New University Algebra: A Theoretical and Practical Treatise, Containing Many New and Original Methods and Applications, for Colleges and High SchoolsIvison, Phinney & Company, 1863 - 420 páginas |
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Página 12
... denominator being the index of the required root . Thus , in a3 , the denominator , 3 , indicates that the cube root of a is required , and the expression is equivalent to Va . Fractional exponents are used to denote both involution and ...
... denominator being the index of the required root . Thus , in a3 , the denominator , 3 , indicates that the cube root of a is required , and the expression is equivalent to Va . Fractional exponents are used to denote both involution and ...
Página 64
... denominator multiplied by the numerator . 2. In any fraction , the reciprocal of the denominator may be regarded as a fractional unit ; and the numerator shows how many times this unit is taken in the fraction . Hence , 3. A fraction is ...
... denominator multiplied by the numerator . 2. In any fraction , the reciprocal of the denominator may be regarded as a fractional unit ; and the numerator shows how many times this unit is taken in the fraction . Hence , 3. A fraction is ...
Página 65
... denominator divides the fraction , and dividing the denominator multiplies the fraction . III . Multiplying or dividing both numerator and denominator by the same quantity , does not alter the value of the fraction . 2d . Change of sign ...
... denominator divides the fraction , and dividing the denominator multiplies the fraction . III . Multiplying or dividing both numerator and denominator by the same quantity , does not alter the value of the fraction . 2d . Change of sign ...
Página 66
... denominator , ( 119 , III ) , we have the following RULE . I. Resolve the numerator and denominator into their prime factors , and cancel all those factors which are common Or , II . Divide both numerator and denominator by their ...
... denominator , ( 119 , III ) , we have the following RULE . I. Resolve the numerator and denominator into their prime factors , and cancel all those factors which are common Or , II . Divide both numerator and denominator by their ...
Página 67
... denominator , as found by ( 105 ) , is a - 1 ; hence , ( 3a2 - 2a - 1 ) ÷ ( a − 1 ) = 3a + 1 ( 4a3 - 2a - 3a + 1 ) ÷ ( a - 1 ) = 4a2 + 2a - 1 And we have for the reduced fraction , 3a + 1 4a2 + 2a - 1 ' Ans . Reduce each of the ...
... denominator , as found by ( 105 ) , is a - 1 ; hence , ( 3a2 - 2a - 1 ) ÷ ( a − 1 ) = 3a + 1 ( 4a3 - 2a - 3a + 1 ) ÷ ( a - 1 ) = 4a2 + 2a - 1 And we have for the reduced fraction , 3a + 1 4a2 + 2a - 1 ' Ans . Reduce each of the ...
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Términos y frases comunes
added algebraic quantity arithmetical progression binomial factors clearing of fractions coefficients cube root degree denote derived polynomial dividend division dollars EXAMPLES FOR PRACTICE exponent expression figure Find the cube Find the logarithm Find the sum find the values following RULE formula fourth geometrical progression geometrical series given equation given number given quantities greater greatest common divisor identical equation imaginary indicated inequality irreducible fraction last term least common multiple less letters minus sign monomial Multiply negative quantity nth root number of terms obtain OPERATION partial fractions permutations positive roots problem proportion quadratic quadratic equation quotient radical sign rational Reduce remainder represent required root result second member second term square root Sturm's Theorem subtracted suppose surd taken third three numbers tion transformed equation transposing trial divisor unknown quantity whence whole number X₁ zero
Pasajes populares
Página 209 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Página 86 - Any term may be transposed from one member of an equation to the other by changing its sign (1, 2).
Página 66 - To reduce a fraction to its lowest terms. A Fraction is in its lowest terms when the numerator and denominator are prime to each other. 1. Reduce - to its lowest terms.
Página 178 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
Página 169 - Subtract the square number from the left hand period, and to the remainder bring down the next period for a dividend. III. Double the root already found for a divisor ; seek how many times the divisor is contained...
Página 31 - That the exponent of any letter in the product is equal to the sum of its exponents in the two factors.
Página 77 - Reduce compound fractions to simple ones, and mixt numbers to improper fractions ; then multiply the numerators together for a new numerator, and the denominators for. a new denominator.
Página 52 - Measure, of two or more quantities, is the greatest quantity that will exactly divide each of them.
Página 266 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Página 169 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.