. Divide 340 by 3 ; 8000 by 4 ; 16000 by 3 ; 28000 by 4.
7. Divide 450 by 5 ; 35000 ^y 5 ; 30000 by 4 ; 25000 by 5.
8. How many 3's in 969 ?
Observe, that 969 = 900 + GO + 9, and that you can find at once the number
of S't" in cjach of these part:?, and then add the resuUs, which will give the
8'6 in 909 thus :
( 900 -^ 3 = 300 )
969 -r- 3 = ] 60 -f- 3 = 20 >• = 333.
( 9 -^- 3 = 9 )
9. How many 2's in 286 ? In 644 ? In 868 ? In 686 ?
10. Divide 888 by 4 ; 699 by 3 ; 484 by 4 ; 24864 by 3.
I I . How many 3's in 969 ? In 639 ? In 396936 ? In 93600 ?
In 3G00OO ? In 693000 ?
13. How many 5'« in 035 ? In 985 ? In 775 ? In 8495 ? lu
C3;35 ? In U5 '^
t
DIVISION,
87
know,
\ep, that
\s. We
the Sec-
\iwos iti
■2^30.
SLATE EXERCISES.
131. Copy each of the following exercises on your slate,
and practice in writing- the quotients at sight of the divisor and
dividend, as directed in (liiO).
1
G)_18
6)24
7)^8
7)70
8)^3
8)16
6 HO
6 )60
7)35
7)21
8^
8)64
6)J:3
6 )54
7)_56
7)_63
8)40
8)96
6)^
6)73
3
7)14
7 )43
8)_56
8)48
6 )36
6)48
7 )77
7)84
8)_73
8)34
6)^3
6)^6
7)_7
7 HO
8)_88
8)80
9)J17
9)18
9)J.5
9)63
9)9
9)90
9)36
0)99
9)81
9)^54
9) 108
132. Divide and explain each of the following examples as
directed in (130).
1 . How many 6's in 30 ? In 346 ? In 3400 ? In 24000 ?
2. How many 8'9 in 50? In5G00? In 3300 ? In 72000?
3. Divide 45 by 9 ; 4500 by 9 ; JJ5 by 7 ; 35000 by 7 : 0400
by 8.
4. Divide 490 by 7 ; 40 by 8 ; 4000 by 8 ; 0300 by 9.
5. How mnny 9's in 450? In 7300? In 54000? In 81000?
6. How many 7's in 380 ? In 4300 ? In 0300 ? In 35000 ?
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88 DIVISION.
WEITTEN EXERCISES.
133. 1. At 4 dollars per barrel, how many barrels of flour
can be bought for §3600 ?
3. How many barrels of apples at $3 per barrel can be bought
for!ft690? For $936?
3. If a ton of coal cost $T, how many tons can be bought for
$147? For!ft3507? For $6300?
4. If a man can earn two dollars a day, how many days will
it take him to earn ,$862 ?
5. At !^5 a cord, how many cords of wood can be bought for
$3500" For $1550? For $4500?
6. If a steamboat run 9 miles an hour, how long will it take
her to go 7200 miles ?
7. If 6 yards of cloth make a suit of clothes, how many suits
cin be made from 3600 yards ? From 4800 yd. ?
8. How many sheep at $4 apiece can be bought for $160 ?
For $280 ? For $3608 ? For $240.8 1
9. If Charles can earn $8 in one week, in how many weeks
can he earn $240 ? $480?
10. At $5 a week, how many weeks' board can be had for
$100 ? For $150 ? Foi; $350 ? '
11. If a stage-coach travel 7 miles an hour, how many hours
will it take her to travel 4200 miles ?
12. A farmer put two bushels of grain in a bag ; how many
bags will it take to h old 4682 bushels ?
13. How many times 3 is 9630! Is 3690? Is 9369?
14. How many calves at $4 apiece can be bought for $2184 ?
For $2800? For $3608?
15. How many times 6 cents are 5460 cents? 1260 cents?
4806 cents ? 3606 cents ?
16. At 4 dollars a barrel, how many barrels "f n]iples can be
bought for 2 180 dollars f For $2840 ? For $3080 ?
17. Divide 284840 by 4 ; by 2.
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DIVISION.
89
OBAL AND SLATE EXEBCISES.
134. 1. How many 4*8 in 14 and how many remaining?
Observe, tht . -^-ou know from the multiplication table that Z fours are 12,
and hcDce you c,.. iell at ouce that 14 contains 3 fours and 2 remaining.
Find in this manner orally the quotient and remainder for
each of the following examples. Then practice upon your
slate in writing the quotients and remainders under each exam-
ple, separating them by a dash, thus :
3)7
5)28
4)36
8)39
3)17
8-1
5—3
6—3
4-7
5—3
^L? ^Ii5 ^11? ^\3 ^)i? ^\3 ^L?? ^11?
4)J1 4)^ 4)33 4)_29 4)J0 4)_13 4)^ 4)J4
5)19 5)34 5)33 5)43 5)29 5)43 5)33 5)33
6)^ Q)m 6)^ 6)^ %)JA 6)_59 6)_33 6)_51
6)58 6)5^ 6)38 6)^ 6 HO' 6^ 6)^ 6)58
7^ 7)^32 7H5 7)_37 7)_35 7)_01 7)^ 7)_60
7)36 7)38 7)53 7)09 7)41 7)53 7)66 7)40
8)19 8)_3G 8)_39 8 )_33 8 )_33 8 )_47 8 1^30 8 )J6
8)38 8)44 8)31 8)33 8)49 8)51 8)38 8)53
9)_24 9)^43 ^)m 9)^79 9)J)0 9)^9 9)^ 9)80
9)30 9)53 9)39 9)87 9)60 9)40 9)39 9)70
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TEST TARGET (MT-S)
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Photographic
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33 WIST MAIN STRHT
WIBSTIR.N.Y. MSaO
(716) 873-4503
90
DIVISION.
OBAL AND WRITTEN EXERCISES.
i
1*55. 1. If one marble cost 4 ct., how many marbles can I
buy for 38 ct., and how many cents remaining V
Solution.— I can buy as many marbles as 4 ct. are contained times In
88 ct., which are 9 and 2 cents remaining.
2. At 6 cents apiece, how many oranges can be purchased for
60 cents ? For 68 cents ? For 79 cents ?
3. If one pound of sugar cost 9 cents, how many pounds can
be bought for 79 cents ? For 84 cents ?
4. At $8 per ton, how many tons of hay can be bought for
$499 ? For $579 ? For $7509 ?
5. If 3 yards of cloth make one coat, how many coats can be
made from 378 yards? From 467 yards?
6. How many times con 5 yards be cut from 359 yards?
From 3058 yards ? From 5556 yards ?
7. In one week there are 7 days ; how many weeks in 489
days? In 3509 days?
8. How many times 4 days are 49 days? 246 days? 15487
days? 60480 days?
9. If 5 bushels of wheat make a barrel of four, how many
barrels can be made from 5059 bushels?
10. There k o 7057 apples in a bin ; how many times can I
take out 2 apples 1 6 apples ?
11. If a boy save $3 a week, how many weeks will it take
him to save $3290 ? $2734 ?
13. At $6 a cord, how many cords of wood can be bought for
$540 ? For $529 ? For $388?
1-3. How many times 8 cherries in 65 cherries? In 76? In
60? In 73? In 79? In 56?
14. If a man build 4 rods of fence in one week, how many
weeks will it take him to build 29 rods? 37 rods? 60 rods?
408 rods?
15. Divide 357 by 4 ; by 6 ; by 8 ; by 9.
1
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DIVISION.
91
SLATE AND WRITTEW EXERCISES.
13G. 1. Find how many 4's in 1-19G.
4 ) 1496 ( 300
(1) 4 X 300 = 1200
396
(3) 4x70 = 380 70
16
(3) 4x4 = 16 4
UencG the quotient is 374
3. The 16 remaining contains
contains 300+10+4 = 374 fours.
Explanation.— 1. We divide 1400
i)y 4 (130), and find lliat it contains,
as (<liowu in (1), 300 fours, equal 1200.
Subtracting 1200 from 1490, we liave
296 yet to be divided.
2. We now divide 290 by 4 (130)
and find that it contains, as shown in
(2), lOfaun; equal 280. Subtracting
the 280 from the 296, we have 16 yet to
be divided.
4 fours, as shown in (3) ; hence the 1496
Perform the division and explain in this manner each of the
following examples :
3. 1573-^3.
3. 1041 -f-3.
4. 1100-^3.
5. 3348-J-4.
G. 4365^9.
7. 1935-^-5.
8. 3478-4-7.
9. 5873-5-8.
10. 5993-f-7.
11. 3888-^6.
13. 6373-5-9.
13. 6873-f-8.
14. If one cord of wood can be bought for 14, how many
cords can be bought for $348 ?
Solution.— As many cords can be bought as $4 are contained times in
$348. Hence, $348+$4 = 87, the number of cords that can be bought.
15. At $7 a barrel, how many barrels of flour can be bought
for $ 413 ? For $581 ? For $3035 ?
10. A lady received $9 a week for teaching and was paid in
all $351 ; how many weeks did she teach ?
17. A f.irraer sold a piece of land at $8 an acre, and received
in all $1433 ; how many acres did ho sell ?
18. At $6 a ton, how many tons of coal can be bought for
$348? For $558? For$3l'r8?
10. At $5 a yard, how nuvny yards of cloth can be bought for
$385? ForiS;875? For $335?
92
DIVISION,
EXERCISES ON CONTRACTED FORM.
137. Find how many 7's there are in 3G95.
(1)
7 ) 2G95 ( 300
7x300= 2100
595
7x80 = 560 80
35
7x5 = 35 5
(3)
7 ) 2695 ( 385
21
59
56
35
85
Explanation.— 06scre>«, first, that the form in (1) is the same as tliat on
which practice was given in the last exercise. Observe, second, that in the
form in (2) the worls: is shortened thus :
1. The multiplication of the divisor 7 by each of the partial quotients is
not written, as in (1).
2. The ciphers are omitted from the products 2100 and 5»j0, the significant
figures 21 and 56 being in each case placed so that the order of the dividend
they are under indicates the order they represent.
3. Only one figure of the dividend is taken down at a time, this being all
that is necessary to give another quotient figure.
Perform the division in each of the following examples, and
■write the work on your slate, as shown in (2).
1.
874-f-2.
12.
2915-5-5.
23.
4865-5-7.
2.
1678-5-2.
13.
4434-5-6.
24.
6642-^9.
3.
1578-^2.
14.
5022-5-6.
25.
5373-4-9.
4.
1035-5-3.
15.
2910-5-6.
26.
7524^9.
5.
2214^3.
16.
3759-5-7.
27.
5688^6.
C.
1752^-3.
17.
0041 -^ 7.
28.
1S954-5.
7.
2572-5-4.
18.
5243-^7.
29.
8613-5-9.
8.
3350 -t-4.
19.
6096^8.
30.
1971-5-3.
0.
1556-f-4.
20.
4632^8.
81.
4784-5-8.
10.
3090-^5.
21.
0064-5-8.
32.
5751-5-9.
11.
i„3:]5-5-5.
22.
3908-4-8.
83.
8613-5-9.
1
1
DIVISION.
93
DBM.
as that on
that in the
uotients is
significant
le dividend
is being all
pies, and
!h-9.
!-;-9.
-^5.
-f-9.
-1-3.
-h8.
-f-9.
-^9.
■
SLATE AND WBITTEN EXEBCISES.
Short Division,
138. 1. Find how many 7's there are in 2695, thus :
7 ) 2095 Explanation.— The work is shortened still more by
I writing only the quotient figures, and holding all the niim-
385 bers in the memory while performing the required oper-
ations, thus:
1. We observe, as in the former plan of working, that 7 is contained
3 hundred times in 26 hundred. Writing the 3 under the hundueds of the
dividend to show that it represents hundreds, we subtract mentally 3 hiiri'
dred times T, or 21 hundred, from the 26 hundred, leaving 5 hundred, or 50
tens, to which we add the 9 (ens of the dividend, making 59 tens.
We proceed in the same manner with the tens and units.
Division by numbers not greater than 13 should always be
performed in this manner. Nothing should ever be written
but the quotient.
This form of division is called Short Division.
Divide and explain in this manner the following :
2. 4018-' 7.
3. 1985-f-5. •
4. 5912^8.
5. 3924-^9.
6. 29432-J-4.
7. 34188-5-6.
8. i4511-^3.
9. 12820-4-5.
10. 68901^7.
11. 38742-i-6.
12. 30976-5-8.
13. 32661 -^9.
14. If a boy earn l"^ in one week, how many weeks will it
take him to earn $2569 ?
16. If a canal-boat travel at the rate of 8 miles per hour,
how long will it take her to travel 4344 miles ? 5376 miles ?
3784 miles ?
16. How many times can 9 bushels of wheat be taken from
7881 bushels ? From 2457 bushels ?
17. How many pieces, each 7 inches long, can be cut from a
roll of paper 3045 inches long ?
18. How many times are $9 contained in $8040 ? In $8415 ?
'i
'.4
i'i
94
DIVISION.
ARITHMETICAL TABLE No. B.
ij^
A.
B.
c.
i>.
K.
F.
«.
H.
1.
J.
1.
4
1
3
9
8
4
7
2
8
7
3
9
5
6
G 8
9 2
2.
;{.
5
2
7
3
8
4
6
3
8
9
6
2
5
7
8
4
7
7
D
4
a
S 7
5 8
8 J
4.
r».
«.
3
7
5
8
3
'2
G
4
9 7
7.
5
S
2
5
9
7
4
3
7
9
3
G
8
4
6
9
o 9
6 8
8.
O.
it
o
9
6
8
O
9
2
5 4
lO.
6
o
4
7
8
8
4
9
5
6
4
9
3
7
7
8
3
6
9
8
8
7
5
4 9
5 8
11.
Iti.
9
7
189. Copy examples from this table as follows :
Dividend three fifjures ; Divisor ofu\
1. Comn^ence opposite 2, and take the numbers for dividends
from Aiic, tlien from BCD, then cde, def, efg, ran, ghi, iiij.
3. For oav?h t^xample, take as the divisor the figure imme-
diately above the right-hand figure of the dividend.
The first six examples from columns abc are :
8)194 4)530 6)383 3)748 8)375 5)539
Dividend five fiffures ; Divisor one.
1. Commence opposite 2, and take the dividend from columns
AncDR, then from bcdep, then cdefo, defgii, efottt, foittj.
3. Take as the divisor, in each example, the figure imme-
diately above the right-hand figure of the dividend.
DIVISION,
95
8.
- —
1.
J.
<J
cV
9
^J
3
7
8
S
9
7
ft^
)
U
>
8
EXEHCISES ON EQUAL FABTS.
140. 1. Make 13 into two equal paris.
12-^-2 = 6
Hence 12 = 2 sixes.
'ExvLANATion.— Observe, that in 12+2=6
the divisor denotes how many times the
quotient 6 can be taken out of 12. Conse-
quently the quotient 6 is one of the two equal parts of 12, and hence 12 =
(j + G.
2. Find one of the two equal parts of 12 ; of 16 ; of 18 ; of 20 ;
of 10; of 16 ; of 14 ; of 24 ; of 22 ; of 56 ; of 08.
3. One of the two equal parts of a number is called one-
hdl/'f and is written 1 over 2, thus J. J of 12 is 12-f-2 = 6.
4. Find one of the . ree equal parts of 12 ; of 18 ; of 27 ; of
15 ; of 33 ; of 24 ; of 36 ; of 99 ; of 48 ; of 87.
5. One of the tJiree equal parts of a number is called one-
thirdf and is written 1 over 3, thus J. J of 15 is 15-^3 = 5.
6. One of the four equal parts of a number is called o^ie'
fourth ; one of the fim equal parts one-fifth, and so on.
7. One of any number of equal parts of a number is written
by placing one over the number that denotes the number of
equal parts into which the given number is made, thus :
One -fourth is written \.
One-Jifth is written l.
One-sixth is written J.
One-tenth is written -j^^
One-twelfth is written ^-^
5.
— ( .
\ of 20 is 20-T- 4
\ of 35 is 35-^ 5
J of 24 is 24-^ G :^^ 4.
-iVof 80is>i0^10
-iV of 84 is 84-r-12 --.
*M
:i
•4
t
t
'J
And so on Avith any number of equal parts.
8. Find onc-eightJi of 8 ; of 24 ; of 48 ; of 50 ; of 73 ; of 40 ;
of 96 ; of 500 ; of 480.
9, If a house and lot is worth $5050, what is one-fourth of it
worth? One-half of it?
96
DIVISION.
WRITTEN EXERCISES.
141, 1. If 60 cents be equally divided among 3 beys, how
many cents will each have ?
3. If 9 oxen cost 480 dollars, what is the price of one ox ?
3. If 8 yards of tweed cost 792 cents, what does one yard
cost?
4. Sold 7 tons of hay for .$119 ; how much did T receive for
one ton V
5. A company of 8 persons own equal shares in a store worth
$25672 ; what is each man worth ?
6. If $5484 be divided into 3 equal parts, what is the value
of each part ?
7. There are 7 farms of equal size that contain in all 2415
acres ; how many acres in each farm ?
8. A farmer has 3864 bushels of wheat, which fill 8 bins of
equal size ; how many bushels in each bin?
9. A father left an estate of $37805 to be divided equally
among his five sons ; how much would each receive ?
10. A grocer bought 7 chests of tea of equal size ; there were
1757 pounds in all ; how many pounds in each chest ?
11. If a railroad train moves 250 miles in 8 hours, how many
miles does it move per hour ?
12. Sold 9 acres of land for $882 ; how much did I receive
for one acre ?
13. Divide $9324 equally among 6 men.
14. A railroad, owned by 9 men who paid equul sums fo»
building it, cost !?258876 ; what did it cost each man ?
15. A grist mill is worth |38052 ; what is one-fourth of it
worth? One-sixth? One-twelfth?
16. Bought 5 houses for $40325 ; how much did I pay for
^ach house ?
17. Sold 4 horses for $580 ; how much did I receive for each
lio vse ?
lcft^
DIVISION.
97
3 bcytf, how-
one ox ?
>es one yard
receive for
store Avorth
s the value
in all 3415
• 8 bins of
ed equaJly
?
tliere were
?
Uow many
I receive
sums fot
rth of it
■ pay for
for each
11
SLATE AND BOARD EXEBCISES.
142 Divide 14800 by 37.
87 ) 14800 ( 400 Explanation.— When the divisor contains
1 AACiCi ^^^ ^^ more figures, we can find the quotient
i'toUU figures by finding how many times the left-hand
^T-'^ ,f the divisor is contained in the fewest
left-hand figures of the dividend that will contain it.
Thus ;], the left-hand figure of the divisor, is contained 4 times in 14, the
two left-hand figures of the dividend ; hence we conclude that 37 is con-
tained In 148 hundvA 4 hundred time •, Multiplying 37 by 4(X/, we find that
.37 X 40() = 14800. Hence 400 is the correct quotient.
Divide in this way the following :
1. 2220-1-74. 7. 60500^65.
3. 7470-J-83.
3. 4340^62.
4. 2100-f-o4.
5. 7C50-i-85.
6. 7360-5-92.
8. 12600^42.
9. 43500-5-87.
10. 28800-5-32.
11. 26500^53.
12. 63600-5-67.
13. 525000-5-75.
14. 252000-5-84.
15. 558000-5-93.
16. 087000-5-43.
17. 768000^96.
18. 623000-5-89.
19. Divide 27300 by 39.
3y ' 27300 ( 700 Observe^ that by pursuing the same course as
' oiyoAA before, we find in this example that 3, the left-
"^^ ^ hand figure of the divisor, is contained 9 times in
27, the two left-hand figures of the dividend ; but
when we mult'ply 89 by 900 we have 85100, a number greater than the divi-
dend, and hence 90' is not the correct quotient. Trying 800 in the same
manner, we find it is too large a quotient ; hence we take 700, which we
find to bo the correct quotient.
The correct quotient figure in examples of this kind can be
found only by trial.
Perform the division in the following:
1. 1350-5-27.
2. 2340-5-39.
8. ll200-^2S.
4. d3600-5-43.
5. 342000-5-38.
6. 20800C-^26.
7. 358000-^25.
8. 273000-5-35.
9. 415000-*-45.
;3
k
:i
t
'5
08
Dl VIISION.
1
SLATE AND BOABD EXEKCISES.
Long Division,
143. 1. Divide 9282 by 26.
26 ) 9282 ( 357
78_
148
130
182
182
Explanation.— 1. When the divisor consists of
two or more figures, the reoults caunot be held in
the memory while we perform the operations ;
hence we proceed thus :
2. We find by trial that 26 is contained in 92
hundred 3 hundred times. Multiplying' the divisor
26 by 3 hundred^ we have 78 hundred, which we
subtract from the 92 hundred, leaving 14 hundred,
or 140 fens, to which we add the 8 tens of the divi-
dend, giving 148 tens.
3. We now find by tried that 26 is contained in 148 tens ^ (ens times.
Multiplying the divisor 26 by 5 tens, we have 130 tens, which we subtract
from the 148 tens, leaving 18 tens, or 180 units, to which we add the 2 units
of the dividend, giving 182 units.
4. We find again by trial that 26 is contained in 182 units 7 units times.
Multiplying the divisor 26 by 7 we have 182, which takon from 1R2 leaves
nothing ; hence the division is complete, and 357 is the quotient of 9282
divided by 26.
P(
jrfonn and explain the division in the follow]
ing:
1.
1125-5-45.
13.
649-5-36.
25.
59653-5-187.
2.
5976-^-83.
14.
120597-J-328.
26.
140378-5-276.
3.
2623-1-43.
15.
46648-^136.
27.
250489-5-382.
4.
16002-^63.
16.
63455^259.
28.
480159^699.
5.
28952-5-56.
17.
92115-4-345.
29.
630121-5-798.
6.
57810-^-94.
18.
91093-5-239.
30.
132525-4-285.
7.
18430-4-81.
19.
103326-5-568.
31.
684187^168.
8.
29822^31.
20.
80307-^439.
32.
89458-4-137.
9.
43890-^93.
21.
100192^351.
33.
361246-4-476.
10.
127098-^614.
22.
120058-5-228.
34.
80084-5-292.
11.
228984-^203.
23.
22796-4-48.
OK
292082-4-387.
12. 48204^-309.
24. 120223-4-64.
36. 77728-4-145.
No
un
GH
ab
ui
al
b
fc
DIVISION,
99
:S£S.
isor consists of
inot be held in
ie operations ;
ontainecl in 92
i»^- the divisor
'ed, vvliieh we
ig 14 hundred,
ms of the divi-
w ^ (eiis times,
ch we subtract
dd the 2 units
f 7 units times,
om 182 leaves
aotient of 9288
59653
i0378
50489
10159
10121-
2525-
4187-
D458-
1246-
3084-
JC82H
f728-f-
i-187.
-5-276.
■f-382.
^699.
-798.
f-285.
-168.
-137.
-476.
-292.
-387.
145.
SLATE ANB OHAL EXERCISES.
144. Take examples lor practice from Arithmetical Table
No. 5, p. 94, as follows :
Dividend four figures ; Divisor two,
1. Commence opposite 2, and take the dividends from col-
umns ABCD, then from bcde, then cdef, defo, efgh, fghi,
GHIJ.
2. For each example take as divisor the figures immediately
above the two right-hand figures of the dividend.
The first five examples from Cv iumns abcd are :
85)_1947 47)_5369 69)^836 36)^8^ 82 ) C7^8
Dividend six figures / Divisor three,
1. Commence opposite 2, and take the dividends from col-
umns ABCDEF, then BCDEFG, CDEFGH, DEFGHI, EFGHIJ.
2. For each example take as divisor the figures immediately
above the three right-hand figures in the dividend.
1. At 12 cents a pound, how many pounds of sugar can be
bought for 36 cents ? For 60 ct. ? For 96 ct. ? For 120 ct. ?
Solution.— Since 1 pound cost 12 cents, as many pounds can be bought
for 30 cents as 12 cents are contained times in 36 cents, which are 3.
3. At $3 a yard, how many yards of cloth can be bought for
$6? Forij^lS? For|75? For $861 ?
3. How many melons at 9 cents each can be bought for i'7
cents ? For 81 cents ? For 815 cents ? For 657 cents ?
4. Tf a man earns $5 a day, in how many days can he earn
$15? $25? $40? $50? $500? $450?
5. At, $4 n head how many sheep cnn be bought for $24?
For$SG? For $48? For $80? For $280?
II'
Ny
I
t
I'l
100
DIVISION.
OBAL AND WRITTEN EXERCISES.
,
. i
14o. 1. If 24 cents are divided equally among G boys, how
many cents will each boy receive ?
Solution.— To give each boy 1 cent requires 6 centti. Hence each boy
will receive as many cents as 6 cents are contained times in 24 cents, which
are 4.
2. What is the price of 1 yard of ribbon, when 5 yards cost
25 ct. ? 35 ct. ? 45 ct. ? 80 ct. ? 100 ct. ? 400 ct. ?
8. How m^lch does a man earn each month, if he receives for
6 months work |56? $60? $150? $360?
4. What is the price of one acre of land, when 7 acres cost
$21? $35? $42? $56? $63? $140? $280?
5. If 3 yards of silk cost $9, what will be the cost of 8 yards ?
Of 12 yards ? Of 15 yards ? Of 45 yards ?
Solution.— Since at $9 for 3 yards the price of 1 yard is $3, the cost of
8 yards is 8 times $3 or $24.
6. If 5 peaches cost 15 cents, what will be the cost of 3
peaches ? Of 7 peaches ? Of 12 peaches ? Of 25 peaches ?
7. If 9 oranges cost 36 cents, what will be the cost of 4
oranges ? Of 16 oranges ? Of 32 oranges ? Of ??7 oranges ?
8. If 25 yards of cloth cost $75, what is the cost of one yard ?
Of 5 yards ? Of 9 yards ? •
9. I paid $270 for 15 tons of hay ; what did I pay for one ton?
For 4 tons ?, For 7 tons ?
10. If James can hoe 336 rows in 21 days, how many rows
can he hoe in 5 days ? In 16 days ?
11. A drover bought cows at $42 per head, and paid for all
$13440; how many did he buy?
12. A grocer bought 283 barrels of molasses, for which he
paid $7358 ; what was the price of one barrel? Of 35 barrels?
Of 160 barrels ?
13. How many pounds of butter at 24 cents per pound will
pay for 16 yards of calico at 12 cents a yard?
el
3
'K.
!ISES.
; boys, how
lence each boy
84 cents, which
5 yards cost
?
! receives for
7 acres cost
of 8 yards?
|3, the cost of
3 cost of S
eaches ?
» cost of 4
ranges ?
one yard ?
3r one ton ?
nany rows
aid for all
which he
) barrels ?
)und will
DIVISION. 101
WBITTEN EXERCISES.
146. 1. If a man earn $325 a year, how long will it take
him to earn $2925 ? $4225 ?
2. A drover paid $8375 for 67 horses ; what did he pay for
each ? What did he pay for 16 horses ?
3. I have a farm worth $8460 ; what is one-half of its value ?
Oue-third V One-f ou rth ? One-fifth ?
4. How many barrels of apples at $4 per barrel will pay for
2 barrels of sugar at $14 a barrel, and 4 pounds of tea at one
dollar a pound ? •
5. If 345 bushels of wheat weigh 11040 pounds, what is the
weight of one bushel? Of 28? Of 96? Of 150?
6. Divide 165164 into 314 equal parts.
7. A farmer raised 2470 bushels of oats on 65 acres of land ;
how much did he raise on 9 acres ? On 20 acres ? On 28 acres ?
On 46 acres ?
8. How many barrels of potatoes at $2 a barrel must be given
for 7 barrels of flour at $8 a barrel ?
9. A person sells 5 cows at $25 each, 8 horses at $75 each,
and agrees to take his pay in sheep at $5 a head ; how many
sheep does he get ?
10. A father dying left an estate of $48064 to be equally
divided among his wife, four sons, and three daughters ; how
much does each receive ?
11. How many dozen of eggs at 12 cents per dozen must be
given for 4 boxes of raisins, each containing 15 pounds, at 15
cents per pound ?
12. In one pound there are 16 ounces ; how many pounds in
15808 ounces ?
13. Divide $97128 into 213 equal parts.
14. I have $60250, with which I buy land at $125 an acre;
how many acres can I buy ?
15. Divide 38950 into 25 equal parts.
K
( ! 'I
I
w
4
t
11
103
D [VISION,
!
, ^
DEFINITIONS.
147. Division is the process of finding how many times
one number is contained in another.
148. The Dividend is the number divided.
141), The Divisor IB the number by which the dividend
is divided,
150. The Quotient is the result obtained by division.
151. The RetnainderiB the part of the dividend left
after the division is performed.
152. Short Division is that form of division in which
no step of the process is written.
1 5?-$. Long Division is that form of division in which
the 8iMractio?i necessary in the process is written.
I 1
I It
BULE.
154. /. Find hoto many times the dimsol' is contained in the
feioeat figures at the left of the dividend that will contain it, and
lorite the resvltfor the first figure of the quotient.
II. Multiply the dioisor by this quotient figure, and subtract
the remit from th" part of the dividend that was used; to the
remainder annex the next lower order of the dividend for a new
partial dividend and divide as before. Proceed in this manner
mth f>ii:h order of the dividend.
III. If there he at last a remainder, place it after the quotient,
with the divisor underneath.
Proof. — Multiply the divisor hy the quotient and add the re-
mainder, ifttny, to the product. This result will he equal to the
dividend, whtu uie dioldon has been performed correctly.
ow many times
APPLICATIONS.
the dividend
y division,
dividend left
ision in wliicli
sion in which
stained in the
mtam it, and
and siibtract
rtst'd; to the
'id for a new
this maimer
the quotient.
add the re-
equal to the
ttly.
OBAIi AND SLATE EXERCISES.
155. Dv\f Measure is used in measuring grain, fruits,
etc.
Table of Units.
2 pints (pt.) make 1 quart . . . qt.
8 quarts " 1 peck . . . pk.
4 pecks " 1 bushel . . bu.
1. In 1 peck how many pints ? In 2 pecks? In 8 pecks?
In 24 quarts ? In 3 bushels ? In 10 bushels ?
2. In 448 pints how many pecks ?
Solution.— Since 2 pints make 1 quart, 448 pints must make as many
quints at» 2 quarts are contained times in 448 quarts, which are 224.
Ai^ain, s^iince 8 quarts make 1 peck, 224 quarts must make as many pecks
as 8 quarts are contained times in 224 quarts, which ai'e 28.
Hence in 448 pints there are 28 pecks.
8. How many bushels in 540 pk. ? In 2080 qt. ? In 1088 pt. ?
In 23272 pt. ? In 15104 qt. ?
4. At 8 cents a quart, how many bushels of peaches can be
bought for $15.36? For $20.48? For $23.04?
Solution.— Since $15.36 are equal 1536 cents, as many quarts of peaches
cuu be bought I'ur $16.36 as 8 cents are contained times in 1536 cents, which
arc li*2, and 192 quarts make 6 bushels.
Observe^ tlie dividend is changed to cents to be of the same name as the
divisor.
5. At 12 cents a peck, how m<j,ny pecks of pctatoes can be
bought for 48 ct. ? For 72 ct. ? For .$8.76 ? For $64.50 ?
6. At 25 cents a yard, how many yards of cloth can bo bought
for for 50 cents? For 75 ct. ? For $1 ? For $9 ?
7. At $4 per chair, how many cliuirs can bo bought for $112?
For $218? For>»^856?
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104 DIVISION,
ORAL AND SLATE EXERCISES.
156. Liquid Pleasure is used to measure all kinds of
liquids.
Table of Units.
4 gills (gi.) make 1 pint . , . pt.
3 pints " 1 quart . . . qt.
4 quarts " 1 gallon . . gal.
31 J gallons " 1 barrel . . bbl.
63 gallons " 1 hogshead . hhd.
1. How many pints in 12 qt. ? In 25 qt. ? In 10 gal. ? In
30 gal. ?
2. How many gallons in 16 qt. ? In 28 qt. ? In 64 pt. ? In
96 pt.? InieOpt?
3. Express 48 pints in gallons ; 72 gills in quarts.
4. In a cistern there are 2835 gal. of water ; how many hogs-'
heads does it contain ?
5. If one quart of molasses cost $.23, what will be the cost
of 4 gal.? 7 gal.? 18 gal. ? 2hhd.V
6. In 5 lihd. how many qt. ? How many gills?
7. At 4 cents a pint, how many gallons of milk can be bought
for $4. 48? For $8.64? For $9.60?
Solution.— 1. Since 1 gallon makes 8 pints, at 4 cents a pint 1 gallon can
be bought for .32 cents.
8. Since 1 gallon can be bought for 32 cents, as many gallons can be
bought for $4.48, or 448 cents, as 32 cents are contained times in 448 cents,
which are 14.
8. At 5 cents a pint for vinegar, how many gallons can be
bought for $4.40? For $5.60? For $7,60?
9. When maple syrup costs 16 cents a quart, how many gal-
lons can be bought f or $1 . 28 ? For $7. 68 ? For $47. 30 ?
10. At cents a quart, how many gallons of kerosene can be
bought for $1.44? For $2.52? For $3.24? For $26.64?
Ex>
3.
3.
4.
DIVISION.
105
Ib'S.
U kinds of
)gal. ? In
14 pt? In
aany hogs-'
e the cost
be bought
i gallon can
Dns can be
I 448 cents,
s can be
lany gal-
e can be
4?
EXERCISES ON EXACT DIVISORS.
1 *>7, 1. What numbers will divide 13 without a remainder ?
A nnmber that \*Ill divide another without a remainder is called an
Exact Divisor.
t
Fiud all the exact divisors of each of the following numbers :
2. 15.
5.
20.
8.
42.
11.
40.
14.
48.
3. 21.
6.
27.
9.
36.
12.
56.
15.
33.
4. 35.
7.
30.
10.
28.
13.
63.
16.
64.
17. Wliat number is an exact divisor of each of the numbers
4, 0, and 10 ? Of each of the numbers 9, 15, and 27 ? •
A number which is ai) exact divisor of each of two or more numbers is
called a Common Divisor.
18. Find the common divisors of each of the following sets of
numbers :
13 and 16.
15 and 25.
18 and 30.
42 and 28.
36 and 63.
60 and 84.
55 and 45.
40 and 64.
48, 28, and 32.
15, 45, and 36.
54, 18, and 48.
28, 42, and 63.
19. What is the Greatest Common Divisor of 8 and 12 ? Of
18 and 30 ?
The greatest number that is an exact divisor of each of two or more num-
bers is called the Oretttrst Common Divisor,
20. Find the greatest common divisor of each of the follow-
ing sets :
15 and 20.
80 and 31.
18 and 27.
82 and 72.
45 and 54.
42 and 35.
23, 55, and 99.
80, 60. and 84.
54, 63, and 72.
21. Wliat is the greatest common divisor of $10 and $15 ?
Of |20 and $50 V Of -f 3o and $84 V 01 ij)^:5 and $63 ?
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106 DIVISION.
EXERCISES ON MULTIPLES.
158. 1. Twenty-four is how many times eight f How
mauy times six? How many times ticeUe f How many times
twenty-four?
A number which is one or more times another number is called a Mul-
tiple of that number.
2. What is a multiple of 3? Of 6? Of 4? Of 8? Of 10?
Of 7? Of 11? Of 9? Of 12?
3. Name three multiples of 9 ; of 5 ; of 8 ; of 12.
4. Find the first three multiples of 17 ; of 23 ; of 29.
Thus, Ist multiple is 1 ; , 2d multiple 17 x 2 = 34, 3d multiple 17 x 3 = 51.
5. Find the first 4 multiples of 25 ; of 37; of 63; of 95; of
84 ; of 235 ; of 347 ; of 836 ; of 793 ; of 965.
6. How many multiples can you find for 19? For 35? For
69 ? For any given number ?
7. Find a number which is a multiple of 4 and of 6.
Thus, 4 X 6 = 24, hence 24 is a multiple of both 4 and 6.
8. Find a number which is a multiple of 7 and of 9 ; of 5 and
of 8 ; of 6 and of 11 ; of 3 and of 9 ; of 9 and of 12.
A number which is a multiple of two or more numbers is called a Com-
mon M%iltlplH of these numbers.
9. Of what numbers is 12 a common multiple f Is 21 ? Is 45 ?
Is 63? Is 48? Is 72? Is 64? Is 88? Is 108?
Find a common multiple :
10. Of 5 and 8. 13. Of 7 and 19.
11. Of 9 and 6. 14. Of 4 and 2*.
12. Of 12 and 7. 15. Of 5 and 37.
16. Of 13 and 29.
17. Of 32 and 28.
18. Of 43 and 15.
I'J. Of how many cents is 20 cents a- multiple? 30 cents?
25 cents ? 56 cents ? 72 cents ?
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nrjUf How
many timegs
called a Mul-
>f8? Of 10?
f29.
le 17x3 = 51.
J3; of 95; of
ror35? For
>f 6.
• 9 ; of 5 and
called a Com-
i21? Is 45?
f 13 and 29.
e 32 and 28.
' 43 and 15.
30 cents?
J
FRACTIONS.
ORAL EXERCISES.
150. 1. One of the two equal parts of a whole thing is
called i>i\e~h<ilfy thus:
One of the two equal
parts of a peach is
ctdlsd one-half of a
2. How many halves are there in one peach? In one apple?
In oy^e dollar? In<?7iecake? In (we of anything ?
3. One of the three equal parts of a whole thing is called
mic-third, thus :
One of the three
equal parts of a pear |
is called one-third
[y of a pear,
4. How many thirds are there in one pear? In one inch ? In
one pound of sugar ? In one of anything ?
5. One of the four equal parts of a whole thino; is called
one-fourth,, thus :
One of the four equal
parts of an orange is
called onc-foiirth of
an orange.
6. How many fourths are there in one orange? In one pie ?
7. What is meant by one Jialfof anything ? One third ? One-
fourth? Two-thirds? Three-fourths? Throe-lhird.s ?
8. One or more of the equal parts of a unit ia called a
Fr4icthni,
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108 FRACTIONS.
SLATE AND ORAL EXEBCISES.
160. 1. Show on your slate, with lines, that a whole can
be made into equal parts of diflFerent sizes, thus :
WHOLE.
EQUAIi FABT8.
wrvaak
Halves,
Thirds.
Fourths.
Fifths.
2. ITow can you find the one-holf of an orange ? The one-
third? Tlie one-fourth? Theoneh^h?
S. What is meant by one-half of anything? One-third?
One-fourth ? One-fifth ?
4. How many halves make a whole pear ? How many thirds ?
How many fourths ? How many fifths ?
5. What is meant by two-thirds of a cake? Three-fourths?
T' 70-fifth3 ? Three-fifths ?
6. Represent witli lines, on your slate, dxtlis, sevenths, eighths,
ninths, tenths, elevenths, twelfths, and so on, thus :
6 sixths,
7 sevenths.
7. How can you find the one-sixth of an apple? The one-
seventh? The one-eighth? The one-ninth? The one-tenth,
and so on ?
8. What is meant by the one-ha^f of a garden? The one -
third? The one seventh? The one twelfth? The one-
fifteenth?
9. If a whole is made into eight equal parts, how is one part
named ? Three parts ? Five parts ? Seven parts ?
10. Wliich is the larger part, one-half or one-third, and why?
ISES.
at a whole can
Salves,
Thirds.
Fourths.
Fifths.
ge? The one-
g? One-third?
w majiy thi?;ds ?
Three-fourths?
emnths, eighths,
6 sixths,
7 sevenths,
pie? The one-
The one-tenth,
ten ? The one-
i? The one.
low is one part
ts?
liird, and why?
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FRACTIONS.
ORAL AND SLATE EXEBCISES.
IGl. 1. A whole apple is equal to how m&ny fifths f
equals
109^
One ivhole
is equal to
Five-fifths.
2. How many fifths can be made of one pie ? Of one pound
of sugar? Of 07ie sheet of paper ? Of one peck of peaches ?
3. A pear can be made into how many halves? Thirds?
Sixths ?^ Ninths' Thirteenths? Sixteenths? Twenty-thirds?
4. What is meant by the two-thirds of a yard of cloth ? Of a
bushel of wheat ? Of a garden ? Of a load of hay ?
5. What is meant by three-fifths of anything ? Five-sevenths f
Nine-tenths ?
6. Equal parts, or fractions, are expressed by figures, thus :
Numerator, ^ Shows the number of equal parts taken.
Dividing Line, Shows that 8 and 3 express a fraction.
Denominator, Q Shows that the whole is made into 3 equal parts*
Read, Two-thirds.
7. Express by figures each of the following examples :
One-half.
Two-fourths.
Three-fifths.
Seven -eighths.
Three-sovenths.
Six-ninths.
Five-sovenths.
Four-ninths.
Seven-tenths.
Five-elevenths.
Ten-thirtcenths-
Six-fourteenths.
Eight-twelfths.
Nine-fifteenths.
Sixteen-twenty-fifths.
Nineteen -forti eths.
Fourteen -thirtieths.
Six-fifteenths.
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FRA CTIONS,
■
OBAL ADD SLATE EXEBCISES.
m
1 !»*> 1 "R^mfl aBi4r. 7 1810 11 8
±o^« 1. iteaa ;,, v, .i, o» i?» i(f»T5> itf» iio> it-
2. What is the numerator of g ? The denominator? What
does the numerator show "l The denominator ?
3. Express by figures nine-tenths. Five-thirteenths. Twenty-
thirty-fifths.
4. How many numbers must be used to express sewn-
fiftccnthH by figures ? What does each number show ?
5. What is meant by ? of an apple ? | of a garden ? ^ of a
farm?
6. tlow can you find the fifth of a sheet of paper? The
three. ifths? The one-ninth ? The five-ninths?
7. How much of an apple is three-thirds of it? Five-fifths
of it?
8. What docs \ of a garden mean ? g of a bushel yt corn ?
9. In order tliat Henry may give ^ of an orange to James,
what must he do with tLe orange, and why ?
10. One-fiftli of GO is how many ? Of 35 ? Of 80 ?
Solution. J of GO = 60-i-5 = 12.
11. Find \ of 27 ; i of 40 ; ^ of 63 ; ^V of 96; ^V of 144.
12. Find g of 35 ; f of 24 ; f of 42.
Solution. J of 35 is 7. Hence J of 35 must be 3 times 7, or 21.
13. Find the | of 15 ; the ^\ of 24 ; the f of 35 ; the f of 45 ;
the » of 80 ; the f of 63 ; the -jV of 72.
14. What is f of $28 ? f of $36 ? j of ,"-63?
Solution. ^ of $28 is $4. Ileuco f of $28 must be 3 times |,4, or $12.
15. What is 4 of 35 pounds of starch ? Of 45 lb. ?
16. A farmer had 84 cords of wood and sold ? of it at $4 a
cord. How murh HiH he receive for what he sold ?
17. Koliert had $03 and gave 5 of it to his brother Henry.
How many dollars has he loft ?
irden? ? of a
FRA CTIO NS.
OBAL EXEBCISES.
Ill
lOJJ. In this cxerciHo study carefully the illustrations given,
1. A fraction may he represented by equal lines, thus :
2
8
l*art taken.
Whole.
Observe, that in |, the denominator 3 represents the w/iole, or
8 tJdrds, and the numerator 2 represents 2 thirds, or tino parts
of the same size as those represented by the denominator.
Hence, 3 equal lines for the denominator, and 2 ecjual lines
of the same length for the numerator represent correctly tho
number of parts that form the whole or unit, the number of
parts taken, and the relation of the parts to each other as rep.
resented by the fraction |.
2. Represent by lines I, ^, |, }, f, ^', f, j%.
3. If you make r/iie-halfot a line into two equal parts, what
kind of parts will you thrn have, and why ?
1
2
2
4
J'nrt taken,
Whole,
Kxnniine this illuBtration carefully, observing what han hcen done to
chanyc the J to J, then answer the question.
4. If onehnlf\B made into three equal 2^arts, what will be the
name of the parts ? If into four equal parts ?
5. In I how many fourths f IIow many sixtJis ? How many
cighthn ? IIow many tenths f How many twelfths, and why Y
G. IIow many sixths can you make of one-half of an apple ?
flow many fourteenths, and why?
7. One-half of a bushel is equal to how many sixths of a
bushel ? Tenths of a bushel, and why ?
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112 REDUCTION OF FRACTIONS.
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164. 1. How many sixtlia in one-third of a line, and why?
1
8
^■a
2
6
Study careftiUy this illustration, then answer the question.
2. In ^ how many ninths, and why ? How many fifteenths ?
3. To make thirds of a sheet of paper into eighteenths, what
must be done with them, and why ?
4. In f, how many twelfths? How many twenty-fourths, and
why?
2x4 2x5
? Illustrate by lines.
3x4 3x5
6. When both the numerator and denominator of a fraction
are multiplied by the same number, what change is made in
the fraction, and why ?
7. When one-fourth of a line is made into three equal pa/rt9,,
what will each of these parts be called, and why ?
1
4
■ ■■
8
12
wmm ^^ ^^ wmmt
HHB m
Study carefully the illustration, then answer the question.
8. Why is \ of an apple equal to f of it ?
9. In ^ of a pound of raisins, how many twentieths of a
pound ?
10. Why is 7 = -. — ?r = •. — X = 1 — 7 ? Illustrate by lines.
4 4x2 4x3 4x4
11. Principle. — Multiplying both numerator and denomina-
tor of a fraction by the same number does not change the value of
the fraction.
H I
REDUCTION OF FRACTIONS, 113
ne, and why ?
y-fourths, and
/entieths of a
ORAL AND WRITTEN EXERCISES.
165. 1. How many thirds of a line in two-sixths of it ?
3^3
6-i-3
1
8
Observe, that when evei-y two of the sixths tire put into one, as shown in
the ilUistration, the whole Hue in made into three equal parts, and one part
taken. Heuce, two-sixths of a line make one-third of it.
3. How many thirds in ^ of one apple ? In f ? In x\ ?
3. Change /^ to fourths ; || to fifths ; ^'^ to halves.
4. Principle. — Dividing both the numerator and denomina-
tor' of a f7'actio7i by the same number does not change the value
of the fraction.
5. UovfmBXij thirds m*^1 Inf? In |§? In^'.
6. Change | and -^^ each to fourths, and explain.
7. Express yV» A* ^^^ ly» ®^ch as sixths.
When two or more fractions have the same denominator, they are eaid
to have a Comnion JDenominator.
8. Change ^ and ^ each to the common denominator 6.
9. Change ^, ^, and ^, each to twelfths; to thirty-sixths.
10. Change ^q, ^^, and J-f , each to fifths, and explain.
11. Express f , f, and /^, each as twenty-fourths.
13. Change | and f to a common denominator.
Observe, § and } can each be changed to ffteenths (1 64—11)
3_3x5_10 4_4x3_13
8 ~ 3 X 5 " 15 ' 5 ~ 5 X 3 ~ 15
Thus,
13. Change to a common denominator § and f ; ^ and f ;
I and f ; f and f ; f and § ; ^ and ^^V- g
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114 REDVCTTON OF FRACTIONS,
WRITTEN EXERCISES.
166. 1. "\^'hat is the length of J of a rope that is 168 feet'
long ? Of I of it ? Of ] of it V Of /^ of it ? Of {\ of it ?
2. A loud of hay weighs 3'268 pounds. What is the weight j
of I of it ? Of ;; of it ? Of 1 1 of it •>
3. A man hud $3143 in the bank, and took out | of it. How
much money had lie still in the bank ?
4. A merchant having a piece of cloth containing 184 yards,]
sold I of it. How much of the piece was still left?
5. What part of a sheet of paper is \ of \ of it? | of ^ of it?'
i of tV of it ? \ of i'^ of it V 1 of ^., of it ?
/ C. Bought a pound of candy and made it into 6 equal parts,
' and gave • of one part to George. What part of the pound
hbii George received ?
7. How many dollars are ^ of ^ of $84 ? ^ of | of $90 ?
8. $13 are | of how many dollars?
Solution.— Siucc $12 arc § of the required number of doUart?, tlie \ of
$12, or $6, must be ii.
Agaiu, biuce $6 are I of the whole, \ mu»t be 3 times $6^ or $18.
^&. $9 are J of how many dollars '[f
10. $34 are 4 of James' money. How much money has he?
11. J- of a farm contains 161 »cres ; how many acres in the
farm ?
12. 36 is f'^^ of what number? 18 is ? of what number?
13. A grocer sold 184 pounds of butter, which is ^ of what
he has still loft. How much butter remains in the store?
14. Change § to tenths; f to fortieths ; ? to eighty-fourths.
15. If I own I of a garden, how many tioenty -fourths of it do
I own? How many ninety-sixthif
16. Change to a common denominator | and | ; y'^ and f ;
f and -J ; ,\ and § ; ? and ^ .
17. Find iV of 480 ; -U^ of 09400 ; f of 301 ; f of 423.
A CTTONS,
CISES.
!1CJ
them
RED rrrrox of fr actions.
ORAL AND WRITTEN EXERCISES.
115
f a rope that is 168 feet I 1C>7. 1. In three eqr tl lines how many fourths of one of
)fit? Of-j'Vofit? 1 them?
What is the weight
IS
1 took out I of it. How
>th containing 184 yards,
ras still left ?
i of i of it? i of ^ of it?
f it ?
de it into C equal parts,
What part of the pound!
84? ^ off of $90?
!cl number of doUare, tlie J of
}e 3 times $6^ or $18.
w much money has he ?
; how many acres in the
f of what number ?
itter, which is f of what
mains in the store ?
is; f to eighty-fourths.
ly twenty -fourths of it do
tor f and | ; ^V and f ;
of 301 ; I of 423.
WHOLE LINES.
POURTHB.
12 fourths.
Solution.- In 1 lin« '-''ire are 4 fourths. Hence in 3 lines there must be
3 times 4 fourth!', which ».re 12 fourths, as shown in the illustration.
2. In 7 i)Ounds of coffee, how many thirds of a pound ?
3. Ilowmany fourths of 1 bushel in 5 bushels? In 9bushels?
In 12 bushels ? In IG bu. ? In 29 bu. ? In 100 bu. ?
4. Express 6 gallons as halves of a gallon; as thirds; as
ninthH ; as fifths ; as tenths ; as twelfths.
5. In 5^ feet, how many thirds of a foot?
SoLt'TiON.— In 1 foot there are 3 thirds, and in 5 feet there must be 6
times 15 thirds, which arc 13 thirds. 15 thirds plus 2 thirds are 17 thirds ;
heuc(! in 5? foot there arc V of a foot.
Obfcrre, 1st. A wliolo number and a fraction written together, as 5S, is
called a Mixiul JS'utnher,
2(1. A fraction whore the numerator is equal to or g^rea^er than the de-
nominaUn", as {, J, is called au Improper I'mctton,
6. How many fourtJis of a yard in 6 J yards ? In 9| yards ?
7. Change to cigJiths 8i| feet ; 5^ pounds ; 9| gallons.
8. Express in twelfths ^:{^ dollars ; Z^» bushels ; 8}^ tons.
9. How many tenths of one bushel in 40-/^ bushels of wheat?
In98i'obn.? In337i«ybu.? In639/'nbu.?
10. How many sixteenths of one pound in l^-^r pounds of
sugar? In9i'\lb. ? In 35^^^,.; lb. ? Inl38Hlh.? In 375^^1. lb.?
11. How many ffteei'ths of one yard in 3f*- yd. ?
12. Express in thirteenths \Z{.^ dollars; 9^^ yards; 37^^^ lb. ;
[39/^ tons; 82 ^'V. gallons.
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lib FRACTIONS.
ORAL AND WRITTEN EXERCISES.
168. 1. What part of one bushel is one peck ? IWv pecks ?
Three pecks ? ^<9i<r pecks ?
2. In 4 pecks how many bushels? In | bushels how many
busliMs?
;]. I low many bushels and fourths of a bushel hi 9 pecks?
In 14 pecks ? In 27 pecks? In 35 pecks?
4. How many bushels in 'f of a bushel?
Solution.— Since it takop 4 fourths of a buj^hel to maico one bushel, in
9 fourths of a bushel there are as many bushels as 4 fourths are contained
times in fourths, whicli are 2{.
5. How many pounds in 1^ of a pound? In ^^- of a pound ? In
^^ of a pound ? In ^>," of a pound ?
0. How many dollars in $!| ? In $V ? In $V • f" $V ?
In IV? In|«'^5? Inl^p-?'
Change each of the following fractions to a whole or mixed
number :
7.
8.
9.
10.
8
m
4 .
18
11.
V-
12.
"9"
13.
V
14.
V
1 R 12 8
16. -V.
17. ^\
18. -^K
19.
20.
21.
22.
ia8i>
il •
1 73 5
an •
1(18 5
7F •
7430
15 B •
23. One pint is what part of a quart? Of a gallon?
24. One quart is what part of a gallon ? 15 (quarts are how
many fourths of a gallon ?
25. How many gallons and fourths of a gallon in ^^ gal. ? In
*^"- gal. ? In J :j^- gal. ? In ^:^"- gal. ?
26. How many quarts in "'i" of a galloii ? In -'j' gal. ?
27. What part of a pound Avoirdupois Is I ounce, and why?
Is 3 oz. ? Is 5 oz. ? la 9 oz. ? Is 13 oz. ?
28. Express ^v, of a pound Avoirdiii)ols as ounces, and explain
why the change can bo mndo.
29. How many pounds and oz. in '^ of a pound, and why?
Tico pecks ?
Is how many
in 9 pecks?
one bushel, in
< are contained
I pound V In
r"*? Tn $V?
olo or mixed
in i2Mi»
n?
rts are how
^^'gal.? Ill
al. ?
, and why ?
[vnd explain
Lud why?
ADDlTIOy OF FRACTIONS. 117
ORAL AND WRITTEN EXERCISES.
lot). 1. Find the sum of 4. fifths, 2 fifths, and 3//«/iS.
Solution.— The sum of 4 fifths + 2 fifths + 3 fifths is 9 fifths, which is
equal to .?, or 1^
2. How many are 7 eighths + 5 eighths? 6 sevenths ■{•
5 secciiths?
3. lIowmanyareHf + v? i + HV A + A + A?
Read and find tlie sum of each of the following examples:
4.
? + ?+!•
7.
4 1 (! _L 6
IT + IT + IT-
10.
7 1 i 1 3
5.
Kl + lJ.
8.
S + "ff + ¥•
11.
Y+7 + ;•
G.
i^+T^ + T^.
9.
4 1 B 1 7
a + TT + ¥•
12.
1 1 1 7 1 «
-8-+8 + S-
13. If you want to express the sum of 5 chairs and 3 tables,
how would you write the number, and why ?
14. To add 2 thirds and 5 sixths, what must be done, and
why ?
Fractions that have different denominators must be changed to others
having the panic denominator before they can be added.
lo. Fhid the sum of k and 'j ; of § and § ; of f and | ; of f
and ^.
10. Find the sum of i + H i J of f + f + ^^ ; of f + -^^ + ^f^.
17. Find the sum of 1+^; of -|+ J ; of ;| + f..
Obsen)e, thirds and fouiiiis can eacli be made into twelfths ; fifths and
third:* into fifteenths ; fourths and (<ixths into twelfths (165—12).
18. Find the sum of f + | ; of f + -| : of Jj + J ; of (• and J.
19. Find the sum of H +f'j; of -fV + iir '< of H + iV
20. Henry paid - of a dollar for peaches and I of a dollar f«r
apples. How much did he pay for both ?
21. "Mary boug-ht ] of a pound of tea at one ame, ^ at another,
and f; at another. How nuich tea did she buy in all ?
22. Paid ? of a dollar for eggs, and 5 of a dollar for coffee;
how much did 1 pay for all?
•'I
>d
1
i
I
H
I
i
ll
118 SUBTRACTION^ OP FRACTIONS.
1 i '11'
MM
•VI
ORAL AND WRITTEN EXERCISES.
1 70. 1. What is the difference betweeu I and f V
Solution. 7 ninths minus 5 ninths are 2 ninths, which are |.
2. What is the difference between i and % ? f and f ? -^
and Y^? Viandrlr? H a^fl r: ?
3. How many are f ^ less than {'q ? {\ less than ^\ ? f| less
than %\ ? I ;] less than f f ? ^¥5 less than f^| ?
4. Find the difference between ^ and ^ ; | and f ; g and f .
Observe, J can be changed io fourths, I to eiuhths, I lo ninths.
Perform the subtraction in the following :
5.
A-i
13. 1-f
21.
8_3
39. 4f-i.
6.
j\-h
14. 1-i
22.
4 3
4'
30. 21-i.
7.
14 a
IS 3'
15. 2-^.
S3.
5_1
tf a-
31. 6i— i
8.
1 7__5
19 «•
16. 5-i
24.
?-|.
32. 3|-|.
9.
19 3
^4' tf
17. 1-f.
25.
^-|.
33. 9H-I
10.
H-1^-
18. 8-f.
26.
I-tV
34. 5,«,-f
11.
4 5
19. 1-?.
27.
l.-J^ s
16 iw
35. 2!1~3.
12.
a7~lS^*
20. 9-i
28.
A-i.
36. 4«-^
37. James had $3 and gave | of a dollar to William. How
much money has he left ?
38. Mary owes a store bill of ^ of a dollar. If she hands the
clerk '\ of a dollar, how much change should she rebeive V
39. Find the difference between ^l and %l ; $|| and $f;.
40. Henry had $4 and gave $| to James. How much had he
left V
Find the difference between :
41. $3;1 and f ». 44. %^ and $42.
42. 5^8 and %l 45. $5f and %\\.
43. .$0| and %%\. 46. $8^ and $3^^.
47. I oz. and | oa.
48. § lb. and \ lb.
49. g gal. and f gal.
JYS.
MULTIPLICATION OF FRACTIONS. 119
'ill
<''>l
SES.
andf? ^
[\? ffless
"• ' and |.
hs.
'*. 2'V
1 4«_r>
iam. How
hands the
eive ?
Id $,■•.
ich had he
and I oa.
md I lb.
and J gal.
ORAL EXERCISES.
171. 1. Find I of ^ of a given line.
Obs!:rve, I of a line is equal | of the same line, thus :
I'art taJceu, wmmmr mmtarj,
Having made the given tMrd into two equal parts, we have
I, and can i\ow take the half of it, thus :
1 of
2
From these two illustrations we have the following
Solution. \ is equal to J, and J of 'i is J ; Lriice, i of J is J.
Solve and explain in this way each of the following :
2.
What is i of l ?
J of i ?
iofi?
iofi?
3.
What is J of-[?
iofi?
iofr^
iof|?
4.
What is 1 of i ?
koik'i
iofi?
iofj?
5.
Wiiat is ! of ; ?
iofj?
iof ■?
iofl?
0.
What is I of J?
i of ] ?
iof^?
iof^?
7. CJcorge had | of a dollar and gave J of what he had to
Ada. What i)art of a dollar did Ada receive?
8. What part of a peach is }, of h of itV i of I of it?
9. Henry owned i of a boat and sold I of it to James. What
part of th(^ boat did James own V
10. What part of a garden is i of .[ of it? 1 of | of it ?
11. Kohert borrowed ;", of Henry's money, and gave I of it to
Maggie. What part of Henry's money did Maggie get?
12. Mary bought I of u cuke and gave } of it to Susie. What
part of the cake did Susie receive ?
18. What part of my money is ] of J of it ? j of >f it ?
w
r
Ill
if:
120 3IUL TIP LIGATION OF FRACTIONS.
ORAL EXERCISES.
172. 1. What part oi' au orange is J of % of it?
Solution.— Since i ol' i of au omuge is -,'5 of it, J of | of it must be 2
times r'j, whicli are ,-4.
3. What part of an apple is \ of } of it? { of 5 of it? ] of
gofit? 1 off of it? ^ off of it? ^ of ^ of it?
Find the required part in the following :
3.
h of f
9.
ioff.
15.
I of |.
21.
I of U-
4.
iof ■.
10.
-1 of tV-
10.
i of |.
23.
hoiil
5.
^ of /v.
11.
^ nf s
T 01 ij.
17.
iof^.
23.
1 nf ~»
U 0^ 1 5*
6.
^of^
13.
1 Of |.
18.
iof iV
24.
1 of "
10 "^ 1 ()•
7.
^of^
13.
^ Of t'^.
19.
4 of A.
25.
iVof t6o
8.
i of ,V
14.
i of t\.
20.
^ of ,v.
26.
iV of /,f.
27. What part of a peach is | of J of it ?
SoLXTTioN.— Since J of J of a peach is fV of it, g of ^ of it must be 2 times
x\, wiiichare ,";.
28. What part of a cake is 5 of 4 of it ? -J of ^ of it ?
29. A boy bought ] of a pound of candy and gave I of it to
Lis sister. What part of the pound did his sister receive ?
30. What part of a gallon is * of ■; of it ? I of | of it?
Find the required part in each of the following :
31. ^ of l 34. ^ of I. 37. I of ^\. 40. -^, of -,\^.
33. li of ?. 35. -iVof •]
38. fl of I.
33. ;| of 5. 36. 3!^ of {\. 39. fV of i
ftl. ^jj 01 yi-ijj.
^'*' Iff 01 (o?T"
43. SuHio had a pear, and gave \ of J of it to Mary. \Miat
part ol' the pear had she then left?
44. A boy had I of a dollar and gave away 2 of it. What
part of a dollar had he ilieu 1 "ft ?
45. Williiini liad ,! of a melon and gave jj of it to Robert.
Wl)at i)art of the whole melon had he then left?
be
*V
bu>
iiii
mi
po
foi^s.
t?
of it miist be 8
of it? I of
TOO'
riT ol'
list be 2 times
'it?
e r^ of it to
'ceive ?
)fit?
A of Air.
A of •' '1
i-y- ^^'llat
it. What
:o Robert.
}[ULTIPLICATION OF FRACTIONS. 121
ORAL AND WRITTEN EXERCISES.
1 7o. 1. At J of a dollar lor one yard of cloth, what will
be the cost of 8 yards ?
Solution.— Since 1 yard cost $J, 8 yards must cost 8 times $J, which are
$V, eq"'i' $^-
2. Fhid the cost of 7 bushels of apples at ^ of a dollar for one
bushi'l. At I of a dolfar. At -| of a dollar.
3. How much will pounds of tea cost at $f per pound ? At
%l per pound? At %l per pound ? At $f per pound?
4. A father gave to each of 3 children ^ <>f a dollar. How
much money did he give away in all ?
5. A man gave to each of 7 beggars i of a dollar. How
much did he give away in all ?
('. \Vliat is the cost of f of a pound of sugar, at 15 cents a
pound ?
Solution.— Suice 1 pound co«t 15 cents, I of a pound must cost I of 15
cents, which are 3 cents, and 5 of a pound must cost 3 times 3 cents, which
are i) cents.
7. What is the cost of \ of a pound of candiea, at 86 cents a
pouu.l ? At 24 cents a pound ? At 48 cents a pound ?
8. Wliat is the cost of !; of au acre of land, at $32 an acre?
At $48 an acre ? At $72 an acre? At $90 an acre ?
9. What is the value of y\ of a garden, worth $48? Worth
$84? Worth $108? Worth $144? Worth $2400?
10. If a load of hay cost $12, what is the value of \ of it?
Of -; of it ? Of ■{ of it ? Of I? of it ?
11. If a farm is worth $0240, what is I of it worth ? f of it?
,\ofit? II of it? (Vofit? If.ofit?
Observe, J of $9240 = $!)240-f-5 == |1818; hence, I of $9"-M0 = $1818x8 =
12. What is the cost of 48 bushels of corn, at !^ of a dollar
per bushel ? At -j'.v of a dollar ? At -j",,- of a dollar ?
13. What is tlto cost of 30 jounds of tea at f of a dollar per
pound? At ;, of a dolliir? ,
G
^
i
V
i
.>•
-.22
3IULTIPLICATI0N OF FRACTIONS,
\ \
%\ '■• ■
ill '
iiU ;
i !•
ORAL AND WRITTEN EXERCISES.
1 74. 1. If 1 biishel of corn cost ^|;, what will be the cost
of 4J bushels V
Solution.— 1. 4^ bushels are equal to V of a bueheL
2. Since ^l is* the cost of 1 bu., i of $3, or $-,\, is tlie cost of \ of a bn.
;]. Since I,'-, in, the cost of \ of a bushel, 19 times f j'^- or $y;;, equal |3t\,
is the cost of V\ or 4^ bushels'.
3. If 1 yard of cloth cost $-', what will he the cost of 3|
yards ? Of 5] yards ? Of 2 ? yards ? Of 4f yards ?
3. If 1 bushel of apples cost $|, what will be the cost of
41 bu. ? Of ^ bu. ? Of 52 bu. ? Of 7^ bu. ? Of 10^ bu. ?
4. Multiply ;i by §; f by | ; f by | ; g by t\ ; -« by «.
Observe^ I multiplietl by s, or ^ x 3, means the same as $ of §, or i of J ;
hence the solution is the same as given (1 72—37).
Perform the work and explain each of the following :
8.
IT
X#.
6.
7. yj X ^, lU. -fg- X Y»
11,
12.
13.
A4
TffTT'
80 '
14.
8.1 V,
15. f^x|.
17. If 1 pint of milk cost 4| cents, v/liat will be the cost of
3? pints ?
Solution.— 1. 3J pints are equal to V- pints, and 4J ccnt« are equal to f
cents.
a. Since I cl. are the cost of 1 pint, J of f ct., or ^^, ct., must be the cost of
J of a pint.
.3. Since 1°, ct. are the cost of J of a pint, 17 times ^^ ct., or '/J- ct., equal
\^^r, cents, must be the cost of Yi or 3? pints.
18. If 1 bushel of pears cost )«;2f , what will be the coat of 4|
bushels ? Of 3i bu. ? Of 71 bu. ? Of 6| bu. ? Of 9| bu. ?
19. What is the cost of 4J! yards of olnth, at $1^ per yard?
At $3i per yard ? At $2^ per yard ? At $4| per yard ?
20. What is the cost of I of a yaixl of cloth at iSG a yard?
21. I of $75 is 2 times what a coat cost ; what was the price
of the coat ?
'lOJYS,
DIVISION OF FE ACTIONS,
123
I be the cost
of iofabu.
■ $r", equal |3i\,
le cost of 3|
i?
e the cost of
10^ bu. ?
of 3, or I of I ;
e tlie cost of
aro equal to f
t be the cost of
' 'ir ct,, fqnal
» coat of 4*
)i^bu.?
i per yard?
rd?
a yard ?
s the price
ORAL AND WRITTEN EXERCISES.
1 7«>. 1. How many times can ^ pound of tea bo taken from
2 pounds ? From 3 pounds ? From 5 pounds ? From 8 pounds ?
Solution.— In 2 pounds there are 4 halves, hence 1 half can be taken 4
times from 2 pound's.
3. How many times can i be taken from 1? From 2?
From J?
o. How many fourths in 2 peaches? In 4 peaches? In
8 peaches ?
4. How many times are %% contained in $3 ? In $4 ? In $8 ?
Solution.— $2 aro equal to %% and 5 are contaiued 3 times in %.
Observe, the dividend and divisor are made, before dividing, into the
same fractional parts.
5. How many times are | of an ounce contained in 3 ounces ?
In G ounces ? In 9 ounces ? In 12 ounces V In 2 ounces ?
6. How many times are i of a gallon contained in 8 gal. ? In
12 gal. ?
7. How many apples at -| of a cent each can be bought for
6 cents?
Solution.— As many as g of a cent are contained times in 6 cei^ts, which
are 9.
8. How many books at |f each can be bought for |6 ? For
$9? For|3? For $12? For $30? For$GO?
9. When coffee can be boiight for %{^ a pound, how many
pounds can be bought for |10 ? For $30 ?
10. How many pounds of butter at $| a pound can be bought
for $3? For $5? For $8? For $4? For $9? For $20?
11. If a bushel of apples costs | of a dollar, how many
bushels can be bought for $15 ?
12. If a yard of cloth costs $^ , how many yards can be bought
for $20?
13. If a quire of paper costs % of a dollar, how many quires
can I get for $18? ^
1
1
J
r
1/ II
124
DIVISION OF Fit ACTIONS,
; V
i' •/'
'rtj
if
ii
'f
\ "
J ,!■'
OBAL AND WRITTEN EXERCISES.
17(>. 1. How many times can g be taken tVom I 'I
Solution.— As many tiiues as 2, the nnmerator of tlio divisor, is con-
tained limes in 6, the numerator of the dividend, which are 3.
2. How many times can JV ^^ taken from {\'i From V\'l
From^"^-? Fromi^? Fromjl? From ^5 ?
8. {-, are contained liow many times in ^.^ 'I In j*. V In \l ''•
In^tf Iiil*? Ini?? Inin In^^?
Perform and explain the division in the following :
fi 48 i_ B Q 40_j_ 7
"• So • 5 0- ^' T(i~Tff'
4 7 8 6_j }• O 14_.
TST -TIT' *• 7T~Tf «'• Tlf~T]I'
4 15-i- a
K 12-!-
10. How many times is ^ of a quart contained in ^ qt. ?
Ob,wrve, the divisor and dividend muet both express the same kind of
equal parts, hence the following:
Solution.— 5 of a quart is equal to 3 of a quart, and 2 of a quart arc con-
tained 2 times in | of a quart.
11, How many times are 5 contained in -{^ ? In |^ ?
Perform and explain the following :
19, 1 2 _i_ 1
13 1 f' -!- 1
14.
15.
HO_i_r)
1 -i _. 4
1fi ion.i.5
. . .. 17 me. ,^3
18. A boy spent || cents in bu;.-ing- pears at | of a cent each.
How many pears did he buy ?
Solution.— lie bouj^ht as mauj' pears as I of a cent are contained times
in 11 c 'nts. I of a cent arc equal to ,", of a cent, and 1",^ of a cent are cou-
tiiined 1) time < in j'i cents ; hence he l)onjj:ht 9 pears.
19 At .$;j n yiii'd, how many yards of cloth can be bought for
$|A? For^'V? For^U-J? For $^2^
30. At $T a peck, how many ]iecka of ])eac]ies can be bought
for jl^ Yi ? For $ ^^ V For ^2 ? For (• 7 ? F( .r $ 1 2 V
'S,
C OMr A It I S X O F X U M B E E S .
1;>5
JISES.
in S V
divisoi", is con-
3.
V From J,]?
" A V In } '^ V
mg
4(»j_ 7
. 4A^ «
• T:t • T3"
in f qt. ?
the eame kind of
r a quart are con-
)f a cent each.
contained times
f a cent are coii-
be bouglit for
'an be bong-lit
V
COMPARISON OP NUMBERS.
177. 1. What part of 4 is 3 ?
Solution.— Since 1 is i of 4, 3 must be 3 times {, or I of 4.
Find the part that
3, 2 is of 7.
y. 4 is of 8;
4. a is of }).
o. () is of 10.
6. 6 is of 18.
7. 9 is of 54.
8. 5 is of 35.
9. 10 is of 24.
10. 8 is of 56.
11. 10 is of 80.
13. 25 is of 100.
13. 200 is of GOO.
14. 2 pocks are what part of 3 pecks ? Of 4 pk. ? Of 7 pk. ?
Of 10 pk. ?
15. 1 peck is what part of a bushel ? Of 2 bu. ? Of 3 bu. ?
Observe, the two nnmbere compared mnst express the same unit; hence
the fiiven bufhelH are expressed in pecks, and then the comparison is made.
1(1. 5 ounces are what part of 9 ounces? Of 15 oz. V Of
35 oz.? Of40oz.?
17. 1 ounce is what part of a pound Avoirdupois? Of a
pound Troy?
18. 1 pint is what part of a quart ? Of 2 qt. ? Of 3 qt. ?
19. 7 pecks are what part of 3 bushels? Of 5 bu. ? Of 9 bu. ? •
Of7bn.?
20. 10 ounces are what part of 2 pounds Avoirdupois ?
21. I of a i)0und is what part of § of a pound?
Obfierve, tliat before two fractions can be compared they must both
exi)rcH>' rqual parts of the same kind ; hence the following :
HoniTioN.— J of a pound is equal to f, and 2 eighths of a pound are ^ of
6 eighths of a pound.
22. ;\ is what part of J ? J is what part of ^ ? Of ^ ?
23. I is what part of -fw ? f is what part of -{^ ?
24. f, is what part of {§ ? f is what part of ||?
35, « is what part of ^ ? f is what part of \^1
20. I', is what part of '^ ? Ms what part of |{}?
••»
y,
i
126
FRA CTIOXS.
I . i
)«' .
DEPHnTIONS.
1 78. A Fractional Unit is one of the equal parts ol
anythinpr regarded as a whole.
1 70. A Fraction is one or more of the equal parts of a
unit or whole.
1.80. The Numerator is the number above the dividing
line in the expression of a fraction, and indicates how many
equal jmi'ts are in the fraction.
181. The Denominator is the number below the divid-
ing line in the expression of a fraction, and indicates how
many equal paints are in the icJiole.
1 81i. The Terms of a fraction are the numerator and de-
nominator.
1 8*?. li eduction is the process of changing the terms of
a fraction without altering its value.
184-. A fraction is reduced to Higher Terms when its
numerator and denominator are expressed by larger numbers.
Thus, I = xV
185. A fraction is reduced to LiOtver Terms when its
mini orator and denominator are expressed by smaller numbers.
Thus, /'^ = 1
1 8(>. A Common Denominator is a denominator that
belongs to two or more fractions.
1 87. A Proper Fraction is one whose numerator is less
than tlio denominator, as f, ^.
1 88. An Improper Fraction is one whose numerator
is f'(iual to or greater than the denominator, as |, -^.
189. A Mixed Nuntber is a number composed of an
integer and a fraction, as 5|, 132-
In
lual parts ot
lal parts of a
the dividing
es how many
o\v the divid-
indicates how
erator and de-
? the terms of
"nis when its
irger numbers.
'ms when its
ailer numbers.
lominator that
nerator is less
3se numerator
7
a*
mposed of an
DENOMINATE NUMBERS.
CANADIAN AND UNITED STATES MONEY.
190. The following table includes Canadian and U. S.
money :
Table op Units.
10 mills (m.) make 1 cent . . . ct.
10 cents " 1 dime . . . d.
10 dimes " 1 dollar . . . |.
10 dollars " 1 eagle . . . E.
$1 = 10 d. = 100 ct. = 1000 m.
1. How many cents in |2? In $4? In $9? In $25?
2. How many dollars in 100 ct. ? In 300 ct. ? In 500 ct. ?
In 1200 ct. ?
3. Change $10 to cents ; $23 ; $^; $95 ; $3:2.
4. In $2 how many mills? In $7? In 53 ct. ? In85ct.?
5. Express 435 cents as dollars and cents.
Observe, the 400 cents mnke ^4, hence the 435 cents make f4 and 35 cents,
which we write thuB : $4.85 (58—3).
6. In 786 cents, how many dollars and cents '? In 932 ct. ?
In 5384 ct.?
7. In 300 eagles how many dollars? How many dimes ?
8. Express 8430 cents in dimes. In dollars.
9. Express in dollars and cents the following
375 ct.
856 ct.
732 ct.
205 ct.
430 ct.
1237 ct.
5786 ct.
8527 ct.
1006 ct.
8020 ct.
605 ct.
807 ct.
426 ct.
503 ct.
130 ct.
5360 ct.
9408 ct.
0210 ct.
3040 ct.
7304 ct.
*«1
» I
128
D E X O Ml XA TE X I' M B E R S .
WRITTEN EXERCISES.
101. The character (i! is followed by the ])rice of a unit or
one article. Thus, 9 yards of cloth @ $'2, means 9 yards of
cloth at $2 a yard.
Find the cost of the following (see Art. 122) :
1. 5 yards of cloth (V? $.20.
2. 9 yards of cloth @ s.35.
3. 7 bu. of wheat @ $1.25.
4. 12 pk. of peaches {il $.85.
5. 8 gal. of vinegar @ $.37.
6. lb. of tea @ $1.48.
7. 9 yards of muslin @ $.38.
8. 14 pairs of boots @ $7.54.
9. 36 yards of ribbon (?. $1.84.
10. 48 yards of silk @ $2.95.
11. 79 bu. of peaches (d} $2.38.
12. 83 acres of land («) $43.25.
13. 56 tons of coal @ $7.45.
14. 93 cords of wood @ $4.53.
15. 237 acres of land @ $65.75.
16. 89 barrels of apples @ $3.46.
17. A farmer sold 46 sheep @ $3, 7 tons of hay @ $14.50,
184 pounds or butter @ $.43, and 35 barrels of apples @ $3.75.
How much did he receive for the whole ?
18. A grocer sold a man 16 lb. tea @ $.85, 96 lb. sugar @
12 ct., 35 lb. butter @ $.38, and 3 barrels of flour @ $8.50.
How much did he receive for the whole ?
19. How much must I pay for the following bill of articles :
89 lb. of coflTee @ $.45.
85 lb. of butter @ $.39.
19 lb. of cheese @ $.18.
89 lb. of flour @ 4 ct.
42 lb. of dry beef (^, 19 ct.
64 lb. of sugar @ 13 ct.
20. A merchant bought 346 yards of cotton @ 9 ct., and 86
yards of silk @ $1.36. How much did he pay for both ?
21. A man bought 385 acres of land @ $49, and 36 head of
cattle C<^ $42.50. What did the whole cost ?
22. What is the difference in the cost of 57 yards of silk @
$2JB5, and 532 yards of muslin @ $.37?
23. Which will cost the most and how much, 84 barrels of
flour (Jl $7.60, or 136 barrels of apples @ '^^Ml
DENGl : T' A. : t. '/ ¥ f/i H E R S .
120
of a unit or
b 9 yards of
bon (7? $1.84.
k @ $2.95.
lies (li) $3.38.
id @ $43.25.
I @ $7.45.
wd @ $4.53.
md @ $65.75.
pples @ $3.46.
hay @ $14.50,
pples @ $3.75.
96 lb. sugar @
flour @ $8.50.
11 of articles :
• @ 4 ct.
beef @ 19 ct.
ir @ 13 ct.
) 9 ct., and 86
both ?
nd 36 head of
rds of silk @
84 barrels of
4-
EXERCISES IN ENGLISH AND OTHER
MONEY.
102. English or Sterling Money is tho money of
Great Britain.
The Standard
Unit of English
money is the Sover-
eign or Poiind Ster-
tiny.
A iSovercign is equal to $4.8661 Canailmn Money.
Table op Units.
4 farthings (far.) make 1 penny . . . d.
12 ponce " 1 shilling . . . s.
20 shillings " 1 pound . . . £.
2 shillings " 1 florin . . . fl.
5 shillings " 1 crown ... or.
193. French Money is the money of France.
The Standard
Unit of French
money is the Franc
of the Republic.
A Franc is equal to $.193 Canadian Money.
Table op Units.
10 millimes (m.) make 1 centime .
10 centimes
10 decimes
1 decime
1 franc
9
ct.
dc.
fr.
LI
j
130
DE2<0 M 1 ^' ATE A UM BEES.
EXERCISES IN ENGLISH AND OTHER
MONEY.
194. German Money is the money of the German
Empire,
The Standard
Unit of the Ger-
man Empire is the
MarTc. The mark
is subdivided into
100 Pfennings.
The coins referred to m Canada are the
Marky equal to 33^*^ cents Canadian Money.
mver Thaler, equal to lA^^ ct. " •*
Siher Groschen, equa' to 21 ct. " "
Pfenning, equal to y^^ of a mark.
1. How many farthings in 1 penny? In 3 pence? In
5 pence? In 9 pence? In 1 shilling? In 20 pence?
2. How many pence in 8 shillings? In 5s. ? In 10s. ? In £1 ?
8. IIow many shillingB in 4 crowns ? In 9 florins? In £G?
4. How many pence in 3s. Od. ? In 5s. 9d, ? In £1 8s. 9d. ?
5. How many decimes in 3 francs? In 7 fr. ? In 12 f r. ?
In 40 f r. ?
G. Express 5 francs in centimes ; in millimes.
7. What is the value in Canadian Money of 1 franc? Of
3fr.? Of7fr. ? OfOfr.? OflOfr.? Of 100 fr. ? OfSOfr.?
Of 400 fr. ?
8. What is the value in Canadian Money of £1? Of £2?
Of £5? Of £10? Of £100? Of £20
9. IIow many pfennings in 1 mark ? In 7 marks ?
• S
s.
OTHER
the German
oney.
«
3 pence? In
ice?
1 10s.? In£l?
ins? In £6?
11 £1 8s. 9d. ?
? In 13 fr.?
1 franc? Of
? OfSOfr.?
£1? Of £21
s?
£> E X MI NA T E N UM B ERS.
13l
EXERCISES IN UNITS OP WEIGHT.
195. 1. Ti'oy JJ'rifjJif is used in weighing- gokl, silver,
and precious stones, and in philosophical experiments.
Table of Units.
V 24 grains (gr.) make 1 pennyweight
20 p<'nnyweights " 1 ounce . . .
12 ounces
1 pound
pwt.
oz.
lb.
2. Aputhcrnrics' Weight is used by physicians and
apothecaries in compounding dry medicines.
V
Table of Units.
20 grains (gr.) make 1 scruple . . sc. or 3 .
scruples " 1 dram . . . dr. or 3 .
8 drams " 1 ounce . . . oz. or § .
13 ounces " 1 pound . . . ft.
Tlie pound, ounce, and grain are the same in Troy and
Apothecaries' weight.
3. How many grains in 2 pwt. ? In 5 pwt. ? In 10 pwt. ?
4. How many scruples in 3 10 ? In 3 15 ? In 3 30 ?
5. Express in grains 5 pwt. ; 10 pwt. 7 gr. ; 8 pwt. 13 gr.
6. Express in ounces 3 lb. 4 oz. ; 5 lb. 9 oz. ; 10 lb. 7 oz.
7. Change to grains 2 lb. oz. ; 5 lb. 10 oz.
8. Express in scruples 3 lb . 4 oz. ; ft) 38 3 5.
9. How many powders weighing each grains can be made
from 33? From 3 15? From 3I 32gr.8'?
Obfifrve, ench number nuiet bo made into gniiii)* before dividing by the
9 grains.
10. How many tablespoons, each weiglilng 3 oz., can be made
from 1 lb. of silver? From 5 lb. ? From 12 lb. 8 oz. ?
11. How many ounc("A in n\ lb. ? Tn 2| lb. ? In 4^ lb. ?
11
f
. I
¥l|i
133
DE NO 3IIXA TE N UMB ERS.
* :!ir
■lit
i 7 n'.
V. t
EXERCISES IN UNITS OF WEIGHT.
190. Avoirdupois Welr/ht is used in weigliiiig gro-
ceries aud all heavy articles and drugs ut wholesale.
lb.
cwt.
T.
ih Table of Units.
10 ounces (oz.) make 1 pound . . .
100 pounds " 1 hundrcdweiglit
20 cwt. or 2000 lbs. " 1 ton ....
1 pound contains 7000 grains Troy.
The following denominations are also used :
-\ 100 pounds of grain or flour make 1 cental.
100 pounds of dry fish " 1 quintal.
19G pounds of flour " 1 barrel.
200 pounds of pork ** 1 barrel.
1. How many ounces in 2 pounds? In 4 lb. V In 10 lb. ?
2. How many are the A of 8 oz. ? i of 10 oz. ? ] of 10 oz. ?
3. How many ounces in % lb. ? In | lb. ? In the J of 2 lb. ?
4. How many pounds in 40 oz. ? In 112 oz. ? In li)2 oz.?
5. In 5 lb. 9 oz., how many ounces ?
G. In 4 cwt. 37 lb., how many pounds? In 13 cwt. 84 lb.?
7. What is the cost of 2 lb. 13 oz. of candy, at 3 cents an
ounce ? Of 4 lb. 7 oz., at 5 cents an ounce?
8. A coal dealer sold 9 T. 12 cwt., at 25 ct. a hundredweight.
How uiuch did he get for the whole ?
Ohaerre^ Iho tons must bo chnnROd to iHuulredwoli^htiH.
0. When coal sells at 35 ct. a hundredweight, what is the
cost of 5 T. 10 cwt. ? Of 8 T. 13 cwt. ? Of 12 T. 18 cwt. ?
10. WHiat is the cost of 5 barrels of flour at 2 ct. a pound V
11. Wliat is the cost of 8 quintals of fish at 7 ct. a pound?
At 9| ct. a pound ?
8
ii
[QHT.
lifc^liing gro
BEN uVIX A TE X U M BEE S,
loo
lb.
CAVt.
T.
1.
al.
1.
1.
n 10 lb. ?
] of 10 oz. ?
e I- of 2 lb. ?
11 11)2 oz.?
ivt. 84 lb. ?
it 3 cents an
idrechvciglit.
wlint is the
? cwt. ?
a pound ?
3t. a pound ?
UNITS OP LENGTH.
li)7. A yard Is the Stcuulavd Uiiii in linear measure.
I. Used
Table
OF Units.
d in measuring lines or ordinary distances
•
12 inches (in.) make
1 foot ....
ft.
n feet
1 yard ....
yd.
5J yd. or 10?. ft. "
1 rod ....
rd.
40 rods
1 furlong . . .
fur
8 furlongs "
1 mile ....
mi.
J] miles "
1 league . . .
1.
II.
Used in measuring roads and boundaries of land.
Tf'fffj inches make 1 link .... 1.
25
links
i(
1 rod . . .
. . rd.
4
rods
(t
1 chain , .
. . ch.
80
chains
<(
1 mile . .
. . mi.
III.
Used in iiwasuring doth sold by the yard.
2} inches (2| in.) make 1 sixteenth of a yard, -j^ yd.
2 sixteenths (4.V in.) " 1 eighth of a yard, \ yd.
2 eighths (0 in.) " 1 fourth of a yard, -| yd.
4 quarters " 1 yard.
IV. Used to measure the kind of distances named.
„^ , . , « ' C degree of Latitude on a Me-
60 geographical or , ^ ) • v * t •* i
nl^ 1 a ^ r J. -i ?■ make 1 < ridian, or of Longitude on
""iW Htatute miles \ ^
860 degrees
1iYd i^tatutjo miles
8 geographical mi.
6 feet
inches
the Equator.
1 circumference of the earth.
1 gpog. mi. \ Tised to measure
1 league ( distances at sea.
( used to measure
( depths at sea.
used to measure the
1 hand •{ height of horses at the
shoulder.
" 1 fathom
HI
m
ii
'
1"
'III
I
'I
I
134 DENO MINA T E :< UMB EliS.
EXERCISES IN UNITS OP LENGTH.
11)8. 1. How many inches in 2 feet? In 4 ft. ? In 7 ft. ?
In 9 ft. ? In 20 ft. ?
2, Express in inches 1 yard ; 3 yards ; 10 yards ; 100 yards,
3. How many inches in 4 yd. 2 ft. 7 in. ?
Solution.— 1. Since 3 feet make one yard, in 4 yd. there muet be 3 times
4 or 12 ft., and 12 feet plut> 2 feet are 14 feet.
2. Since 12 inches make 1 foot, in 14 feet there must be 12 times 14, or
168 inches, and 108 in. phis 7 in. are 175 in. Hence, etc.
Express in inches each of the following :
4. 2 ft. 8 in.
5. 5 ft. 9 in.
6. 9 ft. U in.
7. 1 yd. 2 ft.
8. 3 yd. 1 ft.
9. 7 yd. 2 ft.
10. 2 yd. 1 ft. 7 m.
11. 3 yd. 2 ft. 9 in.
12. 10 yd. 1 ft. 4 in.
13. How many inches in 1^ yard ? In 3^ yd. ? In 5| yd. ?
Obeerve^ J of a yard = 18 inches, and | of a yard = 27 inches.
14. How many inches in 1 rod ? In 2 rods ? In 5 rods ? lu
10 rods ?
15. Express in yards, feet, and inches, 129 inches.
Solution.— 1. Since 12 Inches make 1 foot, there are as many feet in
129 inches as 12 inches are contained times in 129 in., which are 10 and i) in.
remaining.
a. Sirice 3 feet make 1 yard, in 10* feet tliere are 3 yards and 1 foot re-
maiuinff. Hence in 129 inches there are 3 yd. 1 ft. 9 in.
16. Express in feet and inches 30 in. ; 50 in. ; 78 in. ; 100 in. ;
130 in.
17. Express in yards and feet 14 ft. ; 20 ft. ; 29 ft. ; 40 ft. ;
62 ft.
18. How many yards, feet, and inches in 68 in. ? In 95 in. ?
Id 175 in. ? In 273 in. ?
19. How many inches in 1 sixteenth of a yard ? In 2 six-
teenths? In 7 sixteenths ?
I In 7 ft. v
too yards.
let be 3 times
J2 times 11, or
i. 1 ft. 7 in.
1. 2 ft. 9 in.
d. 1 ft. 4 in.
n 5| yd. ?
s.
5 rods? Ill
many feet in
t-e 10 and 9 In.
and 1 foot re-
1. ; 100 in. ;
ft. ; 40 ft. ;
In 95 in.?
In 2 six-
D E N MI iV ^1 TE N UMB ERS.
135
EXERCISES IN UNITS OP SURFACE.
IIM). 1. A Surface has two dimensions, length and
breadth.
2. A Square is a surface bounded i y<l. or 3 ft.
by four equal lines, and having four |
right angles, thus :
This figure represents one sqnare
yard, each side of which is 1 yard or
3 feet long.
3. In 1 row across the top of the
square yard there are 3 sq. ft. ; how
many such rows in the whole surface ?
4. How many sq. ft. in 1 sq. yd.?
In 2 sq. yd., and why?
;3 !^q. ft. X 3 = 9 sq. ft.
Draw figures on your slate representing the number of sq. ft.
in surfaces that are :
5. 5 ft. wide ft. long.
6. 3 ft. wide 7 ft. long.
7. 7 ft. wide 13 ft. long.
8. 9 ft. wide 12 ft. long.
9. 4 ft. wide 16 ft. long.
10. 9 ft. wide 9 ft. long.
11. What is the cost of a walnut board 3 ft. wide and 10 ft,
long, at 13 cents per square foot ?
12. How many square feet in the floor of a room that is
9 feet wide and 13 feet long ?
13. There are 5 rooms in a house and each room is 14 ft. wide
and 16 ft. long; how many sq. ft. in the iloor of all the rooms,
and how much dijj the floor cost at 4 cents a sq. ft. ?
14. How many sq. ft. of boards will it take to cover a side-
walk that is 5 ft. wide and 734 ft. long ?
15. How many square inches in a board 6 in. wide and 18 in.
long? In a board 1 foot square, and why?
10. What will be the cost of putting a floor in a barn that
is 40 feet wide and 70 feet long, at 3 cents per s<j. ft. ?
136
D E N M I N A TE X U Jf B E U S .
1
lit
■ I
t
1?
:< (
11 ^
I
EXERCISES IN UK ITS OP SURFACE.
200. A Square Yard is the Standard Unit in sur-
face measure.
Table of Units.
1. Used ill measuring tlie surface of land, boards, plaster,
etc.
144 gqiiare inches (sq. in.) make 1 square foot . . sq. ft.
9 square feet " 1 square yard . . sq. yd.
30| square yards " 1 S(i. rod or perch, sq id., P.
ICO square rods " 1 square acre . . A.
2. Used hy surveyors in computing the area or contents of
land, and is usually called Surveyors' Measure.
685 square links (sq. 1 .) make 1 pole P.
16 poles " 1 square chain . ?q. ch.
10 square chains " 1 acre A.
640 s(iuare acres " 1 square mile , . sq. mi.
Ohsevve, Gunter's Chain is used in measuring land. It is
32 yards long, and is divided into 100 links.
8. How many square inches in 1 square foot? In 2 sq. ft. ?
In 3 sq. ft. ? In 10 sq. ft. ?
4. How many square feet in 1 square yard? In 2 sq. yd. ?
In 5 Hi], yd. ? In 20 sq. yd. ? In 50 sq. yd. ?
5 How many sq. inches in 1 sq. ft. 97 sq. in. ? In 7 sq. ft.
115 sq. in. ?
0. llow many poles in 9 sq. ch. ? In 10 sq. ch. ?
7. IIow many polos in 2 A. 5 sq. ch. 8 P. ? In 7 A. 9 sq. ch.
13 P. ?
8. IIow many acres in 10 sq. ch. ? In 20 sq. ch. ? In 50
sq. ch.?
9. IIow many acres in 250 sq. ch. ? In 917 P. ?
[FACE.
nit in sur-
irds, plaster,
. sq.
ft.
. B(l.
yd.
1. sq
id., P.
. A.
r contents of
. P.
. ?q.
cli.
. A.
. sq.
mi.
land.
It is .
InSsq
. ft.?
fn 2 sq.
yd.?
In 7 sq. ft.
A. 9 sq
. ch.
2li. ? In 50
D K N M I X A T E .\ UM B E R l^ . 137
EXERCISES IN UNITS OF VOLUME.
301. A So/hlor Volume lias thr-e dimensions — lenyth,
h7'6adth, and thickness.
U02. A Cube is a
eolid or volume bounded
by six equal s(iuares
called faces, thus :
The first of these fig- ^|
ures represents a cubical
yard, and eacli edge rep-
resents one yard long.
The second represents a
cubic foot, and each edge represents one foot long.
1. IIow many square feet in each face of a cubic yard? How
do you find the nuii^ber of square feet ?
2. If a slab a foot thick is taken off\lie top or side of a cubic
yard, how many cubic feet will it contain ?
3. lIow many slabs a foot thick in 1 cubic yard? How many
cubic feet in each slab ?
4. How many cubic feet in 1 cubic yard? In 5 cu. yd. ?
5. Cubic or Solid 3l('<isur(i is used in measuring timber,
wood, stone, etc.
Table op Units.
1728 cubic inches (cu. in.) make 1 cubic foot . . cu. ft.
27 cubic feet " 1 cubic yard . . cu. yd.
6. How many cubic ft t in a slab of stone 1 foot thick, 3 feet
wide, and 5 feet long V In 2 such slabs ?
7. A block of stone is 3 feet deep, 4 feet wide, and 8 feet
long. How many cubic feet does it contain ?
Obfterve, a nlab of the top of t1i.> block 1 foot tliick contains 4 x 8=32 en. ft.,
and there are 3 euch t^labs in the Mock.
8. How many cubic feet of earth in a bank that is 5 feet
deep, 8 feet wide, and 13 foc^t lon^-, nnd what would be the cost
of removing the earth at jj of a cent per cubic foot ?
II
1|'
\%
I
138 D E y MIS A TE 2s UMB Eli S,
EXERCISES IN UNITS OF VOLUME.
203. Wood 3l€asitre is used in measuring wood, rough
stone, and masonry.
204:. A Cofd is a pile of wood, stone, etc., 8 feet long,
4 feet wide, and 4 feet high.
205. A Cord Foot is 1 foot long, 4 feet wide, and 4 feet
high, and contains ^ of a cord.
Table of Units.
1 cord
16 cubic feet make 1 cord foot
8 cord feet or
128 cubic feet
m cubic feet " 1 \ "^"f "' ''""^
* ( or of masonry.
\ "
Cd. ft.
, Cd.
Pch.
. 1. How many cord feet in 1 cord? In 2 Cd. ? In 9 Cd. ?
2. How many cubic feet in 1 cord foot ? In 2 Cd. ft. ? In 6
Cd. ft. ? In 8 Cd. ft. ? In 10 Cd. ft. ?
3. How many cords in 8 Cd. ft. ? In 16 Cd. ft. ? In 56 Cd.
feet?
4. Express, in Cd. and Cd. ft., 368 cubic feet; 696 cu. ft.
5. What is the cost of 3 cords of wood, at 40 cents for every
<;ord foot ?
6. What part of a cord is a cord foot ? 2 Cd. ft. ? 7 Cd. ft. ?
7. A pile of wood is 4 feet wide, 6 feet high, and 16 feet long.
How many cubic feet in it ? How many cords ?
12
lUME.
i^ood, rough
feet long,
e, and 4 feet
Cd. ft.
Cd
Pch.
n 9 Cd. ?
I. ft. ? In 6
? In56Cd.
6 cu. ft.
s for every
7Cd. ft.?
6 feet long.
DENOMINATE NUMBERS. 139
UNITS OP CAPACITY.
206. Liquid Measure is used in measuring all kinds
of liquids, as oil, milk, water, etc.
The measures in use are of various sizes, thus :
Table of Units.
4 gills (gi.) make 1 pint .
2 pints " 1 quart .
4 quarts " 1 gallon
pt.
qt.
gal.
Note. — A barrel of beer contains 36 gals.
A hogshead of beer " 54 gals.
A hogshead of wine " 63 gals. .
The Imperial or standard gallon contains 277.274 cubic inchea-
Units used in measuring liquid medicine :
60 minims (tl|) make 1 fluid drachm . f 3 •
8 fluid drachms " 1 fluid ounce . fj.
16 fluid ounces " 1 pint . . . . O.
8 pints " 1 gallon , . . Cong.
1. How many gills in 2 pints ? In 7 pints ? In 9 pints ? In .
12 pints?
2. In 8 quarts how many pints ? How many gills ?
8. Express in pints 2 gallons ; 7 gallons'; 10 gallons.
4. Express in gallons and quarts 276 gills ; 339 pints.
«
I
140
DE XO MIX A T E X U .V B E R S.
#
\*-'K
EXERCISES IN LIQUID MEASURE.
Ii07. 1. Express in pints 5 gal. 3 qt. 1 pt. ; 12 gal. 3 qt. 1 pt.
2. What is the cost of 4 gal. 3 qt. of milk, at 4 ct. a pint ?
3. IIow many gallons in 93 qt. ? In 03 pints?
4 IIow many mluims in f 3 7 ? In f 3 12 V
5. Express in fluid ounces 2 gal. 7 pints.
6. Express in minims 42 fluid drachms ; 83 fluid drachms.
7. A grocer sold 5 gal. 2 qt. of vinegar, at 4i cents a pint.
How much did he receive for the whole?
8. A farmer sold 5 gal. 3 qt. milk, at 3i cents a pint. IIow
much did he receive for the whole ?
«
Find the cost of each of the following quantities of milk :
9. 7 gal. 3 qt. at 8 ct. a qt. 12. 10 gal. 1 qt. at 8 ct. a pt.
10. 10 gal. 2 (it. at 9^ ct. a qt. 13. 8 gal. 2 qt. at 3i ct. a pt.
11. 9 gal. 3 qt. at 7| ct. a qt. 14. 12 gal. 3 qt. at 4i ct. a pt.
15. What is the cost of 8 gal. 3 qt. of syrup at 14 ct. a qt. ?
10. One quart is what part of a gallon ? Of 2 gal. ?
17. Three quarts are what part of a gallon? Of o gal. ?
18. IIow many gallons in 4 barrels ? In 2 bbl. ? In 12 bbl. ?
In2lbbl.? In 100 bbl.?
19. What is the cust of 4 hogsheads of molasses at 30 cents a
gallon ? Of 7 hhd. at 30 ct. a gal. ?
20. A grocer sold 1 hogshead of syrup at 10 cents a quart.
IIow much did he receive ?
21. What is the cost of 5 f 3 14 f 3 0, r.t 5 cents for each
fluid drachm?
22. A milk dealer supplies a family with 4 quarts of milk
each day for 20 weeks, at 3J- cents a pint. What is the amount
of the bill lor the 20 weeks ?
23. How many pints of water will fill a vessel which holds
19 gal. 3 qt. 1 pt. ?
URE.
tal. 2 (]t. 1 pt.
It. a pint ?
drachms,
cents a pint.
I l)int. IIow
s of milk :
t 8 ct. a pt.
3^, ct. a pt.
t 41 ct. a pt.
L4 ct. a qt. ?
:al. ?
f 5 gal. ?
• InlSbbl.?
at 30 cents a
ents a quart.
ents for eacli
arts of milk
3 the amount
which holds
DEXO 2£ I X A TIC N UJI JJB li S . 141
UNITS OP CAPACITY.
208. /)/'2/ Pleasure is used in measuring grain, roots,
fruits, salt, e+c.
The measures in use are of various sizes, thus :
Table of Units.
2 p'nts (pt.) make 1 quart .
8 quarts " 1 peck .
4 pecks " 1 bushel
qt.
pk.
bu.
The following table shows the weight of a bushel of the
article named :
Wheat, 60 lb.
Clover seed, 60 "
Peas, 00 "
Beans, 60 "
Potatoes, 60 lb.
Corn, 56 "
Rye, 56 •'
Flax seed, 58 "
Buckwheat, 48 lb.
Barley, 48 "
Oats, 34 "
Timothy seed, 48 "
Note.— By the " Weights and Measures " Act of 1873, the
Imperial bushel, containing eight " Imperial gallons " of 277.274
cubic inches in each, is the standard bushel in Canada. The
following articles, according to the same Act, are to be esti-
mated by the Cental of 100 lbs. ; Barley, beans, charcoal, corn,
oats, pease, potatoes, rye, salt, seeds, and wheat. In Great
Britain, 8 bushels make 1 quarter.
\
142 DENO MIX A TE N UM B ERS.
EXEBCISES IN DRY MEASUBE.
209, 1. Express 5 bu. 3 pk. in quarts ; 3 bu. 2 pk. 5 qt. in
pints.
2. How many bushels in 12 pk. ? In 17 pk. ? In 128 qt. ?
3. What is the cost of 7 bu. 3 pk. of peaches, at 50 cents a
peck ? At 35 cents ? At 65 cents ?
4. A grocer sold 3 bu. 3 pk. clover seed for 9 cents a quart.
How much did he receive for the whole?
5. What is the value of a load of beans weighing 2700
pounds, at |1.85 a bushel?
6. A fanner sold 4,250 pounds of oats at 40 cents a bushel,
iiow much did he receive ?
7. A grocer sold 12 barrels of apples, each containing 21^ bu.,
at 33 cents a peck. How much did he receive for the 12 bbl. ?
8. A wheat merchant bought at $1.15 a bushel, 5 loads of
wheat, each weighing 3000 pounds, and 3 loads, each weiglijng
4000. What did he pay for the whole ?
9. What is the cost of 4984 pounds of corn at 5 cents a
bushel ? *
10. What is the cost of 1 bu. 3 pk. of berries, at 4^ ct. a pint?
11. How many bushels in 234 pt. ? In 510 pt. ?
12. A man bought 10 car loads of oats, each weighing 4590.
pounds. How many bushels did he buy ?
13. How many bushels of timothy seed in 360 pounds ? In
540 1b.? In 800 lb.? In 1000 lb. ?
14. What is the cost of 3700 pounds of com meal, when it
can be bought at $1.50 a bushel?
15. A grocer bought 40 bushels of potatoes at 75 cents a
bushel, and sold them at 22 cents a peck. How much did he
gain on the transaction ?
16. When apples sell at 15 ct. a peck, how much are they a
bushel ?
17. How many bushels in 12 pk. ? In 32 qt. ? In 126 qt. ?
12
DENOMINATE NUMBERS.
143
riiE.
2 pk. 5 qt. in
n 138 qt. ?
at 50 cents a
cents a quart.
eigliing 3700
ents a bushel.
aining 2% bu.,
r the 13 bbl. ?
el, 5 loads of
jEch weiglijng
L at 5 cents a
4^ ct. a pint ?
eighing 4590.
) pounds ? In
neal, when it
at 75 cents a
much did he
ch are they a
In 136 qt. ?
UNITS WHICH VARY IN SIZE.
210. 1. circular measure is
the arcs of circles.
Table of
60 seconds (") make 1
60 minutes ** 1
80 degrees " 1
12 signs, or 360° " 1
Observe the following names of parts
180 degrees, or A of a Cir., are
90 degrees, or | of a Cir., are
60 degrees, or J of a Cir., are
30 degrees, or -^^ of a Cir., are
used in measuring angles or
Units.
minute
degree
o
sign
circumference . Cir.
of a circumference :
called a Semi-circumference.
called a Quadrant.
called a Sextant.
called a Sign.
2. A certain class of articles are counted in dozens or scores,
in buying and selling them.
Table of Units.
13 units, or things, make 1 dozen.
13 dozen " 1 gross.
13 gross, or 144 dozen " 1 great gross.
30 things " 1 score.
8. The paper trade use the following :
Table of Units.
34 sheets make 1 quire . . qr.
20 quires " 1 ream . . iin.
3 reams " 1 bundle . . bun.
5 bundles " 1 bale . . . B.
1. How many degrees in one quadrant? In 4 quadrants?
In 7 ? In 5 sextants ? In G signs ?
2. Express 3 degrees in minutes ; 8 degrees ; 3 signs.
3. How many sextants in 1 circumference ? In 3 Cir. ? In
13 Cir. ? In 300°? In 730'?
If
i '
144
D E N M I ]S A T E N U M BE KS,
f
UNITS OP TIME.
Pi
'}y\
't'Jrj'tiui
211. Units of I'ime are used in measuring a portion of
duration.
Table of Units.
60 seconds (sec.) make 1 minute.
GO mmutes
24 hours
7 days
365 days, c •
12 caleudar mo.
366 days
1 hour
1 day .
1 week
m.
hr.
da.
wk.
\ "
1 common year. yr.
1 leap year . . yr.
Divisions of a Year.
525
O
Winter
Spring.
■ \
1 January,
2 y^^^/uary,
March,
4 April,
5 May,
Jan.
Feb.
Mar.
Apr.
May
June
,[aly
Aug.
31 days.
28, in leap year 29 da.
31 days.
30 "
31 "
G June, June 30
Summer. ■{ 7 July, ,laly 31
8 August, Aug. 31
9 September, Sept.
Autumn. \ 10 October, Oct.
11 November, Nov.
Winter. 12 December, Dec. ^_
12 calendar months = 365 days, or 1 year.
NoTT5.— The leap years are those that can be divided by 4 without a
remainder.
1. How many seconds in 4 m. V In 2 hr. ? In 5 hr.?
2. How many minutes in 1 da. ? In 3 da. ? In G da. 7 hr. ?
8. Express in liours 2 weeks ; 5 da. 10 hr. ; 3 wk. 4 da. 3 hr.
4. How many days in 24 hr. 1 In 06 hr. ? In 7220 m. ?
30
31
30
31
8.
0.
10.
11.
12.
13.
a portion of
ANSWERS.
m.
ir.
da.
wk.
yr.
yr.
p year 29 da.
Y 1 year.
iy 4 withont a
a da. 7 hr. ?
:. 4 da. 3 hr.
!30 m. ?
The answers to oral exerclBCS and the more simple examples have been
omitted.
The answers for examples taken from the Arithmetical Tables commenca
on page 150.
4.
5.
(J.
8.
9.
10.
11.
12.
IS.
Art. 5».
'. 20?3.
■. 229G.
22374.
99241.
171703.
20252^.
21400.
2:J085--
2'?02O.
181359.
103465.
352^59.
Art. 57.
1.
3.
4-
n.
a.
7.
S.
iK
10.
11.
12.
13.
6975 lb.
9915 lb.
792 A.
564 bu.
$735.
546.
1411 yd.
$4575.
$109.
425 lb. ;
234 lb.
$1776;
$1378 ;
$3251.
249 bu. ;
483 bu.
438 lb.
$1123;
$1933;
$4263.
Art. 58.
1. 1397.48.
S. $1140.47.
3. $126a41.
Art. 59.
1. $181.36.
2. $1104.37.
3. $1442.49.
4. $749.40.
1.
>)
A.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Art. 60.
$1531.54.
$-,>846.17.
$3457.03.
$1347.38.
$3381.60.
$1701.77.
$1686.37.
$2335.16,
$1836.03.
$1875.30.
$536.23.
$1984.81.
$2168.44.
Art. 61.
1.
.J
3.
4.
5..
G.
7.
8.
$5.98.
$17.03.
$17.10.
$345.47.
$23.60.
$38.39.
$58.20.
$59.90.
9. $13.48.
10. $48.80.
11. $14.65.
12. $71.75.
13. $1159.19.
1.
o
o
o,
4.
Art. 63.
$771.85.
$1901.78.
$4645 pu.
$189.60.
$2107.71.
6'. $4664.64.
7. $1908.02.
8. $29.80.
9. 11609 tr.
10. $36.06.
Art. 83,
1. 276.
2. 347.
3. 367.
4. 176.
5. 178.
6'. 168.
7. 169.
cV. 275.
9. 188.
10. 558.
//. 173.
./;.'. 2252.
./,;. 188.
14. 3528.
ir>. 349.
10. 169.
17.
18.
19.
20.
21.
■'2
23.
24.
25.
20.
27.
28.
29.
30.
31.
32.
33.
34.
4256.
1774.
3587.
2578.
2444.
3555.
3777.
2889.
1788.
3645.
4378.
827.
1487.
2468.
1366.
1579.
1579.
7377.
Art. 89,
1.
2.
3.
4.
5.
0.
'V
/ .
8.
9.
10.
11.
12.
IS.
$45.
$157;
$856;
$353.
$56(J.
187 lb.
$48.
436 A.
54.
71 lb.
188 bu.
29 tous.
91 yd.
$297.
124 tons.
10
■I- 1
146
AJVSWJi^JiS.
jl! iff
IK-;:
Alt. 90.
!|3(>.25.
154.21.
$52.35.
.S29.28.
$227.42.
}ji248.02.
$2:38.87.
$140.52.
$740.88.
$2.^25.08.
$1.81.
$48.57.
S7.(I5.
$24.46.
$.55-
$4.58.
.9
4-
5.
0.
/ .
cV.
1(K
11.
12.
in.
u.
15.
10.
17.
1.
8.
4-
5-
6.
/•
8.
9.
10.
11.
12.
Art. 91.
$327.84.
$11.81.
$105.58.
$80.74.
$218.58.
$382.00.
Oft
$254.56.
$14.03.
$801.88.
$18.49.
$21.31.
Art. 107.
2. 1155.
8. 4844.
4. 5184.
6. 1988.
;,, il
*.; !1
6.
7.
8.
9.
10.
11.
12.
IS.
7077.
47472.
9224.
42545.
42581.
27855.
241 OSO.
354042.
128340.
15.
16.
17.
IS.
19.
20.
21.
24.
25.
26.
27.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
4U
42.
4^?.
44.
45.
46.
47.
395340.
099993.
585228.
752480.
250812.
008882.
418020.
1527921.
2540585.
8505149.
4074450.
1018014.
4588763.
83000.
49800.
74700.
0821000.
4515000.
2709000.
7224000.
353585.
242424. •
545454.
454572.
680003.
899990.
888880.
308080.
249270.
288881.
799992.
100005.
855552.
300008.
111110.
485442.
350070.
101418.
727272.
558455.
192045.
187011.
545480.
351400.
804806.
29^240.
581005.
Art. 113.
1. 25228;
2. 05442.
3. 55705.
4. 10952.
5. 54855.
6*. 32070.
7. 78008.
8. 25110.
9. 581295.
10. 789958.
11. 134714.
12. 444900.
Art. 120.
1. $5019.
2. 25000800'.
3. 1728 1b.
4. 50050 lb.
5. 810000.
6. $13.
7. $535.
8. 95900.
9. $18525.
10. $056.
11. $172.
12. 6240 bu.
13. 287985 yd.
Art. 122.
2. $24.85.
3. $84.88.
//. $459.48.
5. $948.18.
6. $239.90.
7. $258.35.
.S'. $192.98.
9. $128.25.
10. $81,755.
11. $484.42.
12. $55.01.
18. $481.55.
Art. 126.
2. 5442 ^r.
.;. $1455.
//. 8232 oz.
5. 172001b.
6. 74 ct.
7. $28.75.
cS". 1704 1b.
9. 21528 gr.
10. $20.56.
11. 18278 oz.
12. 192015 oz.
13. $0?2.00.
14. $04.16.
15. 792 pwt.
16. 1000 1b.
35000 oz.
Art. 183.
1. 900 bbl.
230 bbl.
312 bbl.
21 T.
501 T.
900 T.
431 da.
700 cd.
310 cd.
900 cd.
800 hr.
000 suits.
800 suits.
40 Hheep.
70 sheep.
902 Hheep.
002 sheep.
80 wk.
00 wk.
20 wk.
30 wk.
70 wk.
11. 000 hr.
12. 2841 bags.
13. 8210.
1280.
8123.
///, 021 calves.
700 calves.
902 calves.
15. 910; 210;
801 ; 001.
4.
5.
6.
8.
9.
10.
17200 lb.
74 ct.
$23.75.
1704 lb.
21528 gr.
$20.56.
13278 oz.
li)2015 oz.
*6?2.00.
$04.16.
792 pwt.
1000 lb.
35G00 oz.
900 bbl.
230 bbl.
312 bbl.
21 T.
501 T.
900 T.
. 431 da.
. 700 cd.
310 cd.
900 cd.
. 800 hr.
. 600 suits.
800 suits.
, 40 slicop.
70 sheep.
902 sheep.
602 sheep.
30 wli.
60 wk.
20 wk.
30 wk.
70 wk.
600 hr.
2341 bags.
3210.
1230.
3123.
621 rnlves.
700 calves.
!»02 calves.
010; 210;
801 ; 601.
ANSWERS.
147
16. 620 bbl.
76'. 749.
7. 345 acres.
0^ 472.
710 bbl.
VJ. 837.
,V. 4h3 bu.
m. 9jr.
920 bbl.
.--fy. 579.
'J. $75 73.
11. Ii;i8.
17. 71210.
,.^7. 758.
/O. 251 lb.
7;.'. 150.
142420.
i-A 496.
77. 32 mi.
L.. 18-1.
.
,?,;. 695.
U. $98.
74. 307-221.
Art. 130.
.?//. 738.
IJ. §1554.
15. 343.
,^. 786.
,.^1. 597.
/4. f287(i4.
76. 245.
S. 347.
,?o-. 836.
15. $9513.
7;. 2G7.
4. 583.
27. 948.
$6342.
IS. 383-156.
.5. 837.
,Av. 379.
$3171.
I'J. idi-'OiH.
a. 485.
2',). 957.
W. Ib2-4l9.
7. 387.
,;^>. 657.
Art. 143.
21. ^b5-157.
S. 354.
.?/. 598.
/. 30.
22. 520-1^0.
0. 734.
SJ. 63!).
:.'. 90.
2.1 474-44.
10. 856.
JJ. 957.
3. 70.
24. 1878-31.
11. 648.
4. 40.
25. 319.
1:J. 607.
Art. 138.
5. 90.
20. 508-170.
IJ. 859.
.9. 574.
G. 80.
27. 65r.-279.
U. 87 cd.
,7. 397.
7. 900.
.,'8. «)80-045.
15. 59 bbl.
//. 739.
cV. 300.
29. 789-499.
83 bbl.
r>. 436.
iK 500.
30. 405.
375 bbl.
6'. 7358.
76*. 900.
31. 4072-91.
10. 39 wk.
;. 5098.
77. 500.
32. O.V2-lv4.
17. 179 acres.
<s'. 4837.
IJ. 80i).
33. 758-438.
18. 58 T.
U. 2564.
7.7. 7000.
34. 274-70.
93 T.
/^y. 9813.
//;. 3000.
.15. 75(i-110.
363 T.
7/. 6457.
15. OUUO.
30. 53(1-8.
/?. 3872.
Hi. 9000.
Art. i;$7.
/.;. 3629.
/;. 8000.
Art. 140.
/. 437.
///. 367 weeks.
IS. 7000.
/. 9vr.; i3yr.
2 839
15. 543 hr.
7. 50.
,:. !;;.125.
/W • \JfttJ •
3 789
072 hr.
J. 00.
ll-.2<'()0.
4. 3 15.
6. 738.
<] 584
473 hr.
./. 400.
3. !^4230.
76'. 876 times.
//. 700.
iit28;M).
273 times.
5. 9000.
$2115.
7 643
17. 435 i)ieces.
11. 8000.
$l(iS)2.
8. 839.
.9. ;is9.
IS. 894 times.
4. 8 1)1.1.
935 times.
Art. 143.
.-■;. 32 lb.
id 738.
/. 25.
89(i lb.
7/. (M7.
Art. 141.
i ,?. 72.
3072 lb.
i;?. 583.
/. 20 ct.
.7. 61.
4800 lb.
7,7. 739.
,?. $54.
//. 254.
(;. 520.
7//. S37.
J. 99 ct.
5. 517.
7. 342 bu.
/.7. 485.
4. *17.
(I. 615.
700 bii.
76', 537.
5. 13209.
7. 227-43.
1()(;4 bu.
17. 803.
6'. $1828.
6'. 002.
174S l)u.
M
? !
148
AXS WERS.
li:
' Up
m
!.'. ^^
' Hj
i
8.
9.
10.
11.
12.
13.
14.
28 bbl.
70 sheep.
$6008.
75 doz.
988 lb.
450.
483 acres.
Art. 156.
4. 45 hlid.
5. $8.68.
$6.44.
$16.56.
$115.93.
G. 1300 qt.
10080 gi.
7. 37 gal
30 gal.
,9. 11 gal.
14 gal.
19 gal.
.9. 3 gal.
13 gal.
74 gal.
10. 4 gal.
7 gal.
Ogal.
74 gal.
Art, 166.
7. $21 ; $12.
8.
9.
10.
11.
12.
IS.
^^' '\() ! CO »
15. ' "
16.
17.
$80.
184 A.
40; 43.
414 lb.
.n .
Iff' ._
15 . no
1J f > ffff-
\h M ;
7 (I .
10 87 .
II' It •
.36 '
215
Art. 168.
15. 35|,
16. 3??.
/7. 58 J.
i5'. 48^.
19. 53 it.
Ji;. 48/ff.
21 641 ^
Art. 169.
15. 1|; li ;
15. 14
•■8 ' ^S-
//J 7 . O t . -f 8
^O- S » '"] J > -1-4
^^- J ft
iq 7.17.17
Art. 170.
41. %^.
42.
14
1 ? > 15 >
4^6.
47.
48.
4D.
$4^.
$5».
W^i oz.
aVgal.
Art. 173.
11.
1^
$6600;
$6720 ;
$3090 ;
$4312 ;
$4381.
$30;
'ir'*8 ;
$27.
9022;!
188. I
Art. 174,
15. I
16. A-
18. $12 J;
19.
$104 ;
$20| ;
$18 iV;
$•36,^,.
H .
$13i^T
$21^^
Art. 175.
8. 8 books ;
12 books ;
4 books ;
16 books ;
40 books ;
80 books.
9. 24 pounds ;
72 pounds.
10. 6 pounds ;
15 pounds
24 pounds
12 pounds
27 pounds
60 pounds.
Art. 176.
11.
2 times ;
4 times.
12. 3.
13. 5.
15.
16.
17.
19.
4.
6.
5.
7.
4 yd.;
7 yd.;
5 yd.;
9 yd.
4 pk. ;
5pk. ;
3pk.;
lOJ pk. ;
18pk.
Art. 177.
20.
26.
27.
U
¥ »
18
28. V
s »
1
Art. 191,
1. $1.00.
o.
4.
5.
6.
rv
/.
S.
9.
10.
11.
12.
13.
14.
15.
10.
17.
18.
19.
20.
21.
22.
23.
$3.15.
;t^8.75.
$10.30.
$8.43.
$105.56.
$6(1. 24.
$141.60.
$188.03.
$8589.75.
$417.30.
$431.29.
$ir)583.75.
$807.94.
$449.87.
$00.12.
!t;73.08.
$148.10.
$3o;}ii,..
$62.89.
$114.80.
Art. 194.
7. $.108;
$.579 ;
$1,851 ;
$1,787;
$1.93;
$19.80;
$5.79;
$77.30.
8. $4,860^;
$9,788;
$24.33|;
$48.665 ;
$480.65 ;
$97.33.
Art. 195.
7. 14400 gr.;
33000 gr.
8. B900;
3 1985.
9. 20; 100; 13.
A lis WEES.
1-n
rt. 19J.
$1.00.
$3. 15.
J|^a75.
$10.20.
12. r?.
$8.'v.
$;}.43.
$105.56.
$141.60.
|18«.08.
*;}r)8o. 75.
$417.20.
|42I.2!>.
$tn582.75.
$<3()7.94.
$449.87.
$00.12.
!^73.03.
1148.10.
$3();{;),,
$62.89.
$114.80.
It. 194.
$.io;};
$.579 ;
$1,351 ;
$1.7;]7;
$1.93;
1^19.80;
S5.79;
^77.20.
HM% ;
^9.733;
^21.331;
;48.665 ;
i486.65 :
97.33.
t. 195.
t400 gr ;
mo gr.
> 960 ;
' 1936.
►;100;13.
6.
8.
10. 6 ; 30 ; 76.
11. 42 oz. ;
27 oz. ;
52 oz.
Art. 196.
4. 2i lb. ;
71b. ;
121b.
89 oz.
437 1b.;
1384 lb.
$1.35;
$3.55.
$48.
9. $40.60:
$60.55 ;
$90.30.
10. $19.60.
Art. 198.
0. 276 iu.
10. 91 in.
11. 141 in.
12. 376 iu.
13. 54 in. ;
126 in. ;
198 in.
14. 198 in. ;
306 in. ;
990 in. ;
1980 in.
16. 3 yd. 1 ft.
9 in.
16. 2 It. 6 in. ;
4 ft. 2 in. ;
17.
6 ft. 6 in. ;
8 ft. 4 in. ;
10 ft. 10 in.
4 yd.
6 yd.
9 yd.
3 ft.
3 ft.
2 ft.
18. 1
13 vd. 1 ft. ;
20 yd. 2 ft.
19.
yd. 2 ft
8iu.
2 yd. 1
11 in.
4 yd. 2
7 in.
7 yd. 1
9 in.
2} in. ;
4^ in. ;
15f in.
ft.
ft.
ft.
Art. 200.
S. 241 pq. in. ;
1123 sq. in.
6". 32 P. ;
160 P.
7. 408 P.;
1276'P.
o. 1 A. i 4i a.. ;
5 A.
9. 25 A.;
5}H A.
Art. 202.
7. 96 cu. ft.
8. 48 cu. ft.;
$3.20
Art. 206.
4. 2 Cd. 7 Cd.
ft.;
5 Cd. 3 Cd.
ft. 8 cu.
ft.
5. $9.60,
6. I Cd. ;
iCd.;
|Cd.
7. 384 cu. ft. ;
3Cd.
Art. 207.
/. 47 pt. ;
101 pt.
2. $1.52.
5. 23i gal.
7 cl. 7 pt.
4. irv'420;
111720.
f 3 368.
n[ 2520.
Fl 4980.
$1.98.
$1.61.
$3.48.
$6.27.
$2.99.
$6.56.
$2.38
$4.42
$4.90.
5.
G.
7.
.9.
9.
10.
11.
13.
13.
u.
15.
16.
17.
18
^%-
lUtr
19.
20.
21.
23.
Tl <ral.
4:|2 -ill.
8(>4 irnl.
3600').7il.
$75.60;
$158.76.
$40.33.
$37.90.
$39.30.
159 pt.
Art. 209.
/. 184 qt. ;
234 pt.
2. 3 bu. ;
4i bu. ;
4 bu.
3. $15.50;
$10.85 ;
$20.15.
4. $10.08.
5. $83.35.
6. $50.
7. $39 60.
8. $546.25.
9. $4.45.
10. $5.01;
11. 3|4 bu. ;
7f A bu.
12. 1350 bu.
13. 7^ l)u.
IU bu.
l()j Ini,
20s bu.
14.
15.
16.
^99.1 Of.
IS5.20.
150
Axs m: ix' s.
ANSWERS TO AKITHMETICAL TABLES.
ii '■'•'•■*
Observe, the answers fo examples taken from the Aritliniotical Tnble*.
are in every case arruu2:ecl in the order the pupil ia directed to take i he
examples from the Ta!)les. The letters over the sets of answers iudicalc
tlie columns of the Table used, and the black figures in the margin the
number of the answer.
Art. 47. Columns of three fignrea.
A.
10
B.
18
c.
12
D
16
E.
10
G.
10
H.
1
21
17
2
11
16
19
19
17
10
15
17
3
12
15
20
15
18
12
16
21
4
13
13
20
20
14
13
20
10
5
13
16
14
19
13
20
17
17
6
12
17
14
16
11
24
20
18
7
17
18
15
17
14
20
18
21
8
22
14
20
17
14
20
21
18
«>
4
Art. 48. Columns offoui
'figures.
A.
14
B.
c.
D.
23
E.
F.
21
G.
24
n.
1
23
21
24
23
2
17
18
26
24
23
20
18
25
«
15
21
24
23
23
19
25
23
4
17
21
23
20
10
22
25
23
5
18
19
21
21
17
28
23
26
<;
20
24
19
25
19
27
27
23
7
26
22
23
23
16
29
26
25
Art. 48. Columns of five figures.
]
2
<>
4
n
A.
B.
c.
D.
E.
F.
o.
20
25
28
28
3'*
'J5
27
'^0
24
30
3'.
28
27
27
10
29
27
20
25
28
30
22
24
30
28
20
30
31
20
20
2 1
30
25
31
30
29
28
27
31
21
30
35
H.
31
27
30
32
31
27
.1 \ S W ERS.
151
'idles.
■tl to t.'iku till"
^woi'f; iiidicali'
Iho luaigia tlit
Art. 48, Columns <:f six f.gures.
A.
23
«.
c.
D.
E.
F.
G.
3(5
n.
1
31
32
36
35
32
33
2
24
32
33
38
30
30
32
34
{i
24
32
34
31
29
30
3(5
39
4
30
31
35
37
28
33
38
37
•5
35
30
34
3(5
27
40
38
35
II.
10
17
15
17
10
21
20
U
17
17
20
18
18
21
21
18
Art. 48. Ciili.imns of seven figures.
A.
B.
39
c.
D.
40
E.
F.
G,
41
II.
1
27
35
37
41
40
2
29
35
40
42
34
44
38
43
:$
32
39
39
40
37
39
43
44
4
39
35
43
43
30
42
40
41
Art. 48. Columns of eight figures.
a.
H.
24
23
18
25
25
23
}5
23
J3
26
7
23
6
25
II.
31
27
30
32
31
27
A.
n.
('.
D.
E.
F.
G.
11.
1
32
42
42
44 1
41
49
47
49
2
37
42
45
49
42
47
45
48
3
41
43
47
46
39
48
51
48
Art. r>5. Exercise loitlt two numbers of two figures.
AB.
BC.
95
CD.
DE.
102
EF.
128
FO.
GII.
1
118
159
92
1)57
2
73
42
127
83
139
97
85
:i
87
78
92
134
15(5
169
, 101
4
109
101
121
119
102
137
182
r>
78
88
95
156
73
143
141
<s
101
117
83
144
ir)3
l:;5
60
7
95
01
121
123
139
99
104
8
81
44
53
141
r)i
127
181
O
80
105
(14
14)
106
171
124
'♦,.
!i t ;
>: '^1
152
a:^s webs.
Art. 55-2. Exercise idth three numbers of two figures.
AB.
138
BC.
CD.
DE.
EF.
FG.
GH.
1
100
216
177
187
182
143
2
140
115
162
142
236
176
183
3
129
100
178
194
161
227
188
4
145
161
130
215
170
222
239
5
143
145
160
204
158
193
150 •
6
141
121
130
219
207
184
161
7
149
101
127
192
236
177
190
8
110
109
111
224
160
220
219
Art. 55-2. Exercise udth four numbers of two figures.
AB.
205
BC.
CD.
DE.
236
EF.
FG.
Gn.
1
173
251
284
261
241
2
182
143
248
202
241
234
267
3
165
166
187
290
229
312
245
4
210
218
204
263
255
•272
248
5
173
149
216
279
212
242
245
O
185
161
136
288
304
263
247
7
175
166
185
272
245
270
228
Art. 55
~2. Exercise with five numbers c
f two fig
ures.
AB.
BC.
CD.
DE.
EF.
FG.
GH.
1
247
201
337
296
289
319
325
2
218
203
257
298
309
319
324
3
230
223
261
338
314
362
254
4
240
222
251
336
309
321
343
6
227
189
222
348
309
320
331
6
211
226
194
368
313
365
285
Art. 55-2. Exercise with six nurr^ers of two figures.
AB.
BC.
CD.
346
DE.
EF.
FG.
GII.
1
283
261
392
357
404
882
2
283
260
331
346
394
369
333
3
260
227
308
413
368
411
349
4
294
202
257
407
403
S99
429
5
253
254
280
428
318
413
369
ANS WE lis.
153
figures.
GH.
143
183
188
339
150
101
190
^^9
figures.
GH.
3li"
267
245
248
245
247
238
ligures,
GII.
325
324
354
343
331
^85_
gurcs.
GII.
882~
333
349
429
309
Art. 55-2. Exercise mth semn nwrnbers of two figures.
AB.
348
BC.
318
CD.
430
DE.
EF.
FG.
454
GIT.
1
440
442
391
2
313
3<;4
378
421
448
418
428
3
314
3(J7
314
483
465
489
435
4
330
327
315
487
415
493
407
Art. 55-2. Exercise with eight numbers of two figures.
1
2
3
AB.
378
307
340
BC.
333
304
333
CD.
407
384
373
DE.
EF.
490
545
374
FG.
515
490
563
503
490
583
GH,
483
514
473
Art. 50-3. Exercise icith three number^ f three figures.
ABC.
BCD.
CDE.
DEF.
EFG.
FGU.
1
1400
1016
3177
1787
1883
1843
2
1415
1103
1643
1436
3376
1783
3
1306
1078
1794
1901
1037
3388
4
1401
1630
1315
3170
1733
2239
5
144->
1409
1704
3058
1593
1950
O
1331
1830
1319
3307
2084
1861
7
1501
1037
1393
1936
2377
1790
8
1109
1111
1124
3300
1020
2219
Art. 50-3. E.r( rcise icith fmx r n umbers of three figures.
ABC.
BCD.
CDE.
DEF,
EFe.
FGH,
1
2073
1751
3536
2384
2801
2641
2
1843
1448
3503
2041
2434
2307
3
1000
1087
1890
2939
2312
3145
4
2118
2304
3003
2055
2572
2748
5
1749
1516
3179
2812
3143
2445
i\
1861
1636
1388
20O4
3003
3647
7
17(56
10^5
1S73
2745
3470
3738
15-4
AXS WE Its.
it ('*.«
'i/1
Art. 50-3. Exercise with five numbers of three figures.
ABC.
3501
BCD.
3037
CDE.
DEF.
2989
EFG.
Fon.
1
3390
2919
3335
15
3203
3057
3598
30(«0
3119
3334
:s
3333
3301
3038
3414
3i(;3
3054
4
3433
3^51
3538
340'.)
3131
3343
5
3389
1933
2348
3509
3130
3331
<S
2130
3394
1908
3713
3155
3585
vVrt. 5<»-3. Exercise icith six numbers of three figures.
ABC.
3801
BCD.
3040
CDF',.
3493
DEF.
3957
EFG.
FGU.
1
3004
4083
ti
3800
2031
3340
3494
3909
3733
:s
3(;37
2308
3113
4168
3711
4149
4
39(53
2057
3007
4100
4099
4039
5
3554
3580
3838
4318
3313
4109
Art. 50-3. Exercise icith seven numbers of three figures.
ABC
BCD.
3330
3078
3714
3315
CDE,
DEF.
4443
4348
4805
4915
EFG.
FGH.
1
:^
4
3518
3104
3107
3337
4340
3831
3183
3187
4454
4518
4089
4193
4591
4338
4935
4907
Art. 56-3. Exercise with eight numbers of three figures.
ABC.
BCD.
3307
3084
3373
CDE.
4715
3890
3703
DEF.
5190
4945
5074
EFG.
5003
5490
4783
FGII.
1
3833
3704
3432
5080
5014
5873
A XS WERS.
155
figures.
AH. iyi\-Q. ExcrcUe in'lh three uumhcrH offo}irfifjiirei^.
Foil.
322o
3224
3054
3243
3231
3585
figures.
FGH,
4082
3733
4149
4029
4109
c figures.
FGH.
4591
4228
4935
4907
figures.
FGII.
5080
5014
5873
AlKD.
BCDE.
10177
CDEF.
21787
DEFG.
EFGII.
1
14010
17882
18843
ti
14102
I10i2
10430
1437(5
:J3783
;5
1307S
• 10794
17901
19627
10288
4
14030
10315
13170
21722
1:239
5
14409
14704
17058
20593
iOiJ'^J
o
13230
12319
13207
22084
20801
.7
15027
10292
12930
1937/
23790
8
mil
11124
11260
22020
10219
Art. r>(>-3. Exercise with four numbers of four figures.
ABCD.
20751
IK'DE.
17530
CDEF.
DEFd.
23801 •
EFGU.
1
25384
28641
2
18448
14502
25041
20434
24367
3
10;587
10890
18929
29312
23145
4
21204
22003
30055
20572
25748
5
17510
15179
21812
28142
21445
«
18036
16388
13904
29062
30047
7
17085
16872
13>745
27470
24728
Art. 5(>-3. Exercise Kith five numbers of four figures.
ABCD,
BCDE.
20390
CDEF.
33989
DEFG.
29919
EFGH.
1
25037
29225
ii
22057
20598
20009
30119
31224
ii
23201
22038
20414
34102
31054
4
24251
22538
25409
34121
31243
5
22922
19248
22509
35120
31231
c;
21294
22908
19713
37155
31585
Art. 5(»-3. Exercise irlth six numbers of four figures.
ABCD.
BCDE.
1
* 28040
20492
2
28031
20340
ii
20;]08
23113 :
4
29057
2f500T
5
25580
25828
CDEF.
DEFG.
3901)4
EFGH.
34957
30082
33494
34<,!()9
39733
3ii;;8
41711
37149
2('100
41099
41020
28318
43213
32169
166
ANS WERS,
Art. 5G-3. Exercise icith
seven numbers of four
Jig fires.
ABCD.
BCDE.
CDEP.
DEFQ.
EFGH.
1
2
3
4
35220
31678
31714
32315
32-^0
26821
27182
33187
42442
38248
31866
31915
41454
42518
48689
49192
44591
45228
46935
41967
An
1 lif
Art. ii
►6-3. Exercise with
eight numbers of four
'figures.
ABCD.
BCDE.
CDEF.
DEFO.
BFOH.
1
2
38267
37084
a4372
32715
30890
33762
47196
38945
37674
52003
49496
56782
50086
55014
47873
Art. 87. Examples taken as directed in 1 cmd 2.
AB.
BC.
CD.
DB.
EF.
FQ.
GB.
1
12
21
19
86
m
78
21
2
33
32
13
67
21
83
73
3
47
68
22
16
38
11
92
4
25
45
51
1
92
21
14
5
6
32
77
36
63
27
27
6
29
3
65
48
17
85
48
7
35
53
27
27
31
1
86
8
' 24
36
41
6
43
29
9
28
25
52
11
88
15
48
Art. 87. Examples taken as directed in 3 and 4.
AB-BC.
BC-CD.
CD-DB.
DB-BF.
BF-FG.
FG-GH.
1
7
31
5
46
37
27
2
16
33
62
72
73
72
3
15
52
18
16
31
84
4
6
38
24
88
18 .
19
5
14
58
26
55
63
26
6
24
51
87
28
17
28
7
8
17
26
37
35
41
8
26
43
28
21
5
46
9
14
34
63
28
19
8
10
89
7
22
71
84
65
?
A XSWEJiS,
157
Art* 88. Examples with three numJbera taken as directed in 1.
ABC.
BCD,
CDE.
DET.
EPO.
PGH.
1
121
219
186
868
322
779
2
332
313
i;J3
07'>
217
827
3
4rt8
678
216
162
389
108
4
245
449
501
H
921
214
5
m
32:3
704
308
027
273
6
297
35
652
48;?
165
348
1
35:j
527
273
269
301
14
8
230
359
406
57
429
291
9
275
252
511
112
885
152
Art. 88. Examples with three figures taken as directed in
o
ABC-BOD.
BCD-CDE.
CDE-DEP.
DEP-BPG.
EPO-PGH.
1
69
305
54
463
373
2
lor
338
628
727
728
8
148
518
184
169
316
4
62
376
288
382
181
5
142
674
255
M7
526
6
249
513
872
283
172
•y
83
174
2(53
365
341
8
267
428
279
205
54
9
13t
337
628
281
192
10
393
78
229
716
845
Art. 88. Examples with four figures taken as directed in
ABCD.
BCDE.
CDEP.
DEPG.
EFGH.
-
1219
2188
1868
8078
3221
A
8313
3133
1321
6783
2173
A
4678
6784
2102
1011
3892
%
2449
4499
5008
79
9214
K
677
32;36
7037
3627
6278
n
2965
348
6517
4885
1652
Hp
8527
5273
2731
2699
3014
^
2359
8594
4057
571
4291
•
2748
2511
5112
1115
8848
158
ANSWFES.
Art. 88. Examples trith four figures taken as diverted in !?.
1'^
ABCD-BCDB.
BCDE-CDEF.
CDEP-DEFG.
DEPO-EFGH.
1
()95
3054
537-
4627
a
l(Mi2
3372
6273
7272
3
1482
51&1
1S;J1
KWl
4
(ii4
37(32
2;JH2
:<ljl!>
5
1426
5745
2517
r>i74
6
W87
5128
8717
2:vJ8
7
826
1737
2635
.•Hi.)!)
8
2572
427!)
2795
2u54
9
1.J37
3371
6281
281)8
10
3U22
771
2284
7155
Art. ll.'». Multiplicand three figures, multiplier one.
ABC.
BCD.
CDE. ^
* DEP.
EFG.
FGII.
GUI.
HIJ.
1
lOJl
5536
2775
1548
6256
1696
3704
3195
3
21H0
3312
4()!»8
2608
7;38
3460
3712
22S0
3
825
5;J13
2384
7704
3160
292.'5
1778
10!>6
4
;i558
2811
33(ki
]4!)6
33!)5
2.577
2985
8748
5
rtii4
2315
4473
3528
2781
2184
1470
21.54
6
2233
1755
i!H4
2316
6;}44
3752
34.38
2-178
7
2«2S
:J474
(«36
4620
22;32
3388
.'5094
3943
8
1392
!m
2808
4795
4295
5373
2928
.5:376
9
1036
12S8
7()14
1868
5400
37!)5
.5337
3748
10
6678
2i:i5
1116
6352
5688
3880
4295
.5.'{46
11
2415
7160
(}678
1644
4374
3472
W80
5154
Art . 1 i .*5. MultipUeand five figures, mvltijilier one.
ABCDB.
BCDEP.
CDEPO.
DBFGH.
EPGHI.
467701
PGHI.T.
1
,50775
4i;)r)48
833256
51692
423195
s
262098
110508
136738
4181(K)
147712
5.5-12S0
3
110384
607701
2!»81«)0
866<»25
442778
6r.i;'.i6
?
5;S43«)6
lH749t»
262395
22-1677
iM2985
773748
B
.592173
417528
191781
3M184
1S.'>17()
164ir)4
9
63! 114
78316
766;)44
231752
714138
28M78
#
526336
289«i20
713232
647388
1190!>4
;3»T!t44
9
554808
172795
2312ft5
617.373
2.57!t28
418:376
466614
7;i8«>8
677400
2133795
608:537
;3():5748
10
297116
312:352
167(188
63.5880
471295
4:37:ilfi
11
342678
268644
8.59374
219472
;389480
521154
■
1
2
a
4
ii
C
1
c
fl.
1(
IJ
1
1
AXSWEES.
159
'ted in !?.
Art. 114. Multiplicand four figures, multipUeT two.
PO-EFGH.
4r,27
-i-i'i-i,
1;W1
5474
.•«),)!>
7155
/• one.
■
HIJ.
3195
aaso
10f>6
»
8748
2154
8-178
3043
5;i7fi
3748
5.'J46
5154
1
ABCD.
BCBE.
CDEF.
DEPG.
EP6H.
PGHI.
OHTJ.
1
115056
574775
a33288
17829<5
537832
236964
394315
2
257712
353508
43(H)08
2()7S08
92300
374112
445680
3
102083
5()2104
2802^1
818720
373175
315<i;]8
183456
4
374031
3«558<)
34481()
202095
;i54707
300895
352i?48
5
8031»8;3
204423
504908
365211
352374
224270
191334
6
25^105
180044
229896
278064
666792
459718
355818
7
3()26:M
30;^5t)
673540
545632
240M8
368524
577524
8
77()()(14
1 135-28
313895
514-125
50722;^
555768
361416
9
13U9(i8
1 i58;u
795898
2-244<lO
574515
447981 i
55^078
10
70r)5*)5
2;nooo
j;wii2
68:}528
t/14980
413015
507046
11
'Mmo
77H1HKS
097(W4
213951
457592
416880
589874
Art. 114. Mnlt>'plicand Hix figures, mvUipUcr four.
ABCDEF.
BCDEFO.
CDEPQH.
DBFGHI.
EFGHIJ.
1
1157047688
57962;55496
341822{W!^2
17!«)fV316()4
542a373115
2
2601853l)(;8
35-181 30-J08
4324351<KM)
272.3363712
9400.38180
3
10;M30!>324
5(W5815520
2897543175
8281094()38
3777576656
4
37952.3721(5
aOHl 503595
341tH)67507
2017412795
3576267948
5
8107588'.«)8
2(W75-^9M1
5074549074
3681039770
3548075534
6
25;i2;il3996
1810<«)3<)61
2;3795 17992
2809423:318
6741964218
T
3082;J73<t40
39730<)21)32
6m12981!<48
55268il7(.24
2427279624
8
7K29307895
lin.l0t)5H25
31()724712^}
5208615768
5104412616
9
141S596798
146779691 K)
8031509115
22720;M387
5809(X)2578
10
70!t21!l7112
23 (772-.'7-J8
13(105329S0
(i9033.">O115
6.506406246
11
2875115404
7825652 IW
7(I(J0293992
2166208380
4618344474
07?.^.
Art. 1159. .Diridend three figures, divisor one.
FGHM.
423195
5.54280
6:.(;08
773748
2HM78
387!)44
418.376
30.3748
43731fJ
521154
2
8
4
5
6
7
8
9
10
11
la
ABC.
BCD.
!
24-2
189-2 1
134
5^5
47-1
92-8 !
149-1
80-a 1
46-7
379 '
lo: A
8f}-ft
95-2
143-1
56-4
322-2
108
60-5
84-3
149-1
147-1
149
239
86-7 I
73-2 '
117-6 !
116-3
31.5-2 ;
105-4 ,
76-8 I
268-1 i
51-4
315-2
111-6
319-1
84-2
M-\
118-<)
23(5-1
1.32
1.39-5
66-3
91-1
59-1
92-7
117-2
106
289-1
3<>-2
123
120-4
98
488
64-5
82
118-2
14.5-4
107-1
88-^1
44
9(J-2
108-1
103
109-5
112-1
56
94-5
82-5
98-1
19.3-3
81-1
96-1
99-1
4.5-5
1.36-1
243-3
171-4
8(1-4
218-1
13(Hi
85-3
165-2
94-1
107-5
94-2
212-1
84-2
74-6
■I
il
160 AyawEES.
Art. 139. Dividend five f'gvres, divisor one.
▲BCDE.
BCDfiF.
CDEFO.
DEFQH.
EFGHI.
FGUI.T.
2
9739
ia^40-3
5315
26118-2
13928-1
4461-4
3
6711-7
I2;ji9-i
13917-2
15979
6627
43718-1
4
56T3-2
10459-a
6248-6
16857-1
24765
61;ifr-6
5
10«89-2
12064-1
41289-1
2866-2
11693-3
9960-3
6
7516-3
10833-1
6480-6
13877-2
4081-1
8832-1
7
17649
14736-1
15789-4
11846-2
8207-2
5622-5
8
12248-3
19132
9245-4
6608-1
19299-1
7218-6
9
4409-2
16139-5
17098
9325-2
6545-5
lir)94-2
10
21619-2
5;i99-6
42988
8538-2
19536-4
19212-1
11
3051-4
10662-4
7731-3
7987-1
9743-3
!t!)73-l
12
19649
11184-1
10526-4
6769-2
14771-4
4824-5
Art. 144. Dividend four fgures, divisor two.
ABCD.
BCOB.
CDEF.
DEFO.
BFOH.
89-79
F€IHI.
99-5
Quur.
2
22-77
182-14
177-4
99-14
8;3-48
3
114-11
47-29
83-69
273-32
104-50
126-49
80-77
4
41-7
8a-7
63-SiO
77-4;i
100-29
99-88
79-35
5
207-30
78-1
iii-as
61-17
199-25
83-as
166-65
6
45-68
303-«
102-18
105-31
34
88-65
78-23
T
91-16
35-42
296-1
182-6
115-26
78-43
8»-26
8
91-19
122-5
101-33
104-12
112-17
99-61
84-12
9
54-26
248-11
71-83
131-8
80-7
96-69
40-M
to
95-25
58-45
220-17
64-88
361-21
102-34
126-45
11
32-26
126-31
47-79
84-5
57-21
106-71
199-7
12
128-8
142-1
249-11
53-21
76-13
61-34
148-18
Art. 144. Dimdend^ix figures, divisor three.
ABCDEF.
BCDBFO.
COEFGH.
DBFGQI.
EFQHIjr,
2
369^310
8397-72
603-177
837-137
2270-333
3
«{85-ij03
442-517
1425-267
1954-2;)0
1684-647
848-621
4
296-106
420-849
9()7-3»4
1700-68
5
1110-117
650-279
1924-400
874-138
605-93
6
1462-98
1309-115
732-592
860-169
478-23
7
636-321
904^«
&5H8-154
730-95
1486-117
8
1812-320
777-5;38
191f}-73
458-826
14<h(-198
9
1002-47
1004-530
1053-530
1698-43
406-714
to
778-50
1239-288
927-439
2178-109
1296-419
11
4<iO-18
764-725
(•(04-25
WH-llO
459-67
12
92;i-6tt9
2300-;i8
1056-153
486-9
974-305
'
t
ne.
•
rem J.
1
4461-4
43718-1
6l;J6-6
.3
9960-3
1
883a-l
2
5522-5
-1
7218-6
-5
11594-2
A
1921^1
-3
9973-1
-4
4824-5
two.
11.
GUU.
-5
83-48
-49
80-T7
-38
79^:^5
-83
166-55
-65
78-23
-43
89-26
U61
m-vz
1-59
40-34
-34
126-45
^71
199-7
-34
148-18
hree.
EFGHIJ.
2270-389
848-621
1700-58
(i0r>-93
478-23
1486-117
14W-198
405-714
1295-418
459-67
974-306