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VIII.FRACTIONS.
PAGE
Definitions
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A.REDUCTION OF FRACTIONS.
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
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BADDITION OF FRACTIONS
To add fractions
To reduce a mixed number to an improper fraction
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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
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D.MULTIPLICATION OF A FRACTION BY AN INTEGER
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E.DIVISION OF A FRACTION BY AN INTEGER
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FREDUCTION OF A COMPOUND FRACTION TO A SIMPLE FRACTION
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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
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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
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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
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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
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
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X.–RATIO, PROPORTION, AND VARIATION.
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To find the ratio of one number to another
To simplify the terms of a ratio, when fractional
To compound two or more ratios
To compare two ratios
To divide a number into parts which shall bear to each other given
ratios
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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To find any required term of an arithmetic series, of which the first
term and the common difference are known 
To find the sum of any number of terms of a given arithmetic series
To find any number of arithmetic means between two numbers
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XIV.GEOMETRIC PROGRESSION,
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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
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PART II.
COMMERCIAL ARITHMETIC.
I.REDUCTION OF INTEGERS.
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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
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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
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III.COMPOUND ADDITION.
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To add several compound quantities of the same kind together
To express in positive terms the sum of several fractions of concrete
quantities.
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IV.COMPOUND SUBTRACTION.
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To subtract one compound quantity from another of th , same kind
To express in positive terms the difference of two fractions of con
crete quantities
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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
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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
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VII.SIMPLE PROPORTION OR RULE OF THREE.
Observations and rule
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VIII.—COMPOUND PROPORTION.
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IX.INTEREST.
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A.SIMPLE INTEREST.
To find the interest due on a given principal at a given rate per cent.
for a given time
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
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
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X.DISCOUNT.
To find the true discount on a debt due at a given time
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XI.COMMISSION, BROKERAGE, INSURANCE.
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.
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
ceeds of the sale of a given amount of other stock
To find the difference in a person's income by transferring money
from one stock to another
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XIIIPROFIT 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.
To find the prime cost of an article, by selling which at a certain
price a given gain or loss per cent. is made
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.
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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
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
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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
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XVEQUATION OF PAYMENTS.
To find the equitable time at which several payments due at different
times may be all paid at once
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XVI.ANNUITIES.
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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
To find the value of a perpetual annuity
To find the present value of a deferred annuity
To determine what annuity may be purchased with a given sum, to
last a given time
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XVII.EXCHANGE
The chain rule
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XVII.BARTER.
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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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