An Introduction to Algebra: With Notes and Observations : Designed for the Use of Schools and Places of Public Education : to which is Added an Appendix on the Application of Algebra to Geometry |
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Page 27
... Required the greatest common measure of the frac tion 3a2-2α - 1 4a3-2a2-3a ... required . In which case the common process has been interrupted in the last step , merely to ... reduce fractions to their lowest or ALGEBRAIC FRACTIONS . 27.
... Required the greatest common measure of the frac tion 3a2-2α - 1 4a3-2a2-3a ... required . In which case the common process has been interrupted in the last step , merely to ... reduce fractions to their lowest or ALGEBRAIC FRACTIONS . 27.
Page 28
... reduce fractions to their lowest or most simple terms . RULE . Divide the terms of the fraction by any number , or quantity , that will divide each of them without leaving a ... required to reduce x3 - b2x x2 28 ALGEBRAIC FRACTIONS .
... reduce fractions to their lowest or most simple terms . RULE . Divide the terms of the fraction by any number , or quantity , that will divide each of them without leaving a ... required to reduce x3 - b2x x2 28 ALGEBRAIC FRACTIONS .
Page 29
... required to reduce x3 - b2x x2 + 2bx + ba to its lowest terms . x2 + 2bx + b2 ) x3b3x ( x x2 + 2bx2 + b2x -2bx2 ... required . And the same answer would have been found , if x3- 2x had been made the divisor instead of x2 + 2bx + b2 . 4 ...
... required to reduce x3 - b2x x2 + 2bx + ba to its lowest terms . x2 + 2bx + b2 ) x3b3x ( x x2 + 2bx2 + b2x -2bx2 ... required . And the same answer would have been found , if x3- 2x had been made the divisor instead of x2 + 2bx + b2 . 4 ...
Page 30
... required . EXAMPLES b 1. Reduce 34 and a to improper fractions . C - Here 33- And a- b C 3X5 + 2 - 5 axc - b α C 2. Reduce x + and x - 15 + 2 17 Ans . 5 5 ac b Ans . C a2 . to improper frac x X tions . α xxx + α x2 + a Here x + Ans . x ...
... required . EXAMPLES b 1. Reduce 34 and a to improper fractions . C - Here 33- And a- b C 3X5 + 2 - 5 axc - b α C 2. Reduce x + and x - 15 + 2 17 Ans . 5 5 ac b Ans . C a2 . to improper frac x X tions . α xxx + α x2 + a Here x + Ans . x ...
Page 31
... reduce an improper fraction to a whole or mixed quantity . RULE . Divide the numerator by the denominator , for the in- tegral part , and place the remainder , if ... required to reduce the fraction mixed quantity ALGEBRAIC FRACTIONS . 31.
... reduce an improper fraction to a whole or mixed quantity . RULE . Divide the numerator by the denominator , for the in- tegral part , and place the remainder , if ... required to reduce the fraction mixed quantity ALGEBRAIC FRACTIONS . 31.
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An Introduction to Algebra; With Notes and Observations: Designed for the ... John Bonnycastle No preview available - 2017 |
Common terms and phrases
Algebra arithmetical arithmetical mean arithmetical series bers coefficient common denominator compound quantity consequently cube root cubic equation decimal denoted Diophantus dividend divisor equal EXAMPLES FOR PRACTICE find the difference find the least find the product find the square find the sum find the value find two numbers fraction required geometrical geometrical progression geometrical series give given number greatest common measure Hence improper frac improper fraction infinite series last term letters loga logarithms mixed quantity multiplied negative nth root number of terms number required PROBLEM proportion quadratic equation question quotient rational reduce the fraction remainder Required the difference Required the sum required to convert required to divide required to find required to reduce result rithm rule second term side simple form square number square root square sought substituted subtracted sum required surd tion triangle unknown quantity Whence α α
Popular passages
Page 10 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 20 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Page 27 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Page 173 - Ios- y" &cFrom which it is evident, that the logarithm of the product of any number of factors is equal to the sum of the logarithms of those factors. Hence...
Page 77 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
Page 93 - It is required to divide the number 24 into two such parts, that their product may be equal to 35 times their difference. Ans. 10 and 14.
Page 93 - It is required to divide the number 60 into two such parts, that their product shall be to the sum of their squares in the ratio of 2 to 5.
Page 94 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the less, is equal to 12 ? Ans.
Page 30 - Multiply the index of the quantity by the index of the power to which it is to be raised, and the result will be the power required.