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GRUMM'ETTS
-♦-♦.-
The Newest and most Ccmpiete
SELF INSTRUCTOR
— FOR —
All who desire to advance them-
selves in Figures.
«
— BY —
J"ose3I3h: o-:RTris/cjb/L-jsirrT.
:)C.
Olaij
PREFACE.
'■"g discoveries have been . """^ ''»^'-
«'^PWaed that any eh,-,; J*"' '°8«»«^ ""dso
.-''w«gthe4Jl;';"f«-^».iH
-'-to, lea™ .,/;^7'.;'"'-'-y other
^«'y short tiB.e. *^'' l-^ok » a
JOSEPH GRDMMETT
««". November, 1877.
> ».
ADDITION,
i?
s caicuJations
^"^ and start-
^ the foJJow.
^hods in the
etiier and so
inary mind,
^»* any other
^ooJc in a
"1^* »n the
*»even. hv
»ty of Wat
culture.
Various suggestions have been made refer-
ring to improved methods of addition. In
practice I have found no better or quicker
method than the following : —
KuLE. — Commence at the bottom of tlie
right hand column ; add thus— 15, 19, 21) ;
set down the 9 in tens place and carry the
two tens to the second column, then add thus
— ^4, 10, 18, 28 ; set down 8 in tens place
and carry two hundreds to the third column,
and add so on to the end. Never add in tliis
manner — 8 and 7 are 15, and 4 are 19, and
3 are 22, and 7 are 29 ; it is just as easy to
name the sum at once, and save time and
labour.
4687
6423 ♦ '
5684
4567
4328
25689
K-TTHiE :DNro. 2.
MULTIPLICATWK
When the multiplier is any number be-
tween 11 and 20, the process is sihiply to
multiply by the unit figure of the multiplier,
set down one figure to the right hand of the
multiplicant and add in the multiplicant.
* . •
What is the cost of 26 yards of goods at
14c per yard 1
26x14
[J-
$3.64
¥ •<
a
Process. — 4 times 6 are 24, set down 4 to
the right of the 6, carry 2, add it to 6 makes
8, then carry 8 ; then 4 times 2 are 8, and 8
to carry makes 16, set down 6, add the 1 to
narrv fn the figure 2 crives 3, then make S3. 64c
the sum.
i1
:ruil,-bi IsTO. 3.
MULTlPLICAriON.
s.» V
To multiply any number of two figures
ty 11.
I
Rule. — Place the sum of the two figures
between them. Multiply 45 by 11 — 4 and 5
are 9 ; place the 9 between the 4 and .5, makes
495 the sum.
Multiply 87 by 11—8 and 7 are 15 ; set
5 between the 8 and 7- then one to carry add
it to 8 makes 9, gives 957 the sum.
tl
jBxrXi:E3 isro. 4.
MULT1PLWAT10N.
To multiply anynumber by It
N..
RULE.-Brmg down the right hand figuw
8 ; tlien add 8 and 7 are 15, bring down 6,
carry 1 to 7 makes 8 ; then 8 and 5 are 13,
bring .lown 3 and carry 1, add it to 5 makes
fi • then 6 and 3 are 9, bring down 9, you
have none to carry ; then bring down the 3,
makes 39358 the sum.
3578x11
39358
!*
i
MUL TfPL 10 A TIOX.
Lt.
b hand figure
ring down 5,
and 5 are 13,
it to 5 makes
r down 9, you
y down the 3,
t'^
\
K*.
i
To multiply when the sum of tlie units inf
10 and the tens are alike.
.Rule.— Multiply the figure in tens, place
by the next larger number, and the tens by
themselves.
Jpjat is thini^t of 86 yards- of goods at
t cents per yard:
84 cents per yard:
86
84
$72.24
Multiply 91 by 99.
w
91
99
9009
MULTrPLWATION.
When the unite of any two numbers are
alike.
Rule.— Multiply units into units, then the
sum of the tens by the units, then the tens
together.
What is the cost of 62 yards of Calico at 32
cents per yard 1
62
32
$19.84 .
PR0CBs8.-^Twice 2 are 4, set the 4 in units
place ; then twice 9 are 18, set down 8, carry
1 : then 3 times fi ar>t\ l« a-nA *y^ ««
makes 1 9— making $ 1 9.84 cents the sum.
B
e.
i^tjxjE zsro, 7.
numbers are
inits, then the
hen the tens
f Calico at 32
bhe 4 in units
town 8, carry
the sum.
MULT J PLICA TfON.
Whon the tens of any two numbers are
alike.
t
I
KuLE.— Multiply units together ; then the
sum of the units by the tens ; then the tens
together.
What is the cost of 64 lbs. of Sugar at 66
cents per pound ?
64
66
$42.24
PROCES8.-r-6 times 4 are 24, set down 4 and
carry 2 ; then 6 times 10 are 60, and carried
2 makes 62. set down 2 and carry 6 ; then 6
times 6 are 36, and carried 6 makes 42. rnVp^
$42.24c the sum.
B
I^"c^XiE isro. a.
h
MUL T! PLICA TION.
To Multiply by 25 or J.
What is the cost of 64 yards of goods at
^5 cents per yard 1
Rule. — Annex two ciphers to the number
of yards and divide by 4, and you will have
the answer in cents.
4)64.00
$16.00
Half yard 4)64.50.00
116.12.50
8.
IRTJXiE IvTO. 9.
MUL TIP Lie A TION.
ot\.
, To multiply by 50 or J.
ds of goods at
to the number
you will have
What is the cost of 79 yards of calico at 50
cents per yard 1
Rule. — Annex two ciphers to the number
of yards and divide by 2, and you will have
the answer in cents.
2)79.00
$39.50
^juarter yard 2)79.25.00
139.62.50
;;
lEaux^s isro. lo.
MUL T I PL 10 A TION.
To Multiply by 12^ or J.
What cost 88 pounds of goods at 12J cents
per pound ? ,
Rule.— Annex two ciphers to the number
of pounds and divide by 8, and you will have
the answer in cents.
8)88.00
1.00 *
laXTLE 3SrO. 11,
MULTIPLICATIOK
To multiply by 1.25 oi|.
What is the cost of 96 yai-ds of jroods at
.25 per yard?
the number
ou will have
RULE.-3- Annex threff ciphera to the num-
ber of yards and divide by 8, and you will
have the answer in cents.
8)96.000
$120.00 '
J.'
uii ^aru o^yo.ou.UUO
1120.62.50
.
II
IRTJXiE 2SrO- 12.
M UL riPL TO A TION.
To Multiply by 250 or J.
What is the cost of 48 yards of goods at
$2.50 pel yard 1
Rut.E. — Ann<ix 3 ciphers to the number of
yards and divide by 4, and you will have the
answer in cents.
4)48.000
1120.00
4 VJirrl iU8 7fi OnO
4 .7 -/
$121.87.50
ie-crx.13 3sro. 13.
TABLJE OF ALIQUOT PARTS.
number of
\\ have the
25 is
k
of
100
60 «
d
tc
75 «
3
7
(t
12^ «
i
«
37^ "
3
?
«
62^ "
5
((
87^ "
7
9
«
64 «
V
<(
18| "
3
«
314 "
6
(C
8J «
iS.
((
161 "
i
tc
33^ "
1
3
tt
661 "
i
t(
83i «
8
tf
(t
To multiply any number by an aliquot part
of 100.
Rule. AnHfiV fwn mnTiAisa Qtirl /liTn'rl^ l^,r
the fractional part.
IRTJIiE l>rO. 14.
TABLE OF ALIQUOT PARTS.
83J is r'ff of 1,000
62^
«
tV
{(
«
66i
((
tV
«
«
125
((
i
cc
«
250
«
((
(«
375
«
((
tt
625
<<
({
<(
876
((
((
«
i To multiply any number by an aliquot
part of 1000.
Rule.— Annex three ciphens and divide
by the fractional part.
rs.
I^TJIiE liTO, 15. ^
MULTIPLICATION.
To multiply a whole number and a half
together.
KuLE.— To the product of the whole num-
ber add half their sum plus J.
What will ^ yards of tape cost at 4J cents
per yard ? ' ' -
D aliquot
d divide
Process.— The sum of 6 and 4 are ten-
half this sum is 5 ; then 4 times 6 are 24 and
6 are 29 ; to this add J. '
29Jc
i^TJXlE nsro. is.
MUL TIP Lie A TION.
To multiply a whole number and a half
together.
Rule. — When the sum is an odd number
take half the next number below it then the
fraction in the answer will be f .
What will 9J yards of goods cost at $2.50
per yard 1
Process. — The sum of 9 and 2 are 11 ; the
next number below 11 is 10, half of 10 is 5 ;
then twice 9 are 18 and 5 to carry makes 23,
to this add f .
^
2|
$23|
nd a half
i number
then the
;at 82.50
K^UXiE 2^<D, 17.
PERCENTAGE.
, Means by the dollar.
A merchant bought goods at 80 cents per
yard, what must he sell them at to gain 25 per
cent, profit on the dollar.
re 11 ; the
.f 10 is 5 ;
makes 23,
Rule.— Multiply |1.25 by the first cost of
the goods and you will have the selling price.
1.25
80
^1.00.00
ORTJXiE JSrO. 18.
.
10
20
40
50
\
(t
«
it
tt
u
«
(t
ti
INTEREST, >»
The base of this rule is 6 per cent.
Findj^the Interest on
$ 5 for 6 days or one week 6 mills.
1 cent.
2 cents.
4 centH.
5 cents.
For 12 days nuiltiplv by 2
" 18 " *' ■ * 3
24 " ** 4
'30 •' ** 5
For one dav divide by 6, and yon will have tlu*
answer in mills.
If yon have dollars and cents together, the
answer will be in hundreds of ntills.
In actual business a month is eqnivalent to 30
days, a year to 360 dayn. Custom has made this
nawful.
For months multiply the dollars by half the
number of months a»^d you will have the answer
in cents. If you have dollars and cents together,
multiply by half the number of n)onths and you
will have the answer in hundreds of cents.
It is all 6 per cent, as a base.
For 1 per cent, divide bv (,
" 7 " add
" 8 . " add
" 9 '- add
" 10 " add i
"11 " add %■
1
If
1
3
I
C(
12
18
24
30
(t
multiply by 2
t*
tt
5
at^
I
lial]
ans
I^TJXiE ITO. 19
8.
8.
8.
To find the price of a lonrl of hay or straw.
Iiavo tli»'
tlier, the
snt to HO
iiade ihirt
half the
le answer
together,
and yoii
8.
What is the cost of 19.50 pounds of Jiay
at $14 per ton.
Rule. — Multiply thouuinbcir of pounds by
half the price per ton, and you will have the
answer in mills.
19.50
i
.3.65.0
IRTJX^E Isl O. 20.
The practice of buying or seJling grain by
the 100 pounds or the cental system, has
many advantages over the bushel.
To find the value per cental when the price
per bushel is given. ^
t5'
Hulk- Het down the price por bushel, and
divide by the number of pounds in the
T>U8heI.
If wheat is 11.20 per bushel how much is
that a centJil or 100 pounds.
60)$1.20
i^TJXiE 2sro. 21.
grain by
item, has
the price
shel, and
I in the
To find the value per bushel when the
price per cental is given.
KuLE. — Set down the price per cental, and
multiply by the number of pounds in the bushel
i? wheat is $2
per cental how much is that
much is
per bushel 1
$2.0
o
i^
11.20
l=lJJXj-:Ei IsTO. 22,
BUSHEL MEASURE,
The following table shows the legal nnniher
of puiinds per bushel : — *'
34 pounds — bushel of oats.
48 pounds — bushel of buckwheat.
48 poundvs — bushel of barley.
GO pounds — bushel of beans.
j
56 pounds—bushel of Rye or Indian corn. |
60 pounds — bushel wheat, peas or clover seed. *