How to Become a
LIGHTNING
CALCULATOR.

Accuracy should be considered first, followed by speed. By the way, fast calculators tend to be the most accurate. Write the numbers in vertical columns to avoid inconsistency. This is crucial. Focus on the outcomes rather than the individual numbers. Instead of thinking of 7 and 4 as 11 and then adding 8 for a total of 19, just say 7, 11, 19, and so on.

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

When adding horizontally, start on the left.

When adding long columns, double-check your work by adding each column individually in the opposite direction before moving on to the next one. Many accountants write down both figures as shown 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 determined by taking the last two figures and the right-hand figures, following the wave line in the illustration. This method is more effective than the old way of writing down the number to carry. If someone wants to review and add a specific column again, the number to carry is readily available and the previous total is already known.

For those who are new to it, adding two columns at once can be a tough job, but many people who do it every day find it just as easy to add two columns as it is to add one. For example, 99 plus 50 equals 149, then adding 6 makes 155, and then 10 plus 50 gives 215, and adding 3 makes 218, and 12 more makes it 230. Carry over 2, and then add 33 plus 12 to get 45, adding 20 makes 65, then adding 6 gives 71, and 30 more makes 101, adding 2 makes 103, and finally adding 23 results in 126.

Much of the information here is gathered from W. D. Rowland’s useful little book called “How to Become Expert with Figures.” You can get this handy book by sending 25 cents in stamps to American Nation Company, Boston.

Write the first right-side number, add the first and second, then the second and third, and so on; next, write the left-side number. Carry over when needed.

219434 × 11 = 2413774

Write down the right-hand number 4. Then say, 4 plus 3 is 7; then, 3 plus 4 is 7; then, 4 plus 9 is 13, write down 3 and carry over 1; then, 9 plus 1 plus 1 is 11, write down the 1 and carry over 1; [4] then, 1 plus 2 plus 1 is 4; then write the left-hand number 2. When multiplying small numbers, like 24 by 11, write the sum of the two numbers between them, making 264, the final product.

To multiply by 101, add two zeros to the number you're multiplying, and then add the original number to this.

2341 × 101 = 234100 + 2341

To multiply by 1001, add three zeros to the number you're multiplying and then add that number again.

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

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

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

To multiply two numbers by two numbers, do the following: Multiply the units by the units for the first number.

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. So, 2 = 2nd figure.[5]
(5 × 8) + 4 carried = 44 = 3rd and 4th figures.

With a bit of practice, anyone can become just as familiar with this rule and as quick in using it as with the usual method.

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

To multiply any number by 3 1/3, add a zero and divide by 3.

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

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

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

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

To multiply by 875, add three zeros, and then divide by 8.

To divide by 25, multiply by 4, and drop the last two digits.

To divide by 125, multiply by 8, and drop three digits.

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

To find the value of any number of articles at 75 cents each, subtract one-fourth of the number from itself and consider the rest as dollars.

Take the first digit from 9 and the second from 10. For example: when subtracting 73 from [6] 100, or when getting 73 cents back from a dollar, take 7 from 9 and 2, and then take 3 from 10 and 7, or 27 cents. Practice this rule. It’s easy and will be especially useful for making change.

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

A number is divisible by 4 when its last two digits can be divided by 4 without a remainder.

To divide by 12 1/2, multiply by 8, then drop the last two digits.

This simple rule is used in many households where multiple discounts are applied to list prices. Let's say the list price of a piano is $500, and you give an agent discounts of 25%, 20%, and 10%.

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

If you want a comprehensive book on quick calculations that includes all the latest methods, along with a wealth of other valuable information related to business, send 25 cents to American Nation Corp., Boston, Mass., for a copy of “How to Become Expert at Figures.”

[7]

The term percentage refers to specific mathematical calculations where 100 serves as the foundation for the computation. Per cent is short for the Latin per centum, which translates to by the hundred. The symbol % represents the term per cent. Therefore, 10% of a number equals 10/100, or 1/10 of that number; 50% equals 50/100, or 1/2, and so on.

Fractional equivalents.

Interest is the amount charged for using money. It essentially refers to the use of money or the benefits gained from using it. The principal is the amount for which interest is paid. The interest rate is the percent of the principal charged for its use over one year. Simple interest is just the interest on the principal alone for the entire duration; compound interest is interest on the principal for the entire time, plus interest on any interest payments after they are due.

To find the exact interest on any amount of money at a certain rate for one year, multiply the amount by the rate and divide by 100.

To calculate the exact interest on any amount of money at a specific rate for a set number of days, multiply the annual interest by the number of days and then divide that result by 365.

Equation of Payments is the method of determining when two or more amounts due at different times can be paid all at once, without causing any loss to either the debtor or the creditor. The time for such payment is referred to as the equated time.

To compare two or more payments, multiply each payment by its time, and then divide the total of those products by the total of the payments.

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

[9]

Less than 1/2 day is denied; 1/2 day or more counts as 1 day. If a date is needed, calculate the adjusted time forward from the specified date.

There are experts who can add very quickly. However, even the best among them can’t add up a column of ones any faster than you can. Here’s how some of the fast addition is done. The operator writes a line of numbers, then another, and so on. The second line, when added to the first, results in nines, except on the far right, where the two numbers add up to ten. The third and fourth lines follow the same pattern, along with however many more he decides to add. The last two lines, however, are written down randomly. To add these columns, he starts anywhere, maybe from the left side, writing down 2 (the number of pairs above), and then by simply adding the two bottom lines, he gets the correct total.

The amount a bank charges for cashing a note or time draft is called a bank discount. This discount is the simple interest paid in advance for the number of days the note has[10] until it matures. Wholesale businesses usually sell goods on credit and accept notes from retailers as payment. These notes are typically not for longer than three months. Some are placed in banks for collection, while others are discounted. When a note is discounted at a bank, the payee endorses it, making it payable to the bank. Both the maker and payee are then responsible to the bank for its payment. If the note earns interest, the discount is calculated and subtracted from the amount due at maturity. Most notes discounted at banks do not earn interest. The time for bank discount is always the number of days from the date of discounting to the date of maturity.

Example. A $250 note, dated July 7th, due in 60 days, is discounted on July 7th at 6%; calculate the proceeds.

This note is due in 63 days, on September 8th. The total interest of $250 for 63 days at 6 percent is $2.59. So, the proceeds will be $250 - $2.59, which is $247.41.

Salespeople usually give change by adding. They count out the money while adding to the total of the purchase until they match the amount on the bill presented. For example, if you buy something that costs $3.35 and pay with a ten-dollar bill, you’ll likely get back 5[11] cents, 10 cents, 50 cents, $1, and $5; the salesperson saying 40, 50, $4, $5; $10. This method is the least prone to mistakes.

Accuracy and speed in counting out change can be best learned through practice at the counter or cash register.

The unitate of a number is the sum of its digits simplified to a single digit.

The unit of the multiplier is 9 and the unit of the multiplicand is 6; 6 times 9 equals 54, and the unit of 54 is 9. Now the unit of the product is also found to be 9, which proves that the work is correct.

This method of calculating interest shows up in some Canadian textbooks, and although it's just a variation of other methods, it's worth mentioning. To calculate the interest on $724 for 5 1/2 months at 6 percent, simply divide by 4 and multiply by 11. The rule is to divide the principal by 4, and then multiply the result by one-third of the product of the rate and the time in months. Six times 5 1/2 equals 33, and one-third of 33 is 11. If you express the time in years, multiply one-fifth of the principal by half the product of the rate and the number of years, and move the decimal point one place to the left.

The swapping of digits often leads to mistakes in calculating accounts and balance sheets. This table is based on the idea that all differences from swapped numbers are multiples of nine. The difference between the misplaced digits equals the error's result divided by nine; for example, 91 - 19 = 72; 72 ÷ 9 = 8; 9 - 1 = 8. Therefore, the effort to find the error can be limited to checking those digits whose swapping would create the difference, as they are the only ones likely to cause the mistake. For instance, if the error in the balance sheet is 81 cents, it might be due to a swap, and the clerk can first look through the cents column of their records for amounts like 90 cents or 09 cents, likely finding the error without needing to check further. Swaps can happen in any decimal or whole number place, and the resulting differences are[14] divisible by nine without a remainder. Beyond this table, the numbers increase in a regular pattern, with each difference growing by nine, as follows:

The result of the difference in a regular series, when divided by nine, gives the numbers switched around like this: 130 - 13 = 117 ÷ 9 = 13, which are the numbers to look for when a discrepancy of 117 appears; however, this rule doesn't work for differences under 81 or for mixed transpositions. An error that can be divided by two might happen if an item is recorded on the wrong side of the ledger.

Reduce the time to months, and then add one-third of the days to the number you found. Multiply this whole number by one-half of your principal to get the interest you need in dollars, cents, and mills, at 6 percent. If only days are provided, multiply one-third of the days by one-half of the principal for the interest at 6 percent. Note these exercises:

$250 at 6% for 8 months and 6 days = 82 × 125 = $10.25.[15]

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

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

In some ways, this rule is better than the well-known 60-day method for calculating interest.

Multiply the principal (the amount of money being borrowed) by the time in days; then divide this result by the number you get by dividing 360 (the number of days in a year for interest) by the interest rate. The result you get will be the interest amount. For example, calculate the interest on $462.50 for one month and eighteen days at a 6% interest rate. An interest month is considered to be 30 days, so one month and 18 days equals 48 days. $462.50 multiplied by 0.48 equals $222.00; then divide 360 by 6 (the interest rate) to get 60, and $222.00 divided by 60 will give you the exact interest, which is $3.70. If the interest rate in the example was 12%, you would divide $222.00 by 30 (because 360 divided by 12 equals 30); for 4%, you would divide by 90; for 8%, you would divide by 45; and you would follow the same method for any other percentage.