New Elementary Algebra: Embracing the First Principles of the Science |
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Common terms and phrases
6a²b² algebraic expression algebraic quantities algebraic sum antecedent arithmetical binomial called cents Charles coefficient common difference completing the square contains contrary signs cost cube Davies denominator denote the number Divide division dollars equal number equation whose roots EXAMPLES extracting the square Find the square Find the sum following RULE Give the rule given number greater greatest common divisor hence indicates last term leading letter least common multiple lemons Let x denote logarithm minuend minus monomial Multiply number added number of apples number of terms perfect square polynomial prime factors progression proportion quan quantities is equal quotient radical ratio Reduce remainder result second degree second member second term square root Substituting this value subtract subtrahend tity transposing trinomial twice units unknown quantity VERIFICATION Write written x²y xy² yards
Popular passages
Page 285 - and hence, A : B : : C : D. That is: If the product of two quantities is equal to the, product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 280 - 2 13. One hundred stones being placed on the ground in a straight line, at the distance of 2 yards apart, how far will a person travel who shall bring them one by one to a basket, placed at a distance of 2 yards from the first stone ? Ans. 11 miles, 840 yards
Page 285 - T) and by clearing the equation of fractions, we have, BC = AD. That is: Of four proportional quantities, the product of the two extremes is equal to the product of the two means. This general principle is apparent in the proportion between the numbers, 2 : 10 : : 12 : 60, which gives, 2 X 60 = 10 X 12 = 120.
Page 72 - Divide the first term of the remainder by the first term of the divisor, for the second term of the quotient. Multiply the divisor by this term, and subtract the product from the first remainder, and so on : IV. Continue the operation, until a remainder is found equal to 0, or one whose first term is not divisible by that of the divisor.
Page 157 - Divide the number 90 into four such parts, that the first increased by 2, the second diminished by 2, the third multiplied by 2, and the fourth divided by 2, shall be equal each to each. This problem may be easily solved by introducing a new
Page 173 - of the second term is the same as the exponent of the given power. The coefficient of the third term is found by multiplying the coefficient of the second term by the exponent of the • leading letter in that term, and dividing the product by
Page 76 - The square of the sum of any 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. 1.
Page 261 - Divide 100 into two such parts, that the sum of their square roots may be 14. Ans. 64 and 36. 14. 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, 15. The sum of two numbers is 8, and the sum of
Page 183 - Since the square or second power of a fraction is obtained by squaring the numerator and denominator separately, it follows that The square root of a fraction will be equal to the square root of the numerator divided by the square root of the denominator. For example, the square root of