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- - - Page, Repeat the general rule. . . . . . . . . . . . . . . . . . . . . . . .” 27 What is to be done with the remainder when *} ib is performed......... • * * * . . . . , s = • * * * * * * * * * How is division proved....... . . . . . . . . . . . . . . . . . . . . 28

When the divisor does not exceed 12 how is the work 31 performed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

When the divisoris 10, 100, 1000, &c. how is divisionl

32 performed..... e - - - - - - - - - - - - - - * - - - - - . . . . . . . ; . How, when the divisor is any digit with ciphers an- ib nexed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - - - - -

How may we proceed when the divisor is large. . . . . . 34 What is Italian division.... . . . . . . . . . . . . . . . . . . . . . ib. When the divisor is a component number or the product of two or more numbers, how may o be performed... . . . . . . . . . . . . . . . . . . . . . . . . . . . What is the rule for finding the true remainder *} ib the divisor is a component number. . . . . . . . . . . . If the divisor be a mixed number how is *} 36

performed. . . . . . . . . . . . . . . . . . . . . . . . . . - - - - How do we proceed when we divide by a greater *} ib less number than the true divisor. . . . . . . . . . . . . How may division be employed to shorten *:: 39. plication. . . . . . . . . . . . . . . . . . . . ... ... . . . . . . . . . . With what particular multipliers may these abbrevi-l. it, ations be usefully employed....... . . . . . . . . . . . . J How may multiplication be employed to shorten *} 40 WIS 1011. . . . . . . . - - - - - - - - - - - - - - - - - - - - - - - - - - - - - With what particular divisors may these abbrevia- } ib tions be usefully employed... . . . . . . . . . . . . . . . . . What are Compound numbers................. ...... 4 How is compound addition performed.............. ib How is compound addition proved................ ib Repeat the several tables of money, weights and ib IneaSures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - - - Repeat the table of the divisions made use of in 52 the sale of corn or grain. . . . . . . . . . . . . . . . . . . . }

What observation is made relative to these articles ... ib. What is a solar year.... . . . . . . . . . . . . . . . . . . . . . . . . . . 61.

- Page. What is a julian year.... . . .. . . . . . . . . . . . . . . . . . . . . . . . 61 How is the year divided . . . . . . . . . . . . . . . . . . . . . . . . ib How may the length of the calendar months. *} 62 remembered... . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . How is leap-year found. . . . . . . . . . . . . . .. . . . . . . . . ib How is Compound Subtraction performed.............. 63 : How is compound subtraction proved ............ ... ib How is compound multiplication performed.......... 70 . How is compound multiplication proved. . . . . . . . ..... ib When the multiplier is a composite number how is } 71 the operation performed........ . . . . . . . --- - - - When the multiplier is 13, 17, 19, or 23, how *} 72 the work be performed.................------• When the multiplier is greater than 23 and not o 73 composite number... . . . . . .... • - ... ... . . . . - - - - How otherwise may we proceed ..... - - - - - - - - - - - - - 74

When the multiplier is 10, 100, 1000 &c. how *} 75

- - - W the work performed in one line............... }.

How may we proceed when the multiplier is large.... ib

How is Compound Division performed.............. 80

How is compound division proved..... . . . . . . . . . . . ib When the divisor is a composite number, how is the , sl work performed. . . . . . . . . . . . . . . . . . . . . . . . . .

When the divisor is greater than 12 and not a 82 composite number, how is the work performed...

... How is division of money by 100 performed.... .... 83 Repeat the second rule.......................... it How may multiplication by a mixed number *} * 84 performed... . . . . . . . . . . . . . . . . . • - - - - - - - - - - - To what uses may Addition in general be applied } 88 (see Practical Questions)....... . . . . . . . . . . . . • .

(see Practical Questions) ..................... To what uses, may Multiplication in general bel. g. applied (see Practical Questions)....... . . . . . . . . .

What is the Square or second power of any number.... ib How is it expressed............... -- - - - - - - it.

To what uses may Subtraction in general be *} 91 - - Page. What is the cube or third power of any number. . . . . . 95 How is it expressed......... • . . . . . . . . . . . . * * * * * * ib What is the fourth, fifth or higher power of any number ib How is any power expressed..................... it

to those of a lower denomination*... . . . . . . . . . .

How are numbers of higher denominations brough } ib What are the particular rules for bringing o 97

qrs. and lbs. into pounds. . . . . . . . . . . . . . . . . . . . How may multiplication be farther applied.......... 99 To what uses may division in general be *} 104° (see practical questions). . . . . . . . . . . . . . . - - - - How are numbers of lower denominations brought to } f those of a higher denomination...... • - - - - - - - How may division be farther applied......... ..... 105

yards, &c. which may be purchased for a given
sum when the price is an even number of shillings

How may multiplication and division be jointly ap- } + plied. . . . . . . . . . . . . . . . - - - - - - . . . . . . . . . . . . . . . +

How may any quantity of one denomination be } 106 brought to that of another denomination........

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What is the rule for finding the number of o .* ib

contrary. . . . . . . . . . . . . . * * * * * * • * * * * * * * * * * * * * * * How may English miles be brought to Irish, and *} its contrary. . . . . . . . - - - - - - - - - - - - - - - - - - - - - - - - --How may coins weights and measures of one coun-T. 107 try be brought to those of another.............. What is a Fraction...... • . . . . . . . . . . . . . . . . . . . . . . . . I How is a fraction written. . . . . . . . . . . . . . . . . . . . . ... 108 What is the numerator of a fraction. . . . . . . . . . . . ... ... ib What is the denominator of a fraction............. . ib. What is a proper fraction....... • “ . . . . . . . . . . . . . . . ib. What is an improper fraction.............. . . .... . . . ib. What is a compound fraction...... .......... ... ... 109 What does a fraction represent...................... ib. • By Multiplication. - + By division.

t To bring quantities of one denomination, into, those of another denomination, - b

- Page. How does the value of a value increase... . . . . . . . ... {j What happens when both terms of a fraction are } ib multiplied by the same number. ... . . . . . . . . . . - And what when both terms are divided by the *} ib number, or by a common divisor........... . . . .” What is the greatest common measure of two *} 110 numbers. . . . . . . - - - - - - - - - - - - - - - - - - . . . . . . . . .” How is the greatest common measure found.... . . . . . ib What is a multiple of two or more numbers.......... 111 How is the least common multiple found. . . . . . . . . . . . ib When the numbers have not a common divisor how ib is the least common multiple found. . . . . . . . . . . . What is reduction of fractions............ . . . . . . 109 How are fractions brought to their least terms. . . . . . 112 In what other manner may this be effected . . . . . . ... ib Repeat some peculiar properties of certain numbers. ib

How may a mixed number be brought to an *} 114

per fraction equal thereto. . . . . . . . . . . . . . . . . . . . How may an improper fraction be brought to its : ib equivalent, whole or mixed number. . . . . . - - - - - How may a whole number be expressed as a *} 115 tion. . . . . - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -How may a whole number be brought to a fraction ib having a given denominator. . . . . . . . . . . . . . . . --- ; How may a compound fraction be brought to a sim- ; ib ple one of equal value. . . . . . . . . . . . . . . . . . • - - - What observations are made on the last rule. ....... ib

be brought to other fractions equivalent thereto X 116

having a common denominator................ How to others having the least common denominator ib , How is the value of a fraction found in terms of *} 117

How may fractions having different to

lower denominations.................... - - -

How may any compound quantity be brought to 118 the fraction of the integer of which it is a part..

How may a fraction of one denomination be brought to that of another denomination still retaining the $ 119 *me value. . . . . . . . . . . . . . . . . . . . . . . . . . . .....

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Page

How are fractions added when they have a common } in denominator. . . . . . . . . . . . . • * * * * * * * * * * * * • . . .

How when they have not a common denominator.... ib.

How are mixed numbers added.......... - - - - - - - - - 1 22

. How are fractions subtracted when they have a com- : 123 mon denominator. . . . . . - - - - - - - - - - - - - - - - - - - -

How when they have not a common denominator. . . . . . ib How is a fraction or a mixed number subtracted - 124 from a whole number. . . . . . . . . . - - - - - - - - - - - - - Howare mixed numbers subtracted from mixed numbers ib How is multiplication of fractions performed........ 125

How is a fraction multiplied by a whole number..... ib What else is to observed in multiplication of fractions 126 How is division of fractions performed...... . . . . . . ib

How is a fraction divided by a whole number........ ‘ ib To what uses in general may fractions be applied 127

(see questions for ea'ercise). . . . . . . . . . . . . . . . What is a Decimal Fraction........................ 129 How are decimals written. . . . . . . . . . - * * * * * * * * * * * * * ib How are operations on decimals performed....... . . ib Do ciphers alter. the value of decimals when placed 1h to the right-hand thereof... . . . . . . . . . • * * * * * * * * } ih What happens when ciphers are placed at the left R. ib. of a decimal, inside the decimal point. . . . . . . . . - } ib What is reduction of decimals , , . . . . . . . . . . . . ... ... 130 How is a vulgar fraction reduced to a decimal. . . . . . ib. How is a decimal expressed as a vulgar fraction. . . . 131 How is the value of a decimal found. . . . . . . . . . . . . . . ib How are numbers of divers denominations *} *132 to their equivalent decimal. . . . . . . . - - - - - - - - - - How is the value of the decimal of pound *} 133 found by inspection. . . . . . . . . . . . . . . . . . . . . . . . How may £ s. d. be brought to their equivalent } ib decimal by inspection........ . . . . . . . . . . . . . . . . . How are decimals added........... -- - - - - - - . . . . . . . 134 How is the total pointed........ • * * * * * * * * * * * * ... ib. How are decimals subtracted................ . . . . . ; 135

How is the remainder pointed.................... ib

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