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To reduce a fraction to its lowest terms

To reduce an improper fraction to a mixed number, or an integer

To reduce an integer to an improper fraction with a given deno-

minator

To reduce fractions to their least common denominator

B.-ADDITION OF FRACTIONS

To add fractions

To reduce a mixed number to an improper fraction

C.-SUBTRACTION OF FRACTIONS

To subtract one simple fraction from another

To subtract one mixed number from another

To subtract several fractions from the sum of several others

D.-MULTIPLICATION OF A FRACTION BY AN INTEGER

E. DIVISION OF A FRACTION BY AN INTEGER

F-REDUCTION OF A COMPOUND FRACTION TO A SIMPLE FRACTION

G.-MULTIPLICATION OF FRACTIONS

To multiply fractions together

To multiply a simple or compound fractional expression by a

simple fraction, or by another compound expression

H.-DIVISION OF FRACTIONS

To divide one fraction by another

To divide a simple or compound fractional expression by a

simple fraction, or by a compound expression

I.-REDUCTION OF COMPLEX FRACTIONS

K-SIMPLIFICATION OF FRACTIONAL EXPRESSIONS

IX.-DECIMAL FRACTIONS.

To write a fraction with ten, or any power of ten for its denominator,

as a decimal fraction

To convert a decimal into a vulgar fraction, or the sum of several frac-

tions

To add decimals

To subtract decimals

To multiply decimals

Abbreviated method of multiplication of decimals, when only a certain
number of decimal places are required in the product

Division of decimals

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Abbreviated method of division of decimals, when only a certain
number of decimal places are required in the quotient

To reduce a vulgar fraction to a decimal

To convert a recurring decimal into a vnlgar fraction

To divide a number into parts which shall bear to each other given

ratios

37

To determine whether four numbers be proportionals in a given order

Having given three numbers, to find a fourth such, that all shall be

proportional

To find a third proportional to two given numbers

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37

38

To find any required term of an arithmetic series, of which the first

term and the common difference are known -

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44

44

To find the sum of any number of terms of a given arithmetic series

To find any number of arithmetic means between two numbers

Definitions

XIV.-GEOMETRIC PROGRESSION.

To find any required term of a given geometric progression.

To find the sum of any number of terms of a geometric series

To find the limit of the sum of an infinite geometric series

To find any number of geometric means between two numbers

XV.-SCALES OF NOTATION.

Observations and definitions

To change an integer from one scale to another

To change a fraction from one scale to another

To add, subtract, multiply, or divide in any scale

To change numbers from a higher denomination to a lower

To change numbers from a lower denomination to a higher

To change numbers from one denomination to another, when no exact

number of the one is contained in one of the other. Or, to ex-

press one quantity in terms of another

II.-REDUCTION OF FRACTIONS.

To express in lower terms the value of a fraction of a simple quantity

To

express in higher terms the value of a fraction of a simple quantity

To express a compound quantity as a fraction of any simple quantity

To express shillings, pence, and farthings as decimals of a pound

To express in positive terms the value of a decimal of a pound

To express in positive terms the value of a fraction of a compound

quantity

To express one quantity, fractional or other, in terms, or as a fraction,

of another. Or, to find the ratio of one to the other

III.-COMPOUND ADDITION.

To add several compound quantities of the same kind together

To express in positive terms the sum of several fractions of concrete

quantities.

IV. COMPOUND SUBTRACTION.

To subtract one compound quantity from another of the same kind

To express in positive terms the difference of two fractions of con-

crete quantities

V.-COMPOUND MULTIPLICATION AND DIVISION.

To multiply by any number a given compound quantity

To divide a compound quantity by any number

To multiply a compound quantity by a vulgar fraction

To multiply a compound quantity by a decimal fraction

To divide a compound quantity by a vulgar fraction

To divide a compound quantity by a decimal fraction

VI.-PRACTICE.

When the quantity of goods is expressed by a simple number, the

price of one being given

When the quantity of goods is not expressed by a simple number

VII. SIMPLE PROPORTION OR RULE OF THREE.

Observations and rule

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To find the interest due on a given principal at a given rate per cent.

To find the amount of a given sum at a given rate for a given time

To find the time in which the interest of a given principal will amount

to a given sum

To find the rate per cent. at which the interest on a given principal

will amount to a given sum in a given time

To find what principal will amount to a given sum at a given rate in a

given time, or to find the present worth of a given sum

B.-COMPOUND INTEREST.

-

-

To find the amount of a given principal at a given rate compound

interest for a given number of terms

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To find the compound interest on a given principal

To find the principal, which at compound interest for a given number of

terms will amount to a given sum

X.-DISCOUNT.

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To find the true discount on a debt due at a given time

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XI.-COMMISSION, BROKERAGE, INSURANCE.

Definitions

To find the commission, or brokerage, on a given sum

To find the expense of insuring a given sum

To find what sum must be insured to cover a given sum and all ex-

penses of insurance

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XII.-STOCKS.

Definitions

To find the cost of a given amount of stock at a given price

To find how much stock can be purchased for a given sum

To find what interest per cent. may be obtained by purchasing stock at

a given price

To find in which of two stocks it is more advantageous to invest

To find what annual income may be realised by investing a given

sum in stock at a given rate

To find what sum must be invested in a given stock to produce a

given income

To find how much of a given stock may be purchased with the pro-

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ceeds of the sale of a given amount of other stock

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To find the difference in a person's income by transferring money

from one stock to another

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XIII-PROFIT AND LOSS.

To find the profit or loss per cent. by selling an article at a certain

gain or loss on the prime cost

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To find at what price an article must be sold to gain or lose so much

per cent.

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To find the prime cost of an article, by selling which at a certain

price a given gain or loss per cent. is made

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Given that by selling goods at a certain price a certain gain or loss

is made, to find what should have been the selling price to have

made another gain or loss

Given that by selling goods at a certain price a certain gain or loss is

made, to find what will be the gain or loss when the selling price

is altered

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XIV.-FELLOWSHIP.

To determine the amount of gain or loss belonging to each partner

in a joint concern, the times of engagement of all being the same

To determine the share of gain or liability of each partner in a con-

cern, according to the number of shares held by each

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To determine the share of gain or loss belonging to each partner in a

concern, the times for which each has been engaged not being the

To determine the liability of each partner in a concern, according to

the number of shares held by each, and the time for which he has

held them

XV-EQUATION OF PAYMENTS.

To find the equitable time at which several payments due at different

times may be all paid at once

XVI.-ANNUITIES.

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Definitions

To find the amount of an annuity forborne for any number of terms

To determine the present value of an annuity to last a given number

of terms

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100

100

To find the value of a perpetual annuity

101

To find the present value of a deferred annuity

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To determine what annuity may be purchased with a given sum, to

last a given time

To find the quantity of one article equivalent in value to a given quan-

tity of another article

To determine the quality of an article, of which a given quantity is

exchanged for a given quantity of another

The nett and bartering prices of one article being given, to determine

the bartering price of another, the nett price being known, or vice

versâ

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