Removing ciphers from the left of a decimal increases its value. Annexing ciphers to a decimal or removing ciphers from its right does not alter its value.

To reduce a Decimal to a Common Fraction.

RULE. Write the figures of the decimal for the numerator, and 1, with as many ciphers as there are places in the decimal, for the denominator, and reduce the fraction to its lowest terms.

To reduce a Common Fraction to a Decimal.

RULE. Annex decimal ciphers to the numerator, and divide it by the denominator.

To reduce Decimals to a Common Denominator.

RULE. Make their decimal places equal by annexing ciphers.

ADDITION AND SUBTRACTION OF DECIMALS

Decimals are added and subtracted the same as whole numbers.

MULTIPLICATION OF DECIMALS

RULE.-Multiply as in whole numbers, and from the right of the product, point off as many decimal places as there are decimal places in both factors.

DIVISION OF DECIMALS

RULE. Make the divisor a whole number by removing the decimal point, and make a corresponding change in the dividend. Divide as in whole numbers, and place the decimal point in the quotient under (or over) the new decimal point in the dividend.

ACCOUNTS AND BILLS

A Debtor is a person who owes another.
A Creditor is a person to whom a debt is due.

An Account is a record of debits and credits between persons doing business.

The Balance of an account is the difference between the debit and credit sides.

A Bill is a written statement of an account.

An Invoice is a written statement of items, sent with merchandise.

A Receipt is a written acknowledgment of the payment of part or all of a debt.

A bill is receipted when the words, "Received Payment," are written at the bottom, signed by the creditor, or by some person duly authorized.

DENOMINATE NUMBERS

A Measure is a standard established by law or custom, by which distance, capacity, surface, time, or weight is determined. A Denominate Unit is a unit of measure.

A Denominate Number is a denominate unit or a collection of denominate units.

A Simple Denominate Number consists of denominate units of one kind.

A Compound Denominate Number consists of denominate units of two or more kinds.

A Denominate Fraction is a fraction of a denominate number. A denominate fraction may be either common or decimal. Reduction of denominate numbers is changing them from one denomination to another without altering their value.

Reduction Descending is changing a denominate number to one of a lower denomination.

RULE. Multiply the highest denomination by the number required to reduce it to the next lower denomination, and to the product add the units of that lower denomination, if any. Proceed in this manner until the required denomination is reached.

Reduction Ascending is changing a denominate number to one of a higher denomination.

RULE. Divide the given denomination successively by the numbers that will reduce it to the required denomination. To this quotient annex the several remainders.

To find the Time between Dates.

RULE.

When the time is less than one year, find the exact number of days; if greater than one year, find the time by compound subtraction, taking 30 days to the month.

PERCENTAGE

Per Cent means hundredths.

Percentage is computing by hundredths.

The elements involved in percentage are the Base, Rate, Percentage, Amount, and Difference.

The Base is the number of which a number of hundredths is taken.

The Rate indicates the number of hundredths to be taken.
The Percentage is one or more hundredths of the base.
The Amount is the base increased by the percentage.
The Difference is the base diminished by the percentage.

To find the Percentage when the Base and Rate are Given.

RULE. Multiply the base by the rate expressed as hundredths.

To find the Rate when the Percentage and Base are Given.

RULE. Divide the percentage by the base.

To find the Base when the Percentage and Rate are Given.

RULE. Divide the percentage by the rate expressed as hundredths.

To find the Base when the Amount and Rate are Given.

RULE. Divide the amount by 1+the rate expressed as hundredths.

To find the Base when the Difference and Rate are Given.

RULE. dredths.

Divide the difference by 1---the rate expressed as hun

PROFIT AND LOSS

Profit or Loss is the difference between the buying and selling prices.

In Profit and Loss,

The buying price, or cost, is the base.

The rate per cent profit or loss is the rate.

The profit or loss is the percentage.

The selling price is the amount or difference, according as it is more or less than the buying price.

COMMERCIAL DISCOUNT

Commercial Discount is a percentage deducted from the list price of goods, the face of a bill, etc.

The Net Price of goods is the sum received for them.

The rate per cent discount is the rate.

The discount is the percentage.

The list price diminished by the discount is the difference.

In successive discounts, the first discount is made from the list price or the face of the bill; the second discount, from the list price or face of the bill diminished by the first discount; and so

on.

COMMISSION

Commission is a percentage allowed an agent for his services. A Commission Agent is one who transacts business on commission.

A Consignment is the merchandise forwarded to a commission agent.

The Consignor is the person who sends the merchandise.

The Consignee is the person to whom the merchandise is sent. The Net Proceeds is the sum remaining after all charges have been deducted.

In buying, the commission is a percentage of the buying price; in selling, a percentage of the selling price; in collecting, a percentage of the sum collected; hence:

The sum invested, or } is the base.

The sum collected

The rate per cent commission is the rate.

The commission is the percentage.

The sum invested increased by the commission is the amount. The sum collected diminished by the commission is the differ

ence.

INSURANCE

Insurance is a contract of indemnity.

Insurance is of three kinds—Fire, Marine, and Life.

Fire Insurance is indemnity against loss of property by fire. Marine Insurance is indemnity against loss of property by the casualities of navigation.

Life Insurance is indemnity against loss of life.

The Insurance Policy is the contract setting forth the liability of the insurer.

The Policy Face is the amount of insurance.

The Premium is the price paid for insurance.

The Insurer, or Underwriter, is the company issuing the policy. The Insured is the person for whose benefit the policy is issued.

In Insurance,

The policy face is the base.

The rate per cent premium is the rate.

The premium is the percentage.