Ray's Algebra, Part First: On the Analytic and Inductive Methods of Instruction, with Numerous Practical Exercises, Designed for Common Schools and Academies, Part 1 |
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Page 40
... changed from plus to minus . 2 . 3 . 4 . 5 . From 5x 7ab 8xy 11a2x Take 3x 3ab 5xy 5a2x Remainder 2x 4ab 3xy 6a2x 6. From 9a , take 4a .. 7. From 11b , take 11b . Ans . 5a . Ans . 0 . Ans . 8axy . 8. From 11axy , take 3axy . 9. From ...
... changed from plus to minus . 2 . 3 . 4 . 5 . From 5x 7ab 8xy 11a2x Take 3x 3ab 5xy 5a2x Remainder 2x 4ab 3xy 6a2x 6. From 9a , take 4a .. 7. From 11b , take 11b . Ans . 5a . Ans . 0 . Ans . 8axy . 8. From 11axy , take 3axy . 9. From ...
Page 41
... changed from plus to minus , and from minus to plus ; hence , in order to subtract a quantity , it is merely necessary to change the signs and add it . Hence , the RULE , FOR FINDING THE DIFFERENCE BETWEEN TWO ALGEBRAIC QUANTITIES ...
... changed from plus to minus , and from minus to plus ; hence , in order to subtract a quantity , it is merely necessary to change the signs and add it . Hence , the RULE , FOR FINDING THE DIFFERENCE BETWEEN TWO ALGEBRAIC QUANTITIES ...
Page 48
... changed by altering their arrangement ? In multiplying one mono- mial by another , how is the coefficient of the product obtained ? 68. If you multiply one of the factors of a product , how does it affect the product ? 69. How may the ...
... changed by altering their arrangement ? In multiplying one mono- mial by another , how is the coefficient of the product obtained ? 68. If you multiply one of the factors of a product , how does it affect the product ? 69. How may the ...
Page 65
... changed . Thus , since is the reciprocal of am ( Art . 51 ) ; 1 am 1 1 And since is the reciprocal of a - m ; am . am α am Also = ab - m ; ' ; bn α 1 = ab - 1 ; -a - 1b - 2 . ab2 From this we see , that any factor may be transferred ...
... changed . Thus , since is the reciprocal of am ( Art . 51 ) ; 1 am 1 1 And since is the reciprocal of a - m ; am . am α am Also = ab - m ; ' ; bn α 1 = ab - 1 ; -a - 1b - 2 . ab2 From this we see , that any factor may be transferred ...
Page 77
... changed , by multiplying one of the quantities by a factor of the other . REVIEW . - 102 . Show , that by dividing the last divisor by the last remainder , the greatest common divisor of two polynomials will exactly divide both the ...
... changed , by multiplying one of the quantities by a factor of the other . REVIEW . - 102 . Show , that by dividing the last divisor by the last remainder , the greatest common divisor of two polynomials will exactly divide both the ...
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Common terms and phrases
acre added algebraic quantities apples arithmetical progression arithmetical series binomial Binomial Theorem bought bushels coefficient common difference complete equation Completing the square cost Divide the number dividend division dollars entire quantity equal EQUATIONS CONTAINING exactly divide exponent expressed extract the square Find a number Find the cube Find the product Find the square Find the sum find the value following examples fraction geometrical progression geometrical series Give an example greater greatest common divisor Hence least common multiple lemons less number letter minus monomial negative quantity number of places number of terms oranges perfect square polynomial positive quantity preceding principle proportion pupil quan question quotient radical sign ratio reduced remainder represent the number required the numbers required to find result second degree second power solution solving square root three numbers tities Transposing twice unknown quantity whole number yards
Popular passages
Page 60 - 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 106 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 178 - 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.
Page 235 - In any proportion the product of the means is equal to the product of the extremes.
Page 124 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take to catch the hare ? Let x be the number of leaps taken by the hound.
Page 217 - If, then, any problem furnishes an equation in which the known term is negative, and greater than the square of half the coefficient of the first power of the unknown quantity, we infer, that the conditions of the problem are incompatible with each other.
Page 64 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 81 - The least Common Multiple of two or more quantities is the least quantity that will contain them exactly. Thus, 6 is the least common multiple of 2 and 3 ; and lOxy is the least common multiple of 2x and by. NOTE. — LCM stands for least common multiple.
Page 232 - If we compare the numbers 2 and 6, by the first method, we say that 2 is 4 less than 6, or that 6 is 4 greater than 2. If we compare 2 and 6 by the second method, we say that 6 is equal to three times 2, or that 2 is one third of 6.