HOW TO CALCULATE.
PRACTICAL RULES, SHORT METHODS, AND PROBLEMS USED IN
BUSINESS COMPUTATIONS.
Rapidity and accuracy in making estimates and in figuring
out the result of business transactions is of the greatest
necessity to the man of business. A miscalculation may involve
the loss of hundreds or thousands of dollars, in many cases,
while a slow and tedious calculation involves loss of time and
the advantage which should have been seized at the moment. It
is proposed in the following pages to give a few brief methods
and practical rules for performing calculations which occur in
everyday transactions among men, presuming that a fair
knowledge of the ordinary rules of arithmetic has previously
been attained.
ADDITION.
To be able to add up long columns of figures rapidly and
correctly is of great value to the merchant. This requires not
only a knowledge of addition, but in order to have a correct
result, one that can be relied upon, it requires concentration
of the mind. Never allow other thoughts to be flitting through
the mind, or any outside matter to disturb or draw it away from
the figures, until the result is obtained. Write the tens to be
carried each time in a smaller figure underneath the units, so
that afterwards any column can be added over again without
repeating the entire operation. By the practice of addition the
eye and mind soon become accustomed to act rapidly, and this is
the art of addition. Grouping figures together is a valuable
aid in rapid addition, as we group letters into words in
reading.
862 \ 
538 / 
674 \ 
843 / 
____ 
2917 
Thus, in the above example, we do not say 3 and 4 are 7 and
8 are 15 and 2 are 17, but speak the sum of the couplet, thus 7
and 10 are 17, and in the second column, 12 and 9 are 21. This
method of grouping the figures soon becomes easy and reduces
the labor of addition about onehalf, while those somewhat
expert may group three or more figures, still more reducing the
time and labor, and sometimes two or more columns may be added
at once, by ready reckoners.
Another method is to group into tens when it can be
conveniently done, and still another method in adding up long
columns is to add from the bottom to the top, and whenever the
numbers make even 10, 20, 30, 40 or 50, write with pencil a
small figure opposite, 1, 2, 3, 4 or 5, and then proceed to add
as units. The sum of these figures thus set out will be the
number of tens to be carried to the next column.

6^{2} 
2 
8 

3 
5^{2} 
4^{1} 

2 
8 
4 

9 
6 
2 

7^{2} 
1 
8^{2} 

8 
3^{2} 
5 

5 
2 
7 

1^{1} 
3 
2^{1} 

5 
8 
8 
_________________ 
5 
0 
2 
8 
SHORT METHODS OF MULTIPLICATION.
For certain classes of examples in multiplication short
methods may be employed and the labor of calculation reduced,
but of course for the great bulk of multiplications no
practical abbreviation remains. A person having much
multiplying to do should learn the table up to twenty, which
can be done without much labor.
To multiply any number by 10, 100, or 1000, simply annex
one, two, or three ciphers, as the case may be. If it is
desired to multiply by 20, 300, 5000, or a number greater than
one with any number of ciphers annexed, multiply first by the
number and then annex as many ciphers as the multiplier
contains.
TABLE.
5 cents equal 1/20 of a dollar.
10 cents equal 1/10 of a dollar.
121/2 cents equal 1/8 of a dollar.
162/3 cents equal 1/6 of a dollar.
20 cents equal 1/5 of a dollar.
25 cents equal 1/4 of a dollar.
331/3 cents equal 1/3 of a dollar.
50 cents equal 1/2 of a dollar.
Articles of merchandise are often bought and sold by the
pound, yard, or gallon, and whenever the price is an equal part
of a dollar, as seen in the above table, the whole cost may be
easily found by adding two ciphers to the number of pounds or
yards and dividing by the equivalent in the table.
Example. What cost 18 dozen eggs at 162/3c per
dozen?
6 
) 
1 
8 
0 
0 

_ 
_ 
_ 
_ 
_ 

$ 
3 
. 
0 
0 
Example. What cost 10 pounds butter at 25c per
pound?
4 
) 
1 
0 
0 
0 

_ 
_ 
_ 
_ 
_ 

$ 
2 
. 
5 
0 
Or, if the pounds are equal parts of one hundred and the
price is not, then the same result may be obtained by dividing
the price by the equivalent of the quantity as seen in the
table; thus, in the above case, if the price were 10c and the
number of pounds 25, it would be worked just the same.
Example. Find the cost of 50 yards of gingham at 14c
a yard.
2 
) 
1 
4 
0 
0 

_ 
_ 
_ 
_ 
_ 

$ 
7 
. 
0 
0 
When the price is one dollar and twentyfive cents, fifty
cents, or any number found in the table, the result may be
quickly found by finding the price for the extra cents, as in
the above examples, and then adding this to the number of
pounds or yards and calling the result dollars.
Example. Find the cost of 20 bushels potatoes at
$1.121/2 per bushel.
8 
) 
2 
0 
0 
0 



2 
5 
0 

_ 
_ 
_ 
_ 
_ 
$ 
2 
2 
. 
5 
0 
If the price is $2 or $3 instead of $1, then the number of
bushels must first be multiplied by 2 or 3, as the case may
be.
Example. Find the cost of 6 hats at $4.331/3
apiece.
3 
) 
6 
0 
0 



4 



_ 
_ 
_ 
_ 
_ 
_ 

2 
4 
. 
0 
0 


2 
. 
0 
0 
_ 
_ 
_ 
_ 
_ 
_ 
$ 
2 
6 



When 125 or 250 are multipliers add three ciphers and divide
by 8 and 4 respectively.
To multiply a number consisting of two figures by 11, write
the sum of the two figures between them.
Example. Multiply 53 by 11. Ans. 583.
If the sum of the two numbers exceeds 10 then the units only
must be placed between and the tens figure carried and added to
the next figure to the left.
Example. Multiply 87 by 11. Ans. 957.
FRACTIONS.
Fractional parts of a cent should never be despised. They
often make fortunes, and the counting of all the fractions may
constitute the difference between the rich and the poor man.
The business man readily understands the value of the
fractional part of a bushel, yard, pound, or cent, and
calculates them very sharply, for in them lies perhaps his
entire profit.
TO REDUCE A FRACTION TO ITS SIMPLEST FORM.
Divide both the numerator and denominator by any number that
will leave no remainder and repeat the operation until no
number will divide them both.
Example. The simplest form of 36/45 is found by
dividing by 9 = 4/5.
To reduce a whole number and a fraction, as 41/2, to
fractional form, multiply the whole number by the denominator,
add the numerator and write the result over the denominator.
Thus, 4 X 2 = 8 + = 9 placed over 2 is 9/2.
TO ADD FRACTIONS.
Reduce the fractions to like denominators, add their
numerators and write the denominator under the result.
Example. Add 2/3 to 3/4.
2/3 = 8/12, 3/4 = 9/12, 8/12 + 9/12 = 17/12 = 15/12.
Ans.
TO SUBTRACT FRACTIONS.
Reduce the fractions to like denominators, subtract the
numerators and write the denominators under the result.
Example. Find the difference between 4/5 and 3/4.
4/5 = 16/20, 3/4 = 15/20, 16/20  15/20 = 1/20. Ans.
TO MULTIPLY FRACTIONS.
Multiply the numerators together for a new numerator and the
denominators together for a new denominator.
Example. Multiply 7/8 by 5/6.
7/8 x 5/6 = 35/48. Ans.
TO DIVIDE FRACTIONS.
Multiply the dividend by the divisor inverted.
Example. Divide 7/8 by 5/6.
7/8 X 6/5 = 42/40. Reduced to simple form by dividing by 2
is 21/20 = 11/20.
Ans.
TO MULTIPLY MIXED NUMBERS.
When two numbers are to be multiplied, one of which contains
a fraction, first multiply the whole numbers together, then
multiply the fraction by the other whole number, add the two
results together for the correct answer.
Example. What cost 51/3 yards at 18c a yard?









1 
8 
c 













5 
 
1 
/ 
3 







_ 
_ 
_ 
_ 
_ 
_ 
1 
8 
x 
5 




= 
9 
0 




1 
8 
x 


1 
/ 
3 
= 

6 











_ 
_ 
_ 
_ 
_ 
_ 









9 
6 
c 



When both numbers contain a fraction,
First, multiply the whole numbers together,
Second, multiply the, lower whole number by the upper
fraction;
Third, multiply the upper whole number by the lower
fraction;
Fourth, multiply the fractions together;
Fifth, add all the results for the correct answer.
Example. What cost 122/3 pounds of butter at 183/4c
per pound?















1 
8 
 
3 
/ 
4 















1 
2 
 
2 
/ 
3 













_ 
_ 
_ 
_ 
_ 
_ 
_ 
_ 






1 
8 
x 

1 
2 
= 

2 
1 
6 










1 
2 
x 
3 
/ 
4 
= 



9 










1 
8 
x 
2 
/ 
3 
= 


1 
2 




3 
/ 
4 
x 
2 
/ 
3 
= 
6 
/ 
1 
2 
= 





1 
/ 
2 













_ 
_ 
_ 
_ 
_ 
_ 
_ 
_ 












$ 
2 
. 
3 
7 
 
1 
/ 
2 
Common fractions may often be changed to decimals very
readily, and the calculations thereby made much easier.
TO CHANGE COMMON FRACTIONS TO DECIMALS.
Annex one or more ciphers to the numerator and divide by the
denominator.
Example. Change 3/4 to a decimal. Ans..75.
We add two ciphers to the 3, making it 300, and divide by 4,
which gives us.75. In the same way 1/2 =.5, or 3/4 =.75, and so
on. When a quantity is in dollars and fractions of a dollar,
the fractions should always be thus reduced to cents and
mills.
