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a² b² algebraic quantities arithmetical arithmetical means cents Clearing of fractions coefficient common denominator common difference complete the square cube root decimal denote Divide dividend division entire quantity equa equal Explain the operation Explain the solution expression Extract the square Find the cube Find the greatest Find the logarithm Find the number Find the square Find the sum find the values fractional exponent Given x² greatest common divisor indicated last term least common multiple letter lowest terms mantissa monomial Multiply negative exponents NOTE number of terms obtain parenthesis perfect square polynomial proportion quadratic equation quadratic form quan quotient ratio Reduce remainder Repeat the Rule second member second power simplest form solution of Problem solved square root subtract Theorem tion tity transposing unknown quantity Whence
Page 95 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Page 279 - Multiply the last term by the ratio, from the product subtract the first term, and divide the remainder by the ratio, less 1; the quotient will be the sum of the series required.
Page 265 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 257 - ... if the circumference of each wheel be increased one yard, it will make only 4 revolutions more than the hind wheel, in the same distance ; required the circumference of each wheel. SOLUTION. Let x = circumference of hind wheel in yards. and y = circumference of fore wheel in yards. 120 Then — = number of revolutions of hind wheel.
Page 104 - An equation of the second degree is one in which the highest power of the unknown quantity is the second power, or square ; as, 3 x2 — 2 x = 65.
Page 90 - SUBTRACTION OF FRACTIONS is the process of finding the difference between two fractions.
Page 257 - Divide the number 60 into two such parts, that their product shall be to the sum of their squares in the ratio of 2 to 5. Ans. 20 and 40.
Page 133 - RULE. Find an expression for the value of the same unknown quantity in each of the equations, and form a new equation, by placing these values equal to each other.