Elements of Arithmetic, Theoretical and Practical: Adapted to the Use of Schools, and to Private Study |
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Page 14
... remainder ; it is evidently the opposite of the foregoing . Only two quantities or numbers can be concerned in a subtraction , for one result ; if more numbers are to be subtracted , it must be done by a new operation . 16. All the ...
... remainder ; it is evidently the opposite of the foregoing . Only two quantities or numbers can be concerned in a subtraction , for one result ; if more numbers are to be subtracted , it must be done by a new operation . 16. All the ...
Page 17
... remainders , leaves nothing ; therefore , if we express this as a division , having the result , or quotient , on the ... remainder , that is still affected with the sign of division by the divisor ; as for instance in the following ...
... remainders , leaves nothing ; therefore , if we express this as a division , having the result , or quotient , on the ... remainder , that is still affected with the sign of division by the divisor ; as for instance in the following ...
Page 21
... Remainder , Proof . 9643187 then take the difference between each of the corres- ponding numbers , beginning by the unit , and write the difference directly under these numbers , the number resulting SUBTRACTION . 21.
... Remainder , Proof . 9643187 then take the difference between each of the corres- ponding numbers , beginning by the unit , and write the difference directly under these numbers , the number resulting SUBTRACTION . 21.
Page 22
... remainder obtained , to the lower number above the line , or the subtrahend , which addition must give the first or upper number for its result . It is therefore proper to accustom beginners to make this proof , in order that they may ...
... remainder obtained , to the lower number above the line , or the subtrahend , which addition must give the first or upper number for its result . It is therefore proper to accustom beginners to make this proof , in order that they may ...
Page 23
... remainder 7 , is written in the proper place . In the place of the hundreds we have then , by the effect of the foregoing borrowing , which is trans- ferred to the place of the thousands a 9 , from which the 2 subtracted gives the remainder ...
... remainder 7 , is written in the proper place . In the place of the hundreds we have then , by the effect of the foregoing borrowing , which is trans- ferred to the place of the thousands a 9 , from which the 2 subtracted gives the remainder ...
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Common terms and phrases
acres added addition amount antecedent applied arithmetical proportion arithmetical series borrowing calculation called capital carried cattle cent ciple common difference compound interest consequents contained continued cube cubic decimal fractions decimal mark decimal system deno denominate fractions determined divided dividend division divisor equation evidently exactly executed expressed factors feet long following example following numbers four rules frac Francs geometric proportion geometric series geometrical ratio given numbers gives improper fraction indicated kind manner mean terms merator metic miles mination mode multiplied mutations nator nature number of terms obtain ounces payments pieces places of figures pounds preceding principles proper fraction quotient reduced remainder result rule of three rules of arithmetic scholar share shown side sign of equality simple smaller square root subdivision subtraction successive things third tion unit unknown quantity vulgar fraction whole numbers write yards
Popular passages
Page ii - In conformity to the act of Congress of the United States. entitled, " an act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies, during the time therein mentioned." And also to an act, entitled, " an act, supplementary to an act, entitled, an act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies, during the times therein mentioned...
Page ii - BBOWN, of the said district, hath deposited in this office the title of a book, the right whereof he claims as author, in the words following, to wit : " Sertorius : or, the Roman Patriot.
Page 42 - If the numerator and denominator of each fraction is multiplied (or divided) by the same number, the value of the fraction will not change. This is because a fraction b/b, b being any number, is equal to the multiplicative identity, 1 . Therefore, Hx8.= 88 _5_x!
Page 111 - A ratio is formed by two numbers, each of which is called a term, and both together, a couplet. Thus, 2 and 6 together form a couplet of which 2 is the first term, and 6 the second. The first term of a ratio is called the antecedent; -the second, the consequent.
Page 197 - What fraction is that, to the numerator of which if 1 be added, the value will be •£ ; but if 1 be adde.d to the denominator, its value will be | ? Let — denote the fraction.
Page 118 - PROPORTION THE PRODUCT OF THE TWO EXTREME TERMS IS EQUAL TO THE PRODUCT OF THE TWO MEAN TERMS.
Page ii - Answers, 6d. Each subject is also accompanied by an example fully worked out and minutely explained. The Exercises are numerous and practical. A Complete System of Arithmetic, Theoretical and Practical; adapted to the Use of Schools and Private Students; containing the Fundamental Rules, and their application to Mercantile Computations ; Vulgar and Decimal Fractions ; Involution and Evolution ; Series ; Annuities, Certain and Contingent. By JAMES TBOTTEB.
Page 53 - The reason for this rule is the same, in reality, as that for the preceding one. 37. |i'or, multiplying the numerator of the dividend by the denominator of the divisor multiplies the dividend by that number.
Page 169 - That is, the first term of an increasing arithmetical series is equal to the last term diminished by the product of the common difference into the number of terms less one. From the same formula...
Page 197 - The sides of two square pieces of ground are as 3 to 5, and the sum of their superficial contents is 30600 square feet. What is the length of a side of each piece ? Ans.