How to become a lightning calculator
Date: 2021-04-13T00:00:00+00:00
Keywords: Mental arithmetic

The Project Gutenberg eBook of How to become a lightning calculator

This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online at www.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook.

Title: How to become a lightning calculator

Author: Anonymous

Release date: April 13, 2021 [eBook #65078]
Most recently updated: October 18, 2024

Language: English

Credits: Demian Katz, Craig Kirkwood, and the Online Distributed Proofreading Team at https://www.pgdp.net (Images courtesy of the Digital Library@Villanova University (http://digital.library.villanova.edu/))

*** START OF THE PROJECT GUTENBERG EBOOK HOW TO BECOME A LIGHTNING CALCULATOR ***

CONTENTS

Instantaneous Addition.

How to Add Two Columns at Once.

Multiplication.

Accurate Interest.

Equation of Payments.

The Lightning Calculator’s Addition.

Bank Discount.

How to Make Change.

Proof of Multiplication in Ten Seconds.

The Canadian Interest Rule.

Table of Transposed Numbers.

Short Method to Find the Interest of a Given Sum.

Interest Computations.

Multum in Parvo
Library.

Vol. I.

February, 1894.
Published Monthly.

No. 2.

How to Become a
LIGHTNING
CALCULATOR.

Smallest Magazine in the World. Subscription
price, 50 cts. per year. Single copies, 5 cents each.

PUBLISHED BY
A. B. COURTNEY,
671 Tremont Street, Boston.

Entered at Post-Office as second-class matter.

Instantaneous Addition.

Accuracy should be first considered, then rapidity. Quick adders, by the way, are the most accurate. Write the numbers in vertical lines, avoiding irregularity. This is important. Keep your thought on results not numbers themselves. Do not reckon 7 and 4 are 11 and 8 are 19, but say 7, 11, 19 and so on.

When the same number is repeated several times, multiply instead of adding.

When adding horizontally begin at the left.

3132
2453 | 12
6471 | 20
7312 | 15
2134 | 21
21502

In adding long columns, prove the work, by adding each column separately in the opposite direction, before adding the next column. Many accountants put down both figures as in the illustration. The sum of the first column is 12; carrying one, the sum of the second is 20; carrying two, the sum of the third column is 15; carrying one, the sum of the fourth column is 21, and the total, 21502, is found by calling off the last two figures and the right-hand figures, following the wave line in the illustration. This method is better than the old one of penciling down the number to carry. If one desires to go back and add a certain column a second time, the number to carry is at hand and the former total is known.

How to Add Two Columns at Once.

2312
3253
2610
1256
3199
12630

To the inexperienced it will be a difficult task to add two columns at once, but many of those who have daily practice in addition find it about as easy to add two columns as one. Say 99 and 50 are 149, and 6 are 155, and 10 and 50 are 215 and 3 are 218, and 12 are 230. Carry 2, and say 33 and 12 are 45, and 20 are 65, and 6 are 71, and 30 are 101, and 2 are 103, and 23 are 126.

Much of the information here contained is compiled from W. D. Rowland’s valuable little volume, entitled “How to become expert with figures.” You can get this handy book by sending 25 cents in stamps to American Nation Co., Boston.

Multiplication.

To Multiply Any Number by 11.

Write the first right-hand figure, add the first and second, the second and third, and so on; then write the left-hand figure. Carry when necessary.

219434 × 11 = 2413774

Put down the right-hand figure 4. Then say, 4 and 3 are 7; then, 3 and 4 are 7; then, 4 and 9 are 13, put down 3 and carry 1; then, 9 and 1 and 1 are 11, put down the 1 and carry 1; then, 1 and 2 and 1 are 4; then write the left-hand figure 2. In multiplying small numbers, such as 24 by 11, write the sum of the two figures between the two figures, making 264, the required product.

To Multiply by 101, 1001, etc.

To multiply by 101, add two ciphers to the multiplicand, and add to this the multiplicand.

2341 × 101 = 234100 + 2341

To multiply by 1001, add three ciphers to the multiplicand, and add to this the multiplicand.

To Multiply by 5, 25, 125.

To multiply by 5, add a cipher and divide by 2.

To multiply by 25, add two ciphers and divide by 4.

To multiply by 125, add three ciphers and divide by 8.

Another Easy Way to Multiply.

82
54
4428

To multiply two figures by two figures, proceed as follows: Multiply units by units for the first figure.

Carry and multiply tens by units and units by tens, (adding) for the second figure. Carry and multiply tens by tens for the remaining figure or figures. In this example proceed as follows:

2 × 4 = 8 = 1st figure.
(4 × 8) + (5 × 2) = 42. Therefore 2 = 2d figure.
(5 × 8) + 4 carried = 44 = 3d and 4th figures.

By a little practice any one may become as familiar with this rule and as ready in its application as with the ordinary method.

To multiply any number by 2 1/2, add one cipher, and divide by 4.

To multiply any number by 3 1/3, add one cipher, and divide by 3.

To multiply by 33 1/3, add two ciphers, and divide by 3.

To multiply any number by 1 3/7, add one cipher, and divide by 7.

To multiply by 16 2/3, add two ciphers, and divide by 6.

To multiply by 14 2/7, add two ciphers, and divide by 7.

To multiply by 875, add three ciphers, and divide by 8.

To divide by 25, multiply by 4, and cut off two figures.

To divide by 125, multiply by 8, and cut off three figures.

To multiply by 12 1/2, add two ciphers, and divide by 8.

To find the value of any number of articles at 75 cents each, deduct one-quarter of the number from itself and call the remainder dollars.

To Subtract Any Number Consisting of Two Figures from 100.

Take the first figure from 9, and the second from 10. For example: in subtracting 73 from 100, or in taking 73 cents change out of a dollar, say 7 from 9 and 2, and 3 from 10 and 7, or 27 cents. Practice this rule. It is simple, and will be found particularly helpful in making change.

Divisions.

A number is divisible by 2 when the last digit is even.

A number is divisible by 4 when the last two digits are divisible by 4.

To divide by 12 1/2, multiply by 8, and cut off two figures.

Simple Discount Rule.

This simple rule is in use in many houses where several discounts are allowed from list prices. Suppose the list price of a piano to be $500, and you allow an agent 25, 20 and 10 off.

100 | | 100 | | 100
25 | | 20 | | 10
75 | × | 80 | × | 90 | = | .540000

Subtract each from 100 and multiply and you get .54. $500 × .54 = $270, the agent’s price.

If you want to get a complete book on quick calculating, comprising all modern methods, together with a vast amount of other valuable matter, pertaining to business, send 25 cents to American Nation Co., Boston, Mass., for a volume of “How to Become Expert at Figures.”

Percentage.

The name percentage is applied to certain arithmetical exercises in which 100 is used as the basis of computation. Per cent. is an abbreviation of the Latin per centum, meaning by the hundred. This sign % is used for the words per cent. Thus, 10% of a number equals 10/100, or 1/10 of the number; 50% equals 50/100, or 1/2, etc.

FRACTIONAL EQUIVALENTS.

50 | % | = | .50 | = | 1/2.
33 1/3 | % | = | .33 1/3 | = | 1/3.
25 | % | = | .25 | = | 1/4.
20 | % | = | .20 | = | 1/5.
16 2/3 | % | = | .16 2/3 | = | 1/6.
12 1/2 | % | = | .12 1/2 | = | 1/8.
10 | % | = | .10 | = | 1/10.
8 1/3 | % | = | .08 1/3 | = | 1/12.
6 1/4 | % | = | .06 1/4 | = | 1/16.
5 | % | = | .05 | = | 1/20.
2 1/2 | % | = | .02 1/2 | = | 1/40.

Accurate Interest.

Interest is the sum charged for the use of money. It is really the use of money or the benefit derived from its use. The principal is the sum for the use of which interest is paid. The rate of interest is the per cent. of the principal charged for its use for one year. Simple interest is the interest on the principal only, for the full time; compound interest is interest on the principal for the full time, and interest on each interest payment after it becomes due.

To find the accurate interest on any sum of money at a given rate for one year, multiply the sum by the rate and divide by 100.

To find the accurate interest on any sum of money at a given rate for any given number of days, multiply the interest for one year by the number of days and divide the product by 365.

Equation of Payments.

Equation of Payments is the process of finding when two or more sums due at different times may be paid at once, without loss to debtor or creditor. The time for such payment is called the equated time.

To equate two or more payments, multiply each payment by its time, and divide the sum of the products by the sum of the payments.

The times of the several payments must be in the same denomination, and this will be the denomination of the answer.

Less than 1/2 day is rejected; 1/2 day or more counts as 1 day. If the date is required, reckon the equated time forward from the given date.

The Lightning Calculator’s Addition.

4379321
5620679
2184509
7815491
2105610
3453173
25558783

There are experts who can add very rapidly. The best of them, however, cannot add up a column of ones any faster than you can. Here is how some of the rapid addition is performed. The operator writes a line of figures, then another, and so on. The second line, however, added to the first makes nines, except at the extreme right, where the two figures add to ten. The third and fourth bear the same relation, and as many more as he chooses to put down. The last two lines, however, are put down at random. Now, to add these columns, he begins anywhere, perhaps at the left-hand side, putting down 2 (the number of pairs above), then by simply adding the two bottom lines, he gets the correct sum.

Bank Discount.

The sum charged by a bank for cashing a note or time draft is called bank discount. This discount is the simple interest, paid in advance, for the number of days the note has to run. Wholesale business houses usually sell goods on time and take notes from the retailers in payment. These notes are not often for a longer period than three months. Some are placed in the banks for collection, others are discounted. When a note is discounted at a bank the payee endorses it, making it payable to the bank. Both maker and payee are then responsible to the bank for its payment. If the note is drawing interest the discount is reckoned on and deducted from the amount due at maturity. Most notes discounted at banks do not draw interest. The time in bank discount is always the number of days from the date of discounting to the date of maturity.

Example. A note of $250, dated July 7th, payable in 60 days, is discounted July 7th, at 6 per cent.; find the proceeds.

This note is due in 63 days, or September 8th. The accurate interest of $250 for 63 days at 6 per cent. is $2.59. The proceeds, then, will be $250 - $2.59, or $247.41.

How to Make Change.

Salesmen usually make change by addition. They have the money to count out, and in doing so they add to the amount of the purchase until they reach the amount of the bill presented. For example, if you buy something worth $3.35 and present a ten-dollar bill in payment, you will probably receive in return 5 cents, 10 cents, 50 cents, $1, and $5; the salesman saying 40, 50, $4, $5; $10. This method is least liable to error.

Accuracy and rapidity in counting out change can best be acquired by practice behind the counter or at the cash-desk.

Proof of Multiplication in Ten Seconds.

The unitate of a number is the sum of its digits reduced to a unit.

252 | = 9 | } | = 54 = 9
321 | = 6
252
504
756
80892 | = 27 = 9

The unitate of the multiplier is 9 and the unitate of the multiplicand is 6; 6 times 9 equals 54, and the unitate of 54 is 9. Now the unitate of the product is found to be 9 also, which is a proof of the correctness of the work.

The Canadian Interest Rule.

4 | 724
| 181 × 11 = 19.91

This rule of computing interest appears in some Canadian text-books, and, though simply a modification of other rules, is worthy of notice. To find the interest on $724 for 5 1/2 months at 6 per cent., all you have to do is to divide by 4 and multiply by 11. The rule is to divide the principal by 4, and to multiply the quotient by one-third of the product of the rate by the time in months. Six times 5 1/2 = 33, and one-third of 33 is 11. If the time be expressed in years, multiply one-fifth of the principal by one-half the product of the rate by the number of years, and remove the decimal point one place to the left.

Table of Transposed Numbers.

DIFFERENCES.
9 | { | 10 | 21 | 32 | 43 | 54 | 65 | 76 | 87 | 98
01 | 12 | 23 | 34 | 45 | 56 | 67 | 78 | 89
18 | { | 20 | 31 | 42 | 53 | 64 | 75 | 86 | 97
02 | 13 | 24 | 35 | 46 | 57 | 68 | 79
27 | { | 30 | 41 | 52 | 63 | 74 | 85 | 96
03 | 14 | 25 | 36 | 47 | 58 | 69
36 | { | 40 | 51 | 62 | 73 | 84 | 95
04 | 15 | 26 | 37 | 48 | 59
45 | { | 50 | 61 | 72 | 83 | 94
05 | 16 | 27 | 38 | 49
54 | { | 60 | 71 | 82 | 93
06 | 17 | 28 | 39
63 | { | 70 | 81 | 92
07 | 18 | 29
72 | { | 80 | 91
08 | 19
81 | { | 90
09
90 | { | 100
010
99 | { | 100
001

Explanation of Foregoing Table.

The transposition of figures is a frequent cause of errors in proving accounts and balance sheets. This table is founded on the fact that all differences between transposed numbers are multiples of nine. The difference between the figures misplaced is equal to the quotient of the resulting error when divided by nine; thus, 91 - 19 = 72; 72 ÷ 9 = 8; 9 - 1 = 8, and the labor of searching for it may be confined to examining those figures the transposition of which would make the difference, as they are the only ones that can cause the error. Thus: if the error in the balance-sheet be 81 cents, it is possibly caused by a transposition, and the clerk can first examine the cents column of his books for items of 90 cents, or 09 cents, alone, with a strong probability of finding the cause of the error without further revision. Transpositions may occur in any decimal or integer place, and the differences caused thereby are divisible by nine without a remainder; but, beyond this table, the numbers ascend in regular progression, each difference increasing by nine, as follows:

108 | { | 120 | ;117 | { | 130 | ;126 | { | 140 | ;etc.
12 | 13 | 14

The quotient of the difference in a regular progression, when divided by nine, gives the figures transposed, thus: 130 - 13 = 117 ÷ 9 = 13, which are the figures to be sought for when a discrepancy of 117 is shown; but this will not apply to differences below 81, nor to mixed transpositions. An error divisible by two may be caused by posting an item to the wrong side of the ledger.

Short Method to Find the Interest of a Given Sum.

Reduce the time to months, and to the number thus found annex one-third of the days, which whole number multiplied by one-half of your principal will produce you the required interest in dollars, cents and mills, at 6 per cent. If days only are given, multiply one-third of the days by one-half of the principal for the required interest at 6 per cent. Note these exercises:

$250 at 6% for 8 mos. 6 ds. = 82 × 125 = $10.25.

$250 at 6% for 93 ds. = 31 × 125 = $3.88.

$250 at 6% for 9 mos. = 9 × 125 = $11.25.

In some respects this rule is superior to the well-known 60-day method of reckoning interest.

Interest Computations.

| | 462.50
| | .48
6 | 360
| 60 | 222.0000 | 3.70

Multiply the principal (amount of money at interest) by the time, reduced to days; then divide this product by the quotient obtained by dividing 360 (the number of days in the interest year) by the per cent. of interest, and the quotient thus obtained will be the required interest. Require the interest of $462.50 for one month and eighteen days at 6 per cent. An interest month is 30 days; one month and 18 days equals 48 days. $462.50 multiplied by .48 gives $222.0000; 360 divided by 6 (the per cent. of interest) gives 60, and $222.0000 divided by 60 will give you the exact interest, which is $3.70. If the rate of interest in the above example were 12 per cent., we would divide the $222.0000 by 30 (because 360 divided by 12 gives 30); if 4 per cent., we would divide by 90; if 8 per cent., by 45; and in like manner for any other per cent.

OUR
MAIL DIRECTORY.

Every person who receives this copy of Multum in Parvo Library will also receive the benefit of the publicity of our Mail Directory, under the following arrangement: We shall forward your name and address during the next two years to many concerns, including publishers, who will mail to you gratuitously sample copies of publications, circulars, catalogues, etc. You will doubtless receive a great many of such, and it may be well to remember that you are receiving them on account of this Directory of ours.

Transcriber’s Notes:

The Table of Contents was created by the transcriber and placed in the public domain.

Use of - to represent division in some expressions is standardized to /.

The following change was made:

p. 15: Extraneous numbers were removed from the example interest computation.

*** END OF THE PROJECT GUTENBERG EBOOK HOW TO BECOME A LIGHTNING CALCULATOR ***

Updated editions will replace the previous one—the old editions will be renamed.

Creating the works from print editions not protected by U.S. copyright law means that no one owns a United States copyright in these works, so the Foundation (and you!) can copy and distribute it in the United States without permission and without paying copyright royalties. Special rules, set forth in the General Terms of Use part of this license, apply to copying and distributing Project Gutenberg™ electronic works to protect the PROJECT GUTENBERG™ concept and trademark. Project Gutenberg is a registered trademark, and may not be used if you charge for an eBook, except by following the terms of the trademark license, including paying royalties for use of the Project Gutenberg trademark. If you do not charge anything for copies of this eBook, complying with the trademark license is very easy. You may use this eBook for nearly any purpose such as creation of derivative works, reports, performances and research. Project Gutenberg eBooks may be modified and printed and given away—you may do practically ANYTHING in the United States with eBooks not protected by U.S. copyright law. Redistribution is subject to the trademark license, especially commercial redistribution.

START: FULL LICENSE

THE FULL PROJECT GUTENBERG LICENSE

PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK

To protect the Project Gutenberg™ mission of promoting the free distribution of electronic works, by using or distributing this work (or any other work associated in any way with the phrase “Project Gutenberg”), you agree to comply with all the terms of the Full Project Gutenberg™ License available with this file or online at www.gutenberg.org/license.

Section 1. General Terms of Use and Redistributing Project Gutenberg™ electronic works

1.A. By reading or using any part of this Project Gutenberg™ electronic work, you indicate that you have read, understand, agree to and accept all the terms of this license and intellectual property (trademark/copyright) agreement. If you do not agree to abide by all the terms of this agreement, you must cease using and return or destroy all copies of Project Gutenberg™ electronic works in your possession. If you paid a fee for obtaining a copy of or access to a Project Gutenberg™ electronic work and you do not agree to be bound by the terms of this agreement, you may obtain a refund from the person or entity to whom you paid the fee as set forth in paragraph 1.E.8.

1.B. “Project Gutenberg” is a registered trademark. It may only be used on or associated in any way with an electronic work by people who agree to be bound by the terms of this agreement. There are a few things that you can do with most Project Gutenberg™ electronic works even without complying with the full terms of this agreement. See paragraph 1.C below. There are a lot of things you can do with Project Gutenberg™ electronic works if you follow the terms of this agreement and help preserve free future access to Project Gutenberg™ electronic works. See paragraph 1.E below.

1.C. The Project Gutenberg Literary Archive Foundation (“the Foundation” or PGLAF), owns a compilation copyright in the collection of Project Gutenberg™ electronic works. Nearly all the individual works in the collection are in the public domain in the United States. If an individual work is unprotected by copyright law in the United States and you are located in the United States, we do not claim a right to prevent you from copying, distributing, performing, displaying or creating derivative works based on the work as long as all references to Project Gutenberg are removed. Of course, we hope that you will support the Project Gutenberg™ mission of promoting free access to electronic works by freely sharing Project Gutenberg™ works in compliance with the terms of this agreement for keeping the Project Gutenberg™ name associated with the work. You can easily comply with the terms of this agreement by keeping this work in the same format with its attached full Project Gutenberg™ License when you share it without charge with others.

1.D. The copyright laws of the place where you are located also govern what you can do with this work. Copyright laws in most countries are in a constant state of change. If you are outside the United States, check the laws of your country in addition to the terms of this agreement before downloading, copying, displaying, performing, distributing or creating derivative works based on this work or any other Project Gutenberg™ work. The Foundation makes no representations concerning the copyright status of any work in any country other than the United States.

1.E. Unless you have removed all references to Project Gutenberg:

1.E.1. The following sentence, with active links to, or other immediate access to, the full Project Gutenberg™ License must appear prominently whenever any copy of a Project Gutenberg™ work (any work on which the phrase “Project Gutenberg” appears, or with which the phrase “Project Gutenberg” is associated) is accessed, displayed, performed, viewed, copied or distributed:

This eBook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook.

1.E.2. If an individual Project Gutenberg™ electronic work is derived from texts not protected by U.S. copyright law (does not contain a notice indicating that it is posted with permission of the copyright holder), the work can be copied and distributed to anyone in the United States without paying any fees or charges. If you are redistributing or providing access to a work with the phrase “Project Gutenberg” associated with or appearing on the work, you must comply either with the requirements of paragraphs 1.E.1 through 1.E.7 or obtain permission for the use of the work and the Project Gutenberg™ trademark as set forth in paragraphs 1.E.8 or 1.E.9.

1.E.3. If an individual Project Gutenberg™ electronic work is posted with the permission of the copyright holder, your use and distribution must comply with both paragraphs 1.E.1 through 1.E.7 and any additional terms imposed by the copyright holder. Additional terms will be linked to the Project Gutenberg™ License for all works posted with the permission of the copyright holder found at the beginning of this work.

1.E.4. Do not unlink or detach or remove the full Project Gutenberg™ License terms from this work, or any files containing a part of this work or any other work associated with Project Gutenberg™.

1.E.5. Do not copy, display, perform, distribute or redistribute this electronic work, or any part of this electronic work, without prominently displaying the sentence set forth in paragraph 1.E.1 with active links or immediate access to the full terms of the Project Gutenberg™ License.

1.E.6. You may convert to and distribute this work in any binary, compressed, marked up, nonproprietary or proprietary form, including any word processing or hypertext form. However, if you provide access to or distribute copies of a Project Gutenberg™ work in a format other than “Plain Vanilla ASCII” or other format used in the official version posted on the official Project Gutenberg™ website (www.gutenberg.org), you must, at no additional cost, fee or expense to the user, provide a copy, a means of exporting a copy, or a means of obtaining a copy upon request, of the work in its original “Plain Vanilla ASCII” or other form. Any alternate format must include the full Project Gutenberg™ License as specified in paragraph 1.E.1.

1.E.7. Do not charge a fee for access to, viewing, displaying, performing, copying or distributing any Project Gutenberg™ works unless you comply with paragraph 1.E.8 or 1.E.9.

1.E.8. You may charge a reasonable fee for copies of or providing access to or distributing Project Gutenberg™ electronic works provided that:

- • You pay a royalty fee of 20% of the gross profits you derive from the use of Project Gutenberg™ works calculated using the method you already use to calculate your applicable taxes. The fee is owed to the owner of the Project Gutenberg™ trademark, but he has agreed to donate royalties under this paragraph to the Project Gutenberg Literary Archive Foundation. Royalty payments must be paid within 60 days following each date on which you prepare (or are legally required to prepare) your periodic tax returns. Royalty payments should be clearly marked as such and sent to the Project Gutenberg Literary Archive Foundation at the address specified in Section 4, “Information about donations to the Project Gutenberg Literary Archive Foundation.”

- • You provide a full refund of any money paid by a user who notifies you in writing (or by e-mail) within 30 days of receipt that s/he does not agree to the terms of the full Project Gutenberg™ License. You must require such a user to return or destroy all copies of the works possessed in a physical medium and discontinue all use of and all access to other copies of Project Gutenberg™ works.

- • You provide, in accordance with paragraph 1.F.3, a full refund of any money paid for a work or a replacement copy, if a defect in the electronic work is discovered and reported to you within 90 days of receipt of the work.

- • You comply with all other terms of this agreement for free distribution of Project Gutenberg™ works.

1.E.9. If you wish to charge a fee or distribute a Project Gutenberg™ electronic work or group of works on different terms than are set forth in this agreement, you must obtain permission in writing from the Project Gutenberg Literary Archive Foundation, the manager of the Project Gutenberg™ trademark. Contact the Foundation as set forth in Section 3 below.

1.F.

1.F.1. Project Gutenberg volunteers and employees expend considerable effort to identify, do copyright research on, transcribe and proofread works not protected by U.S. copyright law in creating the Project Gutenberg™ collection. Despite these efforts, Project Gutenberg™ electronic works, and the medium on which they may be stored, may contain “Defects,” such as, but not limited to, incomplete, inaccurate or corrupt data, transcription errors, a copyright or other intellectual property infringement, a defective or damaged disk or other medium, a computer virus, or computer codes that damage or cannot be read by your equipment.

1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the “Right of Replacement or Refund” described in paragraph 1.F.3, the Project Gutenberg Literary Archive Foundation, the owner of the Project Gutenberg™ trademark, and any other party distributing a Project Gutenberg™ electronic work under this agreement, disclaim all liability to you for damages, costs and expenses, including legal fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE THAT THE FOUNDATION, THE TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH DAMAGE.

1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a defect in this electronic work within 90 days of receiving it, you can receive a refund of the money (if any) you paid for it by sending a written explanation to the person you received the work from. If you received the work on a physical medium, you must return the medium with your written explanation. The person or entity that provided you with the defective work may elect to provide a replacement copy in lieu of a refund. If you received the work electronically, the person or entity providing it to you may choose to give you a second opportunity to receive the work electronically in lieu of a refund. If the second copy is also defective, you may demand a refund in writing without further opportunities to fix the problem.

1.F.4. Except for the limited right of replacement or refund set forth in paragraph 1.F.3, this work is provided to you ‘AS-IS’, WITH NO OTHER WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PURPOSE.

1.F.5. Some states do not allow disclaimers of certain implied warranties or the exclusion or limitation of certain types of damages. If any disclaimer or limitation set forth in this agreement violates the law of the state applicable to this agreement, the agreement shall be interpreted to make the maximum disclaimer or limitation permitted by the applicable state law. The invalidity or unenforceability of any provision of this agreement shall not void the remaining provisions.

1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the trademark owner, any agent or employee of the Foundation, anyone providing copies of Project Gutenberg™ electronic works in accordance with this agreement, and any volunteers associated with the production, promotion and distribution of Project Gutenberg™ electronic works, harmless from all liability, costs and expenses, including legal fees, that arise directly or indirectly from any of the following which you do or cause to occur: (a) distribution of this or any Project Gutenberg™ work, (b) alteration, modification, or additions or deletions to any Project Gutenberg™ work, and (c) any Defect you cause.

Section 2. Information about the Mission of Project Gutenberg™

Project Gutenberg™ is synonymous with the free distribution of electronic works in formats readable by the widest variety of computers including obsolete, old, middle-aged and new computers. It exists because of the efforts of hundreds of volunteers and donations from people in all walks of life.

Volunteers and financial support to provide volunteers with the assistance they need are critical to reaching Project Gutenberg™’s goals and ensuring that the Project Gutenberg™ collection will remain freely available for generations to come. In 2001, the Project Gutenberg Literary Archive Foundation was created to provide a secure and permanent future for Project Gutenberg™ and future generations. To learn more about the Project Gutenberg Literary Archive Foundation and how your efforts and donations can help, see Sections 3 and 4 and the Foundation information page at www.gutenberg.org.

Section 3. Information about the Project Gutenberg Literary Archive Foundation

The Project Gutenberg Literary Archive Foundation is a non-profit 501(c)(3) educational corporation organized under the laws of the state of Mississippi and granted tax exempt status by the Internal Revenue Service. The Foundation’s EIN or federal tax identification number is 64-6221541. Contributions to the Project Gutenberg Literary Archive Foundation are tax deductible to the full extent permitted by U.S. federal laws and your state’s laws.

The Foundation’s business office is located at 809 North 1500 West, Salt Lake City, UT 84116, (801) 596-1887. Email contact links and up to date contact information can be found at the Foundation’s website and official page at www.gutenberg.org/contact

Section 4. Information about Donations to the Project Gutenberg Literary Archive Foundation

Project Gutenberg™ depends upon and cannot survive without widespread public support and donations to carry out its mission of increasing the number of public domain and licensed works that can be freely distributed in machine-readable form accessible by the widest array of equipment including outdated equipment. Many small donations ($1 to $5,000) are particularly important to maintaining tax exempt status with the IRS.

The Foundation is committed to complying with the laws regulating charities and charitable donations in all 50 states of the United States. Compliance requirements are not uniform and it takes a considerable effort, much paperwork and many fees to meet and keep up with these requirements. We do not solicit donations in locations where we have not received written confirmation of compliance. To SEND DONATIONS or determine the status of compliance for any particular state visit www.gutenberg.org/donate.

While we cannot and do not solicit contributions from states where we have not met the solicitation requirements, we know of no prohibition against accepting unsolicited donations from donors in such states who approach us with offers to donate.

International donations are gratefully accepted, but we cannot make any statements concerning tax treatment of donations received from outside the United States. U.S. laws alone swamp our small staff.

Please check the Project Gutenberg web pages for current donation methods and addresses. Donations are accepted in a number of other ways including checks, online payments and credit card donations. To donate, please visit: www.gutenberg.org/donate.

Section 5. General Information About Project Gutenberg™ electronic works

Professor Michael S. Hart was the originator of the Project Gutenberg™ concept of a library of electronic works that could be freely shared with anyone. For forty years, he produced and distributed Project Gutenberg™ eBooks with only a loose network of volunteer support.

Project Gutenberg™ eBooks are often created from several printed editions, all of which are confirmed as not protected by copyright in the U.S. unless a copyright notice is included. Thus, we do not necessarily keep eBooks in compliance with any particular paper edition.

Most people start at our website which has the main PG search facility: www.gutenberg.org.

This website includes information about Project Gutenberg™, including how to make donations to the Project Gutenberg Literary Archive Foundation, how to help produce our new eBooks, and how to subscribe to our email newsletter to hear about new eBooks.

Table of Contents

- How to Become a LIGHTNING CALCULATOR.

- Instantaneous Addition.

- How to Add Two Columns at Once.

- Multiplication.

- To Multiply Any Number by 11.

- To Multiply by 101, 1001, etc.

- To Multiply by 5, 25, 125.

- Another Easy Way to Multiply.

- To Subtract Any Number Consisting of Two Figures from 100.

- Divisions.

- Simple Discount Rule.

- Percentage.

- Accurate Interest.

- Equation of Payments.

- The Lightning Calculator’s Addition.

- Bank Discount.

- How to Make Change.

- Proof of Multiplication in Ten Seconds.

- The Canadian Interest Rule.

- Table of Transposed Numbers.

- Explanation of Foregoing Table.

- Short Method to Find the Interest of a Given Sum.

- Interest Computations.

- Transcriber’s Notes:

- THE FULL PROJECT GUTENBERG LICENSE