Elements of Algebra: Embracing Also the Theory and Application of Logarithms ... |
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Page 21
... , 6a repre- sents that a is to be used six times as a term , or a + a + a + a + a + a = 6a . 60. The reciprocal of a quantity is the quotient arising from dividing a unit by that quantity . 1 1 SECT . I. ] 21 ALGEBRAIC NOTATION .
... , 6a repre- sents that a is to be used six times as a term , or a + a + a + a + a + a = 6a . 60. The reciprocal of a quantity is the quotient arising from dividing a unit by that quantity . 1 1 SECT . I. ] 21 ALGEBRAIC NOTATION .
Page 22
... dividing a unit by that power , and is frequently expressed by a negative exponent . Thus , The reciprocal of a2 is ... divide two or more quantities without leaving a remainder , it is called a common measure of those quanti- ties ...
... dividing a unit by that power , and is frequently expressed by a negative exponent . Thus , The reciprocal of a2 is ... divide two or more quantities without leaving a remainder , it is called a common measure of those quanti- ties ...
Page 39
... Divide the coefficient of the dividend by the coefficient of the divisor . 2. Reject the letters common to both dividend and divisor when they have the same exponent ; but when the exponents are not the same , subtract the exponent of ...
... Divide the coefficient of the dividend by the coefficient of the divisor . 2. Reject the letters common to both dividend and divisor when they have the same exponent ; but when the exponents are not the same , subtract the exponent of ...
Page 40
... Divide 12a2b3x by 3ab2 . 6. Divide 48a3c'd1x3z2 by 8a2d3x3 . 7. Divide 42adx3 by -7adx . 8. Divide 72ab3c2x by 8a3b2x . 9. Divide 120x1y by -8x3y . 10. Divide -84bc2 by -12bc . 11. Divide 256a7bc2 by 8a5b2c3 . 12. Divide 56a b'd by ...
... Divide 12a2b3x by 3ab2 . 6. Divide 48a3c'd1x3z2 by 8a2d3x3 . 7. Divide 42adx3 by -7adx . 8. Divide 72ab3c2x by 8a3b2x . 9. Divide 120x1y by -8x3y . 10. Divide -84bc2 by -12bc . 11. Divide 256a7bc2 by 8a5b2c3 . 12. Divide 56a b'd by ...
Page 41
... Divide the sum of 12a1b3c4 and 8a1b3c1 by the sum of 3ab2c3 + 7ab2c3 . Ans . 2a3bc . 24. Divide the difference of 21a3b1c3d2x1 and 15a3b * c3d2x1 by 6a2bcdx . Ans . ab3c2dx3 . 107. It sometimes occurs in the operations of division ...
... Divide the sum of 12a1b3c4 and 8a1b3c1 by the sum of 3ab2c3 + 7ab2c3 . Ans . 2a3bc . 24. Divide the difference of 21a3b1c3d2x1 and 15a3b * c3d2x1 by 6a2bcdx . Ans . ab3c2dx3 . 107. It sometimes occurs in the operations of division ...
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Elements of Algebra: Embracing Also the Theory and Application of Logarithms ... Davis Wasgatt Clark No preview available - 2014 |
Elements of Algebra: Embracing Also the Theory and Application of Logarithms Davis Wasgatt Clark No preview available - 2018 |
Common terms and phrases
added algebraic arithmetical arithmetical series binomial Binomial Theorem cent coefficients continued fraction cube root cubic equation decimal digits dividend Dividing divisible equal EXAMPLES Expand exponent expression Extract the square factors fifth power figure Find the values following general RULE formula fourth power fourth root geometrical series given number greater greatest common divisor Hence inequation infin infinite series last term least common multiple less letters logarithm monomials Multiply number consisting number of terms obtain order of difference polynomial proposed number quotient radical sign ratio Reduce the equation remainder represent Required the fifth Required the fourth Required the second Required the simplest Required the square Required the third result second power second term share simplest form square root Substituting subtract tens Theorem third power third root three numbers tion Transposing unknown quantities vulgar fraction Whence whole number
Popular passages
Page 165 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 171 - Bring down the first figure of the next period to the remainder for a new dividend, to which find a new divisor as before, and in like manner proceed till the whole be finished.
Page 209 - Several gentlemen made an excursion, each taking the same sum of money. Each had as many servants attending him as there were gentlemen ; the number of dollars which each had was double the number of all the servants, and the whole sum of money taken out was 3456 dollars.
Page 172 - Subtract this square number from the first period, and to the remainder bring down the next period for a dividend.
Page 42 - 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 68 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 233 - If the numerator and denominator of each fraction is multiplied (or divided) by the same number, the value of the fraction will not change.
Page 232 - BY RATIO is meant the relation which one quantity bears to another, with respect to magnitude. It is evident that this relation can exist only between quantities of a similar kind ; thus, a number must be compared with a number; a line with a line; &c. &c. ; and it would be absurd to compare a certain number of feet with a certain number of pomds; &c.
Page 60 - The least common multiple of two or more numbers, is the least number which can be divided by each of them without a remainder.
Page 20 - To raise a whole number or a decimal to any power, use it as a factor as many times as there are units in the exponent.