The Normal Elementary Algebra, Part 1 |
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2ab+b² a²+2ab+b² a²b added Algebra Arithmetic binomial Binomial Theorem cents change the sign CHRISTOPHER SOWER clearing of fractions coefficient common denominator common factors common index complete divisor completing the square cost cube root difference diminished Divide the number dividend divisible equals EXAMPLES expression extracting the root extracting the square figures Find the sum Find the value find x hence highest common divisor indeterminate indicates lowest common multiple lowest terms method minuend minus mixed quantity monomial Multiply negative quantity NOTE.-The OPERATION polynomial positive quantity principles problem pupils quadratic equation quan quotient radical sign ratic Rationalize remainder required the number result Rule.-I second term SIMPLE EQUATIONS solved square root substituting subtract Symbol Theorem tities transposing trial divisor trinomial twice the product units unknown quantity whence zero απ
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Page 91 - Hence for the division of one fraction by another the usual rule again results, as follows: Rule. — Invert the terms of the divisor and proceed as in multiplication. This might naturally be expected by remembering the relation between multiplication and division, and that one is the exact inverse of the other. For the multiplication of a series of fractions into each other these principles work out as follows...
Page 179 - 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. 5th. Double the whole root already found, for a new divisor, and continue the operation as before, until all the periods are brought down. NOTE.
Page 119 - 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 75 - 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 - p^ to its lowest terms.
Page 228 - Find two numbers such that their difference added to the difference of their squares shall be 150, and their sum added to the sum of their squares shall be 330. 4. Find two numbers whose sum is equal to their product and also to the difference of their squares.
Page 44 - Algebra, is the process of finding how many times one quantity is contained in another...
Page 84 - Subtract the numerator of the subtrahend from the numerator of the minuend, and place the difference over the common denominator.
Page 60 - IF the difference of the same powers of two quantities is divisible by the difference of the quantities...
Page 139 - A and B can do a piece of work in 12 days, B and C in 20 days, and A and C in 15 days.