An Elementary Treatise on Algebra: Theoretical and Practical ... |
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Page 35
... lowest terms . The principle on which these reductions rest is that of division , explained in ( Art . 21. ) CASE 3. To find the greatest common measure of the terms of a fraction , divide the greater term by the less , and the last ...
... lowest terms . The principle on which these reductions rest is that of division , explained in ( Art . 21. ) CASE 3. To find the greatest common measure of the terms of a fraction , divide the greater term by the less , and the last ...
Page 37
... lowest terms . CONSIDERATION AND OPERATION . The denominator has a3 as a factor to all its terms , which is not a factor in the numerator , hence this can form no part of the common measure , or the common measure will still be there ...
... lowest terms . CONSIDERATION AND OPERATION . The denominator has a3 as a factor to all its terms , which is not a factor in the numerator , hence this can form no part of the common measure , or the common measure will still be there ...
Page 38
... lowest terms . Here we find that neither term will divide by the other , but if these quantities have a common divisor , such divisor will still exist if we multiply one of the terms by any num ber whatever , to render division ...
... lowest terms . Here we find that neither term will divide by the other , but if these quantities have a common divisor , such divisor will still exist if we multiply one of the terms by any num ber whatever , to render division ...
Page 39
... lowest terms . а3 - ах - ах2 + x3 Ans . Common divisor a2 - x2 . Reduced fraction a2 + x2 а - х . 6. Find the greatest common measure , and reduce the fraction a - y to its lowest terms . ay Ans . Common divisor a2 - y2 . Red . frac ...
... lowest terms . а3 - ах - ах2 + x3 Ans . Common divisor a2 - x2 . Reduced fraction a2 + x2 а - х . 6. Find the greatest common measure , and reduce the fraction a - y to its lowest terms . ay Ans . Common divisor a2 - y2 . Red . frac ...
Page 40
... lowest terms . a ( a2 - b2 ) _a ( ab ) ( a + b ) _a2 - ab a2 + 2ab + b2 ( a + b ) ( a + b ) ( a + b ) ( a + b ) a + b .. x5b2x3 x4-64 .2 Reduce x2 - 1 3. Reduce xy + y to its lowest terms . Ans . x3 x2 + b2 . to its lowest terms . Ans ...
... lowest terms . a ( a2 - b2 ) _a ( ab ) ( a + b ) _a2 - ab a2 + 2ab + b2 ( a + b ) ( a + b ) ( a + b ) ( a + b ) a + b .. x5b2x3 x4-64 .2 Reduce x2 - 1 3. Reduce xy + y to its lowest terms . Ans . x3 x2 + b2 . to its lowest terms . Ans ...
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An Elementary Treatise on Algebra: Theoretical and Practical Horatio Nelson Robinson No preview available - 2016 |
Common terms and phrases
2d power 3d term 4th power added algebraic arithmetical arithmetical mean arithmetical series assumed binomial square cent Clearing of fractions coefficients common difference Completing the square compound interest compound quantity cube root cubic equation distance Divide the number dividend division divisor dollars equa equal roots equation becomes EXAMPLES Expand exponents factors find the values following rule four numbers fourth fraction will produce geometrical progression geometrical series give greater greatest common measure Hence improper fraction last term least common multiple less letter logarithm lowest terms method miles mixed quantity moon number of terms numbers in geometrical Observe operation primitive equation principle problem produce the series quadratic equations quotient remainder represent Required resolved second power shillings simple equations solution square root substitute subtract suppose Theorem third three numbers tion Transpose unknown quantity unknown term whole numbers
Popular passages
Page 11 - If equal quantities be divided by the same, or by equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be altered.
Page 33 - To reduce a mixed quantity to an improper fraction, multiply the integer by the denominator of...
Page 195 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means as 7 to 3. What are the numbers?
Page 184 - If the sum of an arithmetical series is 567, the first term 7, and the common difference 2; what is the number of terms?
Page 202 - There are two numbers, which are to each other, as 16' to 9, and 24 is a mean proportional between them. What are the numbers ? Ans. 32 and 18. 13. The sum of two numbers is to their difference as 4 to 1, and the sum of their squares is to the greater as 102 to 5. What are the numbers 1 Ans.
Page 145 - Prob. 9. It is required to divide the number 18 into two such parts, that the squares of those parts may be to each other as 25 to 16.
Page 42 - Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Page 155 - Any trinomial can be separated into two binomial factors, when the extremes are squares and positive, and the middle term is twice the product of the square roots of the extremes.
Page 191 - When three magnitudes, a, b, c, have the relation of a: c: : a—b : b—c ; that is, the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion.
Page 143 - A and B, set out to meet each other; A leaving the town C at the same time that B left D. They travelled the direct road...